Math in Focus

This handy Math in Focus Grade 1 Workbook Answer Key Chapter 7 Numbers to 20 detailed solutions for the textbook questions.

Math in Focus Grade 1 Chapter 7 Answer Key Numbers to 20

Count how many stickers the Fill in the blanks.

Question 1.

Answer:

Draw how many stickers you have. Then fill in the blanks.

Question 2.

I have _______ stickers.
Answer: I have 11 stickers

Write about the number of stickers everyone has. Fill in the blanks with the correct names.

Question 3.
____ has more stickers than _____________
Answer:
Pete has more stickers than Ty.

Question 4.
________ has fewer stickers than _______
Answer:
Ty has fewer stickers than Pete

Question 5.
_____________ has the greatest number of stickers.
Answer:
Pete has the greatest number of stickers.

Question 6.
_____________ has the least number of stickers.
Answer:
Ty has the least number of stickers.

Put On Your Thinking Cap!

Challenging Practice

Question 1.
Class 1A of Greenfield School holds a basketball contest. Find out who won.
CLUES
Rita scores the least number of baskets. John scores 3 more baskets than Rita. Dion scores more baskets than Rachel but less than Frank.

Write the names next to the number of baskets scored.

Who won the contest? ____

Answer: Frank won the contest

Fill in the blanks.

Question 2.
10 + ___ = 15
Answer: 5
10 + 5 = 15

Question 3.
10 + ___ = 11
Answer: 1
10 + 1 = 11

Question 4.
10 + ___ = 18
Answer: 8
10 + 8 = 18

Question 5.
___ + 10 = 14
Answer: 4
4 + 10 = 14

Question 6.
___ + 10 = 17
Answer: 7
7 + 10 = 17

Write the correct names.

Question 7.
These are the numbers of 12 players on a team.

Whose names have the following numbers?

Answer:

Put On Your Thinking Cap!

Problem Solving

Use the clues on the next page. Help Tony find which numbers his counters covered.

Read what Tony’s friends said.
Circle the numbers that were covered on Tony’s card.

Answer:

Chapter Review/Test

Vocabulary

Unscramble the letters to spell each number.

Question 1.
15 fieetfn
_______
Answer:
Fifteen

Question 2.
11 evleen
________
Answer:
Eleven

Question 3.
18 egeethni
_______
Answer:
Eighteen

Question 4.
20 twynet
_____________
Answer:
Twenty

Fill in the blank with the correct word.

place-value chart compare

Question 5.
You can show numbers as tens and ones in a _______
Answer:
You can show numbers as tens and ones in a place-value chart

Question 6.
When you ____ 12 and 15,12 is the number that is less.
Answer:
When you Compare 12 and 15,12 is the number that is less.

Concepts and Skills

Count. Write the number.

Question 7.

Answer: 13

Question 8.

Answer: 17

Fill in the blanks.

Question 9.

Set ___ has ___ more oranges than Set ____
Set ___ has ___ fewer oranges than Set ____.
Which is the greater number? ____
Answer:

Complete the number pattern.

Question 10.
13, 14, ___, ____, 17, ___, 19
Answer: 13, 14, 15, 16, 17, 18, 19

Question 11.
19, 17, ___, 13, 11, ___
Answer:
19, 17, 15, 13, 11, 9

Write the numbers in order from least to greatest.

Question 12.

Answer:

Write the numbers in order from greatest to least.

Question 13.

Answer:

Problem Solving
Read the clues.
Then cross out the numbers to solve.

Example

I am greater than 13.
I am less than 17.
Of the numbers that are left:
I am not the least.
I am not the greatest.
What number am I? 15

Question 14.

I am less than 20.
I am more than 13.
I am less than 17.
I am 4 more than 12.
What number am I? _______
Answer: I am number 15

Question 15.

a. I am more than 10.
I am less than 20.
I am more than 12.
I am less than 15.
Of the numbers that are left: I am the greater number. What number am I? ____
Answer:

b. Draw the number in the place-value chart.

Answer:

Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 2 Lesson 2.3 Multiplying and Dividing Integers to finish your assignments.

Math in Focus Grade 7 Course 2 A Chapter 2 Lesson 2.3 Answer Key Multiplying and Dividing Integers

Math in Focus Grade 7 Chapter 2 Lesson 2.3 Guided Practice Answer Key

Lesson Objective

• Multiply and divide integers.

Hands-On Activity

Explore Multiplication Rules Using Repeated Addition

Work individually.

You can think of multiplying integers as repeated addition.

Step 1
Use a number line to model and complete the multiplication of integers as repeated addition.

a) Evaluate 3 – 2.

3 • 2 means three groups of 2.
3 • 2 = 2 • 3
= 2 + 2 + 2
= 6

Commutative property of multiplication:
Two or more numbers can be multiplied in any order.

b) Evaluate 3 • (-2).

3 • (- 2) means three groups of -2.
3 • (-2) = (-2) • 3
= -2 + (-2) + (-2)
=
The expression 3 • (-2) can also be written as 3(-2).
The expression (-2) • 3 can also be written as -2(3).

Step 2.
Copy and complete the table using repeated addition.

Answer:

Math Journal
Study the pattern in the table from step 2.
a) What do you observe about the sign of the product of two positive integers?
Answer:
I observed the product of two positive integers with ‘ + ‘ sign.

b) What do you observe about the sign of the product of a positive and a negative integer?
Answer:
I observed the product of a positive and a negative integer with ‘ – ‘ sign.

Step 3.
Use a number line to model and complete the multiplication as addition of the opposite.

a) Evaluate -3 • 2.

You can say that -3 • 2 is the opposite of three groups of 2, 6.
-3 • 2 = -(3)(2)
=
Answer:
I can say that -3 • 2 is the opposite of three groups of 2, 6.
-3 • 2 = -(3)(2)

b) Evaluate -3 • (-2).

You can say that -3 • (-2) is the opposite of three groups of -2, -6.
-3 • (-2) = -(3)(-2)
= -()
=
Answer:
I can say that -3 • (-2) is the opposite of three groups of -2, -6.
-3 • (-2) = -(3)(-2)
-()

Step 4.
Copy and complete the table using addition of the opposite and your results from Step 2.

Answer:

Math Journal Based on your observations in Step 1 to Step 4,

a) What do you observe about the sign of the product of two integers with the same sign?
Answer:
I observed the product of two integers with the same sign results ‘ + ‘ sign.

b) What do you observe about the sign of the product of a positive integer and a negative integer? of integers with different signs?
Answer:
I observed the product of a positive integer and a negative integer  with ‘ – ‘ sign.

Evaluate each product.

Question 1.
9(-8)
Answer:
9(-8) = – 72
Explanation:
Perform multiplication operation on above two numbers. Multiply 9 with -8 the product is -72. The product of a positive integer and a negative integer  is represented with ‘ – ‘ sign.

Question 2.
-7 • (-5)
Answer:
-7 • (-5) = -(7)(-5) = -(-35) = 35
Explanation:
Explanation:
Perform multiplication operation on above two numbers. Multiply -7 with -5 the product is 35. The product of two integers with the same sign results ‘ + ‘ sign.

Question 3.
3(-4)(6)
Answer:
3(-4)(6) = (-12)(6) = -72
Explanation:
Perform multiplication operation on above three numbers. First multiply 3 with -4 the product is -12. Next multiply -12 with 6 the product is -72. The product of a two positive integers and a negative integer  is represented with ‘ – ‘ sign.

Think Math
Will the product of three negative numbers be positive or negative? What about the product of four negative numbers? Explain your answers.
Answer:
The product of three negative numbers is negative.
The product of four negative numbers is positive.
Explanation:
Odd numbers of negative integers will have a negative product. Even numbers of negative integers will have a positive product.

Solve.

Question 4.
In a regional golf championship, Steven plays four rounds. The score for a round is recorded as positive (over par) or negative (under par). If Steven scores 6 points under par for all four rounds, what is his total score for his game?
• (-6) =
His score is points.
Answer:
4 • (-6) = -24
His total score is -24 points.
Explanation:
In a regional golf championship, Steven plays four rounds. It is represented with the number 4. Steven scores 6 points under par for all four rounds. Here under par is represented with ‘-‘ sign. 6 points is represented with -6. Multiply 4 with -6 the product is -24. His total score is -24 points.

Question 5.
The price of a stock falls $2 each day for 9 days. Find the total change in the price of the stock during this time.
Answer:
$2 • 9 = $18
The price of a stock falls by $18.
Explanation:
The price of a stock falls $2 each day for 9 days. Multiply $2 with 9 the product is $18. The total change in the price of the stock during this time falls by $18.

Evaluate each quotient.

Question 6.
-36 ÷ (-4)
Answer:
-36 ÷ (-4) = 9
The quotient is 9.
Explanation:
Perform division operation on above two numbers. Divide -36 by -4 the quotient is 9. Even numbers of negative integers will have a positive quotient.

Question 7.
-35 ÷ 5
Answer:
-35 ÷ 5 = -7
The quotient is -7.
Explanation:
Perform division operation on above two numbers. Divide -35 by 5 the quotient is -7. Odd numbers of negative integers will have a negative quotient.

Question 8.
45 ÷ (-3)
Answer:
45 ÷ (-3) = -15
The quotient is -15.
Explanation:
Perform division operation on above two numbers. Divide 45 by -3the quotient is -15 Odd numbers of negative integers will have a negative quotient.

Solve.

Question 9.
Find the change in elevation per minute of a hiker who descended 320 feet in 40 minutes.
Answer:
-320 ÷ 40 = -8 feet/min
Explanation:
A hiker who descended 320 feet in 40 minutes is represented with -320 feet in 40 minutes. The change in elevation per minute of a hiker who descended 320 feet in 40 minutes is -8 feet/min.

Math in Focus Course 2A Practice 2.3 Answer Key

Evaluate each product.

Question 1.
5 • (-7)
Answer:
5 • (-7) = -35
Explanation:
Perform multiplication operation on above two numbers. Multiply 5 with -7 the product is -35. The product of a positive integer and a negative integer  is represented with ‘ – ‘ sign.

Question 2.
12 • (-9)
Answer:
12 • (-9) = -108
Explanation:
Perform multiplication operation on above two numbers. Multiply 12 with -9 the product is -108. The product of a positive integer and a negative integer  is represented with ‘ – ‘ sign.

Question 3.
-6 • 8
Answer:
-6 • 8 = -48
Explanation:
Perform multiplication operation on above two numbers. Multiply -6 with 8 the product is -48. The product of a negative integer and a positive integer is represented with ‘ – ‘ sign.

Question 4.
-3 • 15
Answer:
-3 • 15 = -45
Explanation:
Perform multiplication operation on above two numbers. Multiply -3 with 15 the product is -45. The product of a negative integer and a positive integer is represented with ‘ – ‘ sign.

Question 5.
-4 • (-12)
Answer:
-4 • (-12) = -(4) • (-12) = -(-48) = 48
Explanation:
Perform multiplication operation on above two numbers. Multiply -4 with -12 the product is 48. The product of two integers with the same sign results ‘ + ‘ sign.

Question 6.
-8 • (-20)
Answer:
-8 • (-20) = -(8) • (-20) = -(-160) = 160
Explanation:
Perform multiplication operation on above two numbers. Multiply -8 with -20 the product is 160. The product of two integers with the same sign results ‘ + ‘ sign.

Question 7.
-14 . 0
Answer:
-14 • 0 = 0
Explanation:
Perform multiplication operation on above two numbers. Multiply -14 with 0 the product is 0.

Question 8.
0 • (-50)
Answer:
0 • (-50) = 0
Explanation:
Perform multiplication operation on above two numbers. Multiply 0 with -50 the product is 0.

Question 9.
-3 • 12 • 7
Answer:
-3 • 12 • 7= (-36)• 7 = -252
Explanation:
Perform multiplication operation on above three numbers. First multiply -3 with 12 the product is -36. Next multiply -36 with 7 the product is -252. The product of a two positive integers and a negative integer is represented with ‘ – ‘ sign.

Question 10.
8 • (-4) • 2
Answer:
8 • (-4) • 2= (-32)• 2 = -64
Explanation:
Perform multiplication operation on above three numbers. First multiply 8 with -4 the product is -32. Next multiply -32 with 2 the product is -64. The product of a two positive integers and a negative integer is represented with ‘ – ‘ sign.

Question 11.
20 • 5 • (-5)
Answer:
20 • 5 • (-5) = 100 • (-5)= -500
Explanation:
Perform multiplication operation on above three numbers. First multiply 20 with 5 the product is 100. Next multiply 100 with -5 the product is -500. The product of a two positive integers and a negative integer is represented with ‘ – ‘ sign.

Question 12.
-4 • 10 • (-6)
Answer:
-4 • 10 • (-6) = -40 • (-6) = 240
Explanation:
Perform multiplication operation on above three numbers. First multiply -4 with 10 the product is -40. Next multiply -40 with -6 the product is -240. The product of a two negative integers and a positive integer is represented with ‘ + ‘ sign.

Question 13.
-7 • (-2) • 10
Answer:
-7 • (-2) • 10 = 14 • 10 = 140
Explanation:
Perform multiplication operation on above three numbers. First multiply -7 with -2 the product is 14. Next multiply 14 with 10 the product is 140. The product of a two negative integers and a positive integer is represented with ‘ + ‘ sign.

Question 14.
9 • (-6) • (-4)
Answer:
9 • (-6) • (-4) = (-54) • (-4) = 216
Explanation:
Perform multiplication operation on above three numbers. First multiply 9 with -6 the product is -54. Next multiply -54 with -4 the product is 216. The product of a two negative integers and a positive integer is represented with ‘ + ‘ sign.

Question 15.
-2 • (-8) • (-7)
Answer:
-2 • (-8) • (-7) = 16 • (-7) = -112
Explanation:
Perform multiplication operation on above three numbers. First multiply -2 with -8 the product is -16. Next multiply 16 with -7 the product is -112. The product of a three negative integers is represented with ‘ – ‘ sign.

Question 16.
-5 • (-12) • (-3)
Answer:
-5 • (-12) • (-3) = 60 • (-3) = -180
Explanation:
Perform multiplication operation on above three numbers. First multiply -5 with -12 the product is 60. Next multiply 60 with -3 the product is -180. The product of a three negative integers is represented with ‘ – ‘ sign.

Question 17.
14 • 0 • (-15)
Answer:
14 • 0 • (-15) = 0 • (-15) = 0
Explanation:
Perform multiplication operation on above three numbers. First multiply 14 with 0 the product is 0. Next multiply 0 with -15 the product is 0.

Question 18.
-30 • (-2) • 0
Answer:
-30 • (-2) • 0 = 60 • 0 = 0
Explanation:
Perform multiplication operation on above three numbers. First multiply -30 with -2 the product is 60. Next multiply 60 with 0 the product is 0.

Question 19.
-6 • (-7) • 2 • 5
Answer:
-6 • (-7) • 2 • 5
= 42 • 2 • 5
= 84 • 5
= 420 
Explanation:
Perform multiplication operation on above three numbers.
First multiply -6 with -7 the product is 42.
Next multiply 42 with 2 the product is 84.
Multiply the obtained product 84 with 5 the product is 420.
The product of a two negative integers and two positive integer is represented with ‘ + ‘ sign.

Question 20.
-8 • (-2) • (-4) • 12
Answer:
-8 • (-2) • (-4) • 12
= 16 • (-4) • 12
= -64 • 12
= -768
Explanation:
Perform multiplication operation on above three numbers.
First multiply -8 with -2 the product is 16.
Next multiply 16 with 4 the product is -64.
Multiply the above product -64 with 12 the product is -768.
The product of a three negative integers and a positive integer is represented with ‘ – ‘ sign.

Question 21.
-9 • (-5) • (-4) • (-3)
Answer:
-9 • (-5) • (-4) • (-3)
= 45 • (-4) • (-3)
= -180 • (-3)
= 540
Explanation:
Perform multiplication operation on above three numbers.
First multiply -9 with -5 the product is 45.
Next multiply 45 with -4 the product is -180.
Multiply the above product -180 with -3 the product is 540.
Even numbers of negative integers will have a positive product.

Evaluate each quotient.

Question 22.
125 ÷ (-25)
Answer:
125 ÷ (-25) = -5
The quotient is -5.
Explanation:
Perform division operation on above two numbers. Divide 125 by -25 the quotient is -5. Odd numbers of negative integers will have negative quotient.

Question 23.
300 ÷ (-15)
Answer:
300 ÷ (-15) = -20
The quotient is -20.
Explanation:
Perform division operation on above two numbers. Divide 300 by -15 the quotient is -20. Odd numbers of negative integers will have negative quotient.

Question 24.
-100 ÷ 25
Answer:
-100 ÷ 25 = -4
Explanation:
Perform division operation on above two numbers. Divide -100 by 25 the quotient is -4. Odd numbers of negative integers will have negative quotient.

Question 25.
-32 ÷ 4
Answer:
-32 ÷ 4 = -8
Explanation:
Perform division operation on above two numbers. Divide -32 by 4 the quotient is -8. Odd numbers of negative integers will have negative quotient.

Question 26.
-480 ÷ (-12)
Answer:
-480 ÷ (-12) = 40
Explanation:
Perform division operation on above two numbers. Divide -480 by -12 the quotient is 40. Even numbers of negative integers will have positive quotient.

Question 27.
-144 ÷ (-24)
Answer:
-144 ÷ (-24) = 6
Explanation:
Perform division operation on above two numbers. Divide -144 by -24 the quotient is 6. Even numbers of negative integers will have positive quotient.

Question 28.
0 ÷ (-8)
Answer:
0 ÷ (-8) = 0
Explanation:
Perform division operation on above two numbers. Divide 0 by -8 the quotient is 0.

Question 29.
0 ÷ (-111)
Answer:
0 ÷ (-111) = 0
Explanation:
Perform division operation on above two numbers. Divide 0 by -111 the quotient is 0.

Solve. Show your work.

Question 30.
While returning to the glider port, Laura descended at minute for 3 minutes. Calculate her change in altitude.
Answer:

Question 31.
A scuba diver took 6 minutes to rise to the surface at a minute. How far was he below sea level?
Answer:

Question 32.
An elevator descends 1,500 feet in 60 seconds. Find the change in height per second.
Answer:
1,500 ÷ 60 = 25 feet/sec
Explanation:
An elevator descends 1,500 feet in 60 seconds. Here descends represented with negative sign. The change in height per second is -25 feet/sec

Question 33.
A scientist measures the change in height per second of a diving osprey as -198 feet per second. Find the change in position of the osprey after 2 seconds.
Answer:

The change in height per second of a diving osprey as -198 feet per second.
1 sec = -198 feet
2 sec = ?
-198 • 2 = -396 feet
The change in position of the osprey after 2 seconds is -396 feet.

Question 34.
Math Journal
Margaret wrote -25 ÷ (-100) = \(\frac{-25}{-100}\) = –\(\left(\frac{1}{4}\right)\) and
-2 • (-2) = -4. Discuss and correct her mistakes.
Answer:
-25 ÷ (-100) = 1/4
Perform division operation on above two numbers. Divide -25 by -100 the quotient is 1/4. Even numbers of negative integers will have positive quotient.
-2 • (-2) = 4
Perform multiplication operation on above two numbers. Multiply -2 with -2 the product is 4. The product of two integers with the same sign results ‘ + ‘ sign.

Question 35.
Math Journal Umberto has trouble solving -12 ÷ 3 • 2 ÷ (-4). Write an explanation to help him.
Answer:
To evaluate -12 ÷ 3 • 2 ÷ (-4)
Umberto can do it from left to right. Perform any two operations at one time, and use the rules for sign multiplication and division.
-12 ÷ 3 • 2 ÷ (-4)
= -4 • 2 ÷ (-4)
= -8 ÷ (-4)
= 2

Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 2 Lesson 2.2 Subtracting Integers to finish your assignments.

Math in Focus Grade 7 Course 2 A Chapter 2 Lesson 2.2 Answer Key Subtracting Integers

Math in Focus Grade 7 Chapter 2 Lesson 2.2 Guided Practice Answer Key

Hands-On Activity

Materials:

• counters

Subtract Integers

Work in pairs.

A zero pair can be added to any expression without changing its value. It is the same thing as adding 0 to a number.
Sometimes, you add zero pairs in order to subtract.

Step 1.
Use counters to model and complete the subtraction of a positive integer.

a) Evaluate 5 – (+2) and compare with 5 + (-2).

Answer:

b) Evaluate -5 – (+2) and compare with -5 + (-2).

Answer:

Step 2
Use counters to evaluate each expression.
a) 6 – 4 and 6 + (-4)
Answer:

b) -6 – 4 and -6 + (-4)
Answer:

Step 3
Use counters to model and complete the subtraction of a negative integer,

a) Evaluate 5 – (-2) and compare with 5 + 2.

Answer:

b) Find -5 – (-2) and compare with -5 + 2.

Answer:

Step 4
Use counters to evaluate each expression.

a) 7 – (-3) and 7 + 3
Answer:

b) -7 – (-3) and -7 + 3
Answer:

Math Journal Based on your results in step 1 to step 4, explain how you can subtract integers.

Copy and complete.

Question 1.
21 – 30
21 – 30 = 21 + Rewrite subtraction as adding the opposite.
Using absolute values,
|-30| – |21| = 30 – 21 Subtract the absolute values, because the addends have different signs.
= Simplify.
21 – 30 = 21 +
= Use a negative sign, because -30 has a greater absolute value.
=
Answer:
Rewrite subtraction as adding the opposite.
21 – 30 = 21 + (-30) 
Using absolute values,
|-30| – |21| = 30 – 21
Subtract the absolute values, because the addends have different signs.
= 9
21 – 30 = 21 + (-30)
= -9 Use a negative sign, because -30 has a greater absolute value.
= -9

Question 2.
A fishing boat drags its net 35 feet below the ocean’s surface. Then it lowers the net by an additional 12 feet. Find the new position relative to the surface of the fishing net.
-35 – = -35 + Rewrite subtraction as adding the opposite.
Using absolute values,
+ = Add the absolute values because the addends have the same sign.
-35 – = -35 + Use the common sign, a negative sign, for the sum.
= Simplify.
The fishing net’s new position is feet below the surface of the ocean.
Answer:
Rewrite subtraction as adding the opposite.
-35 – 12 = -35 + (-12) 
Using absolute values,
|-35| +  |-12| = 47
Add the absolute values because the addends have the same sign.
-35 – 12 = -35 + (-12)
Use the common sign, a negative sign, for the sum.
= -47
The fishing net’s new position is 47 feet below the surface of the ocean.

Solve.

Question 3.
A submarine was at 1,200 feet below sea level, It then moved to 1,683 feet below sea level. How many feet did the submarine descend?

Answer:
1,683 – 1,200 = 493 feet
The submarine descend to 493 feet below sea level.
Explanation:
A submarine was at 1,200 feet below sea level, It then moved to 1,683 feet below sea level. Subtract 1,200 feet from 1,683 feet the difference is 493 feet. The submarine descend to 493 feet below sea level.

Copy and complete.

Question 4.
17 – (-4)
17 – (-4) = 17 + Rewrite subtraction as adding the opposite.
= Add.
Answer:
17 – (-4)
Rewrite subtraction as adding the opposite.
= 17 + 4 
= 21
Explanation:
Perform subtraction operation one above numbers. Rewrite subtraction as adding the opposite. Add 17 with4 the sum is 21.

Evaluate each expression.

Question 5.
-25 – (-9)
Answer:
-25 – (-9)
Rewrite subtraction as adding the opposite.
= -25 + 9
= -16
Explanation:
Perform subtraction operation one above numbers. Rewrite subtraction as adding the opposite. Add -25 with 9 the sum is -16.

Question 6.
-19 – (-7) – (-6)
Answer:
-19 – (-7) – (-6)
= -19 + 7 + 6
= -19 + 13
= -6
Explanation:
Perform subtraction operation one above numbers. Rewrite subtraction as adding the opposite. Add 7 with 6 the sum is 13. Next add -19 with 13 the sum is -6.

Copy and complete.

Question 7.
Find the distance between 3 and -2.
Method 1
Use a number line to plot the points and count the units.

The distance between 3 and -2 is units.
Method 2
Use absolute value to find the distance between integers with opposite signs.
Distance between 3 and -2:
|3 – | = | | Rewrite subtraction as adding the opposite.
= units Add.
The distance between 3 and -2 is units.
Answer:
Use a number line to plot the points and count the units.

The distance between 3 and -2 is 5 units.
Method 2
Use absolute value to find the distance between integers with opposite signs.
Distance between 3 and -2:
Rewrite subtraction as adding the opposite.
|3 – (-2) | = | 3 + 2 |
= 5 units
The distance between 3 and -2 is 5 units.

Question 8.
A particular town has an elevation of 8 feet below sea level. Another town on top of a mountain has an elevation of 2,421 feet above sea level. What is the difference in the elevations of the two towns?

Elevation of town below sea level: ft
Elevation of town on top of mountain: ft
Difference between the two elevations:
| – | = | | Rewrite subtraction as adding the opposite.
= ft Add.
The difference in the elevations of the two towns is feet.
Answer:
Elevation of town below sea level: -8 feet
Elevation of town on top of mountain: 2,421 feet
Difference between the two elevations:
Rewrite subtraction as adding the opposite.
| 2,421 – (-8) | = | 2,421 + 8 |
= 2,429 feet 
The difference in the elevations of the two towns is 2,429 feet.

Math in Focus Course 2A Practice 2.2 Answer Key

Evaluate each expression.

Question 1.
7 – 18
Answer:
7 – 18 = -11
Explanation:
Perform subtraction operation on above two numbers. Subtract 18 from 7 the difference is -11.

Question 2.
20 – 30
Answer:
20 – 30 = -10
Explanation:
Perform subtraction operation on above two numbers. Subtract 30 from 20 the difference is -10.

Question 3.
53 – 109
Answer:
53 – 109 = -56
Explanation:
Perform subtraction operation on above two numbers. Subtract 109 from 53 the difference is -56.

Question 4.
45 – (-16)
Answer:
45 – (-16)
= 45 + 16
= 61
Explanation:
Perform subtraction operation on above two numbers. Rewrite subtraction as adding the opposite. Add 45 with 16 the sum is 61.

Question 5.
-7 – (-5)
Answer:
-7 – (-5)
= -7 + 5
= -2
Explanation:
Perform subtraction operation on above two numbers. Rewrite subtraction as adding the opposite. Add -7 with 5 the sum is -2.

Question 6.
-94 – (-68)
Answer:
-94 – (-68)
= -94 + 68
= -26
Explanation:
Perform subtraction operation on above two numbers. Rewrite subtraction as adding the opposite. Add -94 with 68 the sum is -26.

Question 7.
-6 – 8 – 12
Answer:
-6 – 8 – 12
= -14 – 12
= -26
Explanation:
Perform addition operation on above numbers. Add -6 with -8 the sum is -14. Add -14 with -12 the sum is -26.

Question 8.
-23 – 17 – 7
Answer:
-23 – 17 – 7
= -40 – 7
= -47
Explanation:
Perform addition operation on above numbers. Add -23 with -17 the sum is -40. Add -40 with -7 the sum is -47.

Question 9.
-8 – (-4) – 5
Answer:
-8 – (-4) – 5
= – 8 + 4 -5
= -13 + 4
= -9
Explanation:
Perform subtraction operation on above numbers. Rewrite subtraction as adding the opposite. Add -8 with -5 the sum is -13. Add -13 with 4 the sum is -9.

Question 10.
-5 – (-10) – 6
Answer:
-5 – (-10) – 6
= – 5 + 10 – 6
= 5 – 6
= -1
Explanation:
Perform subtraction operation on above numbers. Rewrite subtraction as adding the opposite. Add -5 with 10 the sum is 5. Add 5 with -6 the sum is -1.

Question 11.
-20 – (-16) – (-7)
Answer:
-20 – (-16) – (-7)
= -20 + 16 + 7
= -20 + 23
= 3
Explanation:
Perform subtraction operation on above numbers. Rewrite subtraction as adding the opposite. Add 16 with 7 the sum is 23. Add -20 with 23 the sum is 3.

Question 12.
-11 – (-8) – (-14)
Answer:
-11 – (-8) – (-14)
= -11 + 8 + 14
= -11 + 22
= 11
Explanation:
Perform subtraction operation on above numbers. Rewrite subtraction as adding the opposite. Add 8 with 14 the sum is 22. Add -11 with 22 the sum is 11.

Evaluate the distance between each pair of integers.

Question 13.
4 and 20
Answer:
Use a number line to plot the points and count the units.

The distance between 4 and 20 is 16 units.

Question 14.
16 and 52
Answer:
52 – 16 = 36
The distance between 16 and 52 is 36.

Question 15.
-15 and 36
Answer:
Use absolute value to find the distance between integers with opposite signs.
Distance between -15 and 36:
Rewrite subtraction as adding the opposite.
|-15 + 36 | = | 15 + 36 |
= 51 units
The distance between -15 and 36 is 51 units.

Question 16.
-7 and 41
Answer:
Use absolute value to find the distance between integers with opposite signs.
Distance between -7 and 41:
Rewrite subtraction as adding the opposite.
|-7 + 41 | = | 7 + 41|
= 48 units
The distance between -7 and 41 is 48 units.

Question 17.
-28 and -3
Answer:

The distance between -28 and -3 is 25 units.

Question 18.
-19 and -8
Answer:
Use a number line to plot the points and count the units.

The distance between -19 and -8 is 11 units.

Solve. Show your work.

Question 19.
Rick leaves to go skiing in Burlington, Vermont, when the temperature is -4°C. The temperature drops 10°C when a cold front moves in. What is the new temperature?
Answer:
-4°C – 10°C = -14°C
The new temperature is -14°C.
Explanation:
When the temperature is -4°C Rick leaves to go skiing in Burlington, Vermont. The temperature drops 10°C when a cold front moves in. Which is represented as -10°C. Add -4°C with -10°C the sum is -14°C. The new temperature is -14°C.

Question 20.
The water level of the Dead Sea dropped from 390 meters below sea level in 1930 to 423 meters below sea level in 2010. By how much did the water level drop from 1930 to 2010?
Answer:
423 – 390 = 33 meters
The water level drop 33 meters below sea level from 1930 to 2010.
Explanation:
The water level of the Dead Sea dropped from 390 meters below sea level in 1930 to 423 meters below sea level in 2010. Subtract 390 meters from 423 meters the difference is 33 meters.

Question 21.
Math Journal Florence has only $420 in her bank account. Describe how to find the amount in her account after she writes a check for $590.
Answer:
$420 – $590 = -$170
Explanation:
Florence has only $420 in her bank account. Then she writes a check of $590. Subtract $590 from $420 the difference is -$170. The amount in her account is -$170.

Question 22.
Math Journal Darren has trouble simplifying 15 – (-36). Write an explanation to help him.
Answer:
15 – (-36)
= 15 + 36
= 51
Explanation:
Perform subtraction operation on above numbers. Rewrite subtraction as adding the opposite. Add 15 with 36 the sum is 51.

Question 23.
The wind-chill temperature at 10 P.M. was -8°F. One hour later, the wind-chill temperature had fallen to -28°F. Write an expression to represent the change in temperature. Then find the change in temperature.
Answer:
(-28) – (-8) 
= -28 + 8
= -20°F
The change in temperature is -20°F.
Explanation:
The wind-chill temperature at 10 P.M. was -8°F. One hour later, the wind-chill temperature had fallen to -28°F. The expression to represent the change in temperature is -(28) – (-8). After solving the expression the change in temperature is -20°F.

Question 24.
The lowest point in North America is in Death Valley, California, which is 86 meters below sea level at its lowest point. The highest point is Denali, a mountain in Alaska, with an elevation of 6,198 meters above sea level. What is the difference in their elevations?

Answer:
6,198 m – (-86m)
= 6,198 m + 86 m
= 6,284 m
The difference in their elevations is 6,284 meters.
Explanation:
The lowest point in North America is in Death Valley, California, which is 86 meters below sea level at its lowest point. It is represented as -86 meters. The highest point is Denali, a mountain in Alaska, with an elevation of 6,198 meters above sea level. The difference in their elevations is 6,284 m.

Question 25.
Belinda has two freezers. Freezer A keeps frozen foods at a temperature of -20°F, while Freezer B keeps frozen foods at a temperature of -4°F. She transferred a package of frozen food from one freezer to the other.
a) What is the temperature difference between the two freezers?
Answer:
-4°F – (-20°F)
= -4°F + 20°F
= 16°F
The temperature difference between the two freezers are 16°F.

b) If the temperature of the package rises after the transfer, from which freezer was the package taken?
Answer:
The package was taken from freezer A. Freezer A keeps frozen foods at a temperature of -20°F, while Freezer B keeps frozen foods at a temperature of -4°F. The temperature -4°F is greater than -20°F. The temperature of the package rises after the transfer.

Question 26.
You and a friend are playing a video game. Your score so far is 340 points and your friend’s score is -220 points. What is the difference between your scores?
Answer:
340 – (-220)
= 340 + 220
= 560
The difference between our scores is 560 points.

Question 27.
Two record low monthly temperatures for Anchorage, Alaska, are -34°F in January and 31°F in August. Find the difference between these two temperatures.
Answer:
31°F – (-34°F)
= 31°F + 34°F
= 65°F
The difference between the two temperatures is 65°F.
Explanation:
Two record low monthly temperatures for Anchorage, Alaska, are -34°F in January and 31°F in August. Add 31°F with 34°F the sum is 65°F. The difference between the two temperatures is 65°F.

Question 28.
Town X is 120 feet above sea level, Town Y is 25 feet below sea level, and Town Z is 30 feet below sea level. How high is
a) Town X above Town Y?
Answer:
Town X is 120 feet above sea level. Above sea level is represented with +120 feet.
Town Y is 25 feet below sea level. Below sea level is represented with -25 feet.
-25 feet + 120 feet = 95 feet.
Town X is 95 feet higher than Town Y.

b) Town Y above Town Z? Town X
Answer:
Town Y is 25 feet below sea level. Below sea level is represented with -25 feet.
Town Z is 30 feet above sea level. Below sea level is represented with -30 feet.
-25 feet – (-30) feet = 5 feet.
Town Y is 5 feet higher than Town Z.

c) Town X above Town Z?
Answer:
Town X is 120 feet above sea level. Above sea level is represented with +120 feet.
Town Z is 30 feet below sea level. Below sea level is represented with -30 feet.
-30 feet + 120 feet = 90 feet.
Town X is 90 feet higher than Town Z.

Question 29.
Math Journal
a) Find |8 – 12| and |8| – |12|. Is |8 – 12| equal to |8| – |12|?
Answer:
|8 – 12|
= |-4|
= 4
|8| – |12|
= 8 – 12
= -4
No, |8 – 12| is not equal to |8| – |12|

b) Find |12 – 8| and |12| – |8|. Is |12 – 8| equal to |12| – |8|?
Answer:
|12 – 8|
= |4|
= 4
|12| – |8|
= 12 – 8
= 4
Yes, |12 – 8| equal to |12| – |8|

c) Joe thinks that to find the distance between two integers m and n, he can write |m| – |n| or |n| – |m|. Use your answer in a) and b) to explain why you agree or disagree.
Answer:
Disagree
Explanation:
The distance between any two integers is a positive number. So, we need to find |m – n| or |n – m|.
For example, if the numbers are 8 and 12, |8 – 12| = 4, and |12 – 8| = 4.
So, the distance between 8 and 12 is 4. But |8| – |12| = 8 – 12 = -4.
Since distances must always be positive, So Joe is incorrect.

Question 30.
Math Journal Use the data in the following table. Which two gases have boiling points that are closest in value? Explain.

Answer:
In the above table we can observe gases and temperatures. Two gases having boiling points that are closest in value are Oxygen and Nitrogen. The boiling point for oxygen is -297°F and the boiling point for Nitrogen is -321°F.

Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 2 Lesson 2.1 Adding Integers to finish your assignments.

Math in Focus Grade 7 Course 2 A Chapter 2 Lesson 2.1 Answer Key Adding Integers

Math in Focus Grade 7 Chapter 2 Lesson 2.1 Guided Practice Answer Key

Copy and complete.

Question 1.
Evaluate -3 + (-2).
Method 1
Use a number line to model the sum of two negative integers.

Answer:

Start at -3. Then add -2. Because you are adding a negative integer, -2, you make a jump of 2 to the left.

Method 2
Use absolute values to find the sum of two negative integers.
|-3| = Write the absolute value of each integer.
|-2| =
|-3| + |-2| = + Add the absolute values.
= Simplify.
-3 + (-2) = Use the common sign, a sign, for the sum.
Answer:
|-3| = 3
|-2| = 2
|-3| + |-2| = 3 + 2
= 5
-3 + (-2) = -5 Used the common sign, a negative sign, for the sum.

Question 2.
Evaluate -15 + (-7).
Method 1
Use a number line to model the sum of two negative integers.

Answer:

Start at -15 then add -7. Because we are adding a negative integer, -7, we make a jump of 7 to the left.
Method 2
Use absolute values to find the sum of two negative integers.
|-15| =
|-7| =
|-15| + |-7| = +
=
-15 + (-7) =
Answer:
|-15| = 15
|-7| = 7
|-15| + |-7| = 15 + 7
= 22
-15 + (-7) = -22

Evaluate each sum.

Question 3.
9 + (-9)
Answer:
9 – 9 = 0
Explanation:
Perform addition operation on above two numbers 9 and -9. Add 9 with -9 the sum is o.

Question 4.
-21 + 21
Answer:
-21 + 21 = 0
Explanation:
Perform addition operation on above two numbers -21 and 21. Add -21 with 21 the sum is o.

Hands-On Activity

Materials:

• counters

Find the sum of integers with different signs.

Work in pairs.

A zero pair has a value of zero.
(+1) + (-1) = (-1) + (+1)
= 0
Removing a zero pair does not change the value of an expression. For example:
(+1) + (-1) + 2 = 2 because
(+1) + (-1) + 2 = 0 + 2
= 2

Step 1.
Use counters to model and find the sum of two integers with different signs.
a) Evaluate 3 + (-2).

Answer:

A zero pair has a value of zero.
(+2) + (-2) = (-2) + (+2)
= 0
Removing a zero pair does not change the value of an expression.
(+2) + (-2) + 1 = 1 because
(+2) + (-2) + 1 = 0 + 1
= 1

b) Evaluate (-3) + 2

Answer:

A zero pair has a value of zero.
(+2) + (-2) = (-2) + (+2)
= 0
Removing a zero pair does not change the value of an expression.
(-2) + (+2) + (-1)  = -1 because
(-2) + (+2) + (-1) = 0 + (-1)
= -1

Step 2.
Use counters to model and find each sum.
a) 7 + (-2) and (-7) + 2
Answer:

b) (-8) + 5 and 8 + (-5)
Answer:

Math Journal
Explain how to add two integers with different signs. How are the absolute values of the addends related to the sum?

Evaluate each sum.

Question 5.
-10 + 3
Answer:
-10 + 3 = -7
Explanation:
Perform addition operation on above two numbers -10 and 3 the sum is -7.

Question 6.
-9 + 2
Answer:
-9 + 2 = -7
Explanation:
Perform addition operation on above two numbers -9 and 2 the sum is -7.

Question 7.
11 + (-23)
Answer:
11 + (-23) = -12
Explanation:
Perform addition operation on above two numbers 11 and -23 the sum is -12.

Evaluate each sum.

Question 8.
10 + (-3) + 6
Answer:
10 + (-3) + 6
= 16 + (-3)
= 13
Explanation:
Perform addition operation on above numbers. First add 10 with 6 the sum is 16. Next add the sum 16 with -3 the sum is 13.

Question 9.
-7 + (-23) + 15
Answer:
-7 + (-23) + 15
= -30 + 15
= -15
Explanation:
Perform addition operation on above numbers. First add -7 with -23 the sum is -30. Next add the sum -30 with 15 the sum is -15.

Solve.

Question 10.
A submarine ¡s at 400 feet below sea level. If it ascends 150 feet and then descends 320 feet, how far is ¡t above or below sea level?

You can think of the submarine ascending as an adding a positive integer, and descending as adding a negative integer. So, the verbal description can be translated as -400 + 150 + (-320).

Answer:
-400 + 150 + (-320) = -570
A submarine is 570 feet below sea level.
Explanation:
The submarine ascending as an adding a positive integer, and descending as adding a negative integer. A submarine ¡s at 400 feet below sea level. It ascends 150 feet and then descends 320 feet. Add -400 with 150 and -320 the sum is -570 feet.

Math in Focus Course 2A Practice 2.1 Answer Key

Evaluate each sum using a number line.

Question 1.
-3 + (-9)
Answer:

Explanation:
To evaluate the sum of two negative integers use a number line as we can observe in the above image. Start at -3. Then add -9. Because i am adding a negative integer, -9, I make a jump of 9 to the left. The sum of two negative integers is -12.

Question 2.
-8 + (-4)
Answer:

Explanation:
To evaluate the sum of two negative integers use a number line as we can observe in the above image. Start at -8. Then add -4. Because i am adding a negative integer, -4, I make a jump of 4 to the left. The sum of two negative integers is -12.

Question 3.
7 + (-7)
Answer:

Explanation:
To evaluate the sum of two integers use a number line as we can observe in the above image. Start at 7. Then add -7. Because i am adding a negative integer, -7, I make a jump of 7 to the left. The sum of two integers is 0.

Question 4.
-9 + 9
Answer:

Answer:
To evaluate the sum of two integers use a number line as we can observe in the above image. Start at -9. Then add 9. Because i am adding a positive integer, 9, I make a jump of 9 to the right. The sum of two integers is 0.

Question 5.
-10 + 6
Answer:

Explanation:
To evaluate the sum of two integers use a number line as we can observe in the above image. Start at -10. Then add 6. Because i am adding a positive integer, 6, I make a jump of 6 to the right. The sum of two integers is -4.

Question 6.
-17 + 9
Answer:

Explanation:
To evaluate the sum of two integers use a number line as we can observe in the above image. Start at -17. Then add 9. Because i am adding a positive integer, 9, I make a jump of 9 to the right. The sum of two integers is -8.

Evaluate each sum using the absolute values.

Question 7.
-23 + (-9)
Answer:
Use absolute values to find the sum of above two negative integers.
|-23| = 23
The absolute value of -23 is 23.
|-9| = 9
The absolute value of -9 is 9.
Add the absolute values.
|-23| + |-9| = 23 + 9
= 32
-23 + (-9) = -32
Use the common sign, a negative sign, for the sum.

Question 8.
-11 + (-34)
Answer:
Use absolute values to find the sum of above two negative integers.
|-11| = 11
The absolute value of -11 is 11.
|-34| = 34
The absolute value of -34 is 34.
Add the absolute values.
|-11| + |-34| = 11 + 34
= 45
-11 + (-34) = -45
Use the common sign, a negative sign, for the sum.

Question 9.
-15 + (-7)
Answer:
Use absolute values to find the sum of above two negative integers.
|-15| = 15
The absolute value of -15 is 15.
|-7| = 7
The absolute value of -7 is 7.
Add the absolute values.
|-15| + |-7| = 15 + 7
= 22
-15 + (-7) = -22
Use the common sign, a negative sign, for the sum.

Question 10.
12 + (-18)
Answer:
Use absolute values to find the sum of above two integers.
|12| = 12
The absolute value of 12 is 12.
|-18| = 18
The absolute value of -18 is 18.
Add the absolute values.
|12| + |-18| = 12 + 18
= 30
12 + (-18) = -6
Use the common sign, a negative sign, for the sum.

Question 11.
-40 + 26
Answer:
Use absolute values to find the sum of above two integers.
|-40| = 40
The absolute value of -40 is 40.
|26| = 26
The absolute value of 26 is 26.
Add the absolute values.
|-40| + |26| = 40 + 26
= 66
-40 + 26 = -14
Use the common sign, a negative sign, for the sum.

Question 12.
-75 + 19
Answer:
Use absolute values to find the sum of above two integers.
|-75| = 75
The absolute value of -75 is 75.
|19| = 19
The absolute value of 19 is 19.
Add the absolute values.
|-75| + |19| = 75 + 19
=94
-75 + 19 = -56
Use the common sign, a negative sign, for the sum.

Evaluate each sum.

Question 13.
-8 + 4 + 5
Answer:
-8 + 4 + 5
= -8 + 9
= 1
Explanation:
Perform addition operation on above numbers. First add 4 with 5 the sum is 9. Next add -8 with 9 the sum is 1.

Question 14.
5 + (-10) + (-6)
Answer:
5 + (-10) + (-6)
= -5 + (-6)
= -11
Explanation:
Perform addition operation on above numbers. First add 5 with -10 the sum is -5. Next add -5 with -6 the sum is -11.

Question 15.
-6 + (-8) + (-12)
Answer:
-6 + (-8) + (-12)
= -14 + (-12)
= -26
Explanation:
Perform addition operation on above numbers. First add -6 with -8 the sum is -14. Next add -14 with -12 the sum is -26.

Question 16.
-13 + (-17) + 7
Answer:
-13 + (-17) + 7
= -30 + 7
= -23
Explanation:
Perform addition operation on above numbers. First add -13 with -17 the sum is -30. Next add -30 with 7 the sum is -23.

Question 17.
-20 + 16 +(-7)
Answer:
-20 + 16 +(-7)
= -4 + (-7)
= -11
Explanation:
Perform addition operation on above numbers. First add -20 with 16 the sum is -4. Next add -4 with -7 the sum is -11.

Question 18.
-11 + (-8) + 14
Answer:
-11 + (-8) + 14
= -19 + 14
= -5
Explanation:
Perform addition operation on above numbers. First add -11 with -8 the sum is -19. Next add -19 with 14 the sum is -5.

Solve. Show your work.

Question 19.
The temperature is originally recorded as -4°F. What will the temperature be if the temperature rises 20°F?
Answer:
-4°F + 20°F = 16°F
Explanation:
The temperature is originally recorded as -4°F. The temperature rises to 20°F. Add -4°F with 20°F the sum is 16°F. The temperature is 16°F.

Question 20.
Mr. Lawson parked his car in a parking garage 33 feet below street level. He then got in an elevator and went up 88 feet to his office. How far above street level is his office?
Answer:

Answer:
88 – 33 = 55 feet
His office is 55 feet above street level.
Explanation:
Mr. Lawson parked his car in a parking garage 33 feet below street level. He then got in an elevator and went up 88 feet to his office. Subtract 33 feet below street level from 88 feet the difference is 55 feet. His office is 55 feet above street level.

Question 21.
A hiker starts hiking in Death Valley at an elevation of 143 feet below sea level. He climbs up 400 feet in elevation. What is his new elevation relative to sea level?
Answer:
A hiker starts hiking in Death Valley at an elevation of 143 feet below sea level. Below sea level is represented with negative number which is -143 feet.
He climbs up 400 feet in elevation. The word ‘climbs up’ represents positive number which is 400 feet.
– 143 feet + 400 feet = 257 feet
His new elevation is 257 feet above seal level.

Question 22.
Elizabeth was playing a board game with her friends. On her first turn, she moved 6 spaces forward. On her second turn, she moved another 5 spaces forward. On her third turn, she moved 4 spaces backward. How many spaces forward or backward from her starting point was she after her third turn?
Answer:
6 + 5 – 4
= 11 – 4
= 7
After her third turn Elizabeth moved 7 spaces forward from her starting point.
Explanation:
Elizabeth was playing a board game with her friends. On her first turn, she moved 6 spaces forward. Forward spaces are represented with positive number. On her second turn, she moved another 5 spaces forward. Forward spaces are represented with positive number. Add 6 with 5 the sum is 11. On her third turn, she moved 4 spaces backward. Backward spaces are represented with negative number. Subtract 4 from 11 the difference is 7. After her third turn Elizabeth moved 7 spaces forward from her starting point.

Question 23.
In the U.S. Open Golf Tournament, each qualifying golfer plays four rounds. The score for a round is recorded as positive (over par) or negative (under par). If a golfer scores -4, 6, 3, and -2 in the four rounds, what is the golfer’s total score for the tournament?
Answer:
The golfer scores -4, 6, 3, and -2 in four rounds.
-4 + 6 + 3 -2
= 9 – 6
= 3
The golfer’s total score for the tournament is 3.

Question 24.
Math Journal
In a game, all scores with even numbers are recorded as positive numbers. Odd numbers are recorded as negative numbers. Explain how to find David’s total score in this game if his individual scores during the game are 9, 12, 7, 18, and 19.
Answer:
The individual scores during the game are 9, 12, 7, 18, and 19.
Here the scores with even numbers are recorded as positive numbers.
The scores with Odd numbers are recorded as negative numbers.
The scores are -9, 12, -7, 18, -19
David’s total score is calculated by adding the given scores.
– 9 + 12  -7 + 18 – 19
= 30 – 9 – 7 – 19
= 30 – 35
= -5
David’s total score in this game is -5.

This handy Math in Focus Grade 2 Workbook Answer Key Chapter 14 Practice 2 Reading and Writing Time detailed solutions for the textbook questions.

Math in Focus Grade 2 Chapter 14 Practice 2 Answer Key Reading and Writing Time

Write the time in words.

Example

Question 1.

Answer:

three fifteen or 15 minutes after 3.

Question 2.

Answer:

eleven forty or 40 minutes after eleven.

Question 3.

Answer:

one twenty-five or 25 minutes after 1

Question 4.

Answer:

three thirty five or 35 minutes after 3

Question 5.

Answer:

eight fifty-five or 55 minutes after 8.

Write the time

Example

Question 6.

The time is _____________.
Answer:

The time is 1:45

Question 7.

The time is _____________.
Answer:

The time is 2:00

Question 8.

The time is _____________.
Answer:

The time is 6:20

Question 9.

The time is _____________.
Answer:

The time is 9:05

Question 10.

The time is _____________.
Answer:

The time is 2:55

Draw the minute hand to show the time.

Example

The time is 3:55.

Question 11.

The time is 6:30.
Answer:

Question 12.

The time is 10:15.
Answer:

Question 13.

The time is 8:00.
Answer:

Question 14.

The time is 12:40.
Answer:

Question 15.

The time is 9:05.
Answer:

Draw the hour hand to show the time.

Example

The time is 10:00.

Question 16.

The time is 11:30.
Answer:

Question 17.

The time is 7:15.
Answer:

Question 18.

The time is 4:20.
Answer:

Question 19.

The time is 2:50.
Answer:

Question 20.

The time is 3:40.
Answer:

Draw the hands to show the time.

Example

The time is 7:15.

Question 21.

The time is 4:30.
Answer:

Question 22.

The time is 1:20.
Answer:

Question 23.

The time is 9:25.
Answer:

Question 24.

The time is 7:00.
Answer:

Question 25.

The time is 9:50.
Answer:

Draw the hands to show the time. Then write the time in words.

Example

Question 26.

Answer:

five ten or 10 minutes after 5

Question 27.

Answer:

eleven forty or 40 minutes after 11

Question 28.

Answer:

six fifty five or 55 minutes after 6

Question 29.

Answer:

one twenty-five or 25 minutes after 1

Question 30.

Answer:

twelve-fifteen or 15 minutes after 12

This handy Math in Focus Grade 2 Workbook Answer Key Chapter 14 Practice 1 The Minute Hand detailed solutions for the textbook questions.

Math in Focus Grade 2 Chapter 14 Practice 1 Answer Key The Minute Hand

Question 1.
Fill in the boxes with the number of minutes.

Answer:

Fill in the blanks.

Example

Question 2.

The minute hand points to ___________ minutes.
Answer:

The minute hand points to 35 minutes.

Question 3.

The minute hand points to ___________ minutes.
Answer:

The minute hand points to 20 minutes.

Question 4.

The minute hand points to ___________ minutes.
Answer:

The minute hand points to 55 minutes.

Write the time.

Question 5.

Answer:

3 o’clock                                                      5 minutes after 3 o’clock

Question 6.

Answer:

7 o’clock                                                20 minutes after 7 o’clock

Question 7.

Answer:

10 o’clock                                                     45 minutes after 10 o’clock

Draw the minute hand to show the time.

Question 8.
15 minutes after 4 o’clock

Answer:

Question 9.
40 minutes after 6 o’clock

Answer:

Question 10.
50 minutes after 1 o’clock

Answer:

Question 11.
35 minutes after 10 o’clock

Answer:

This handy Math in Focus Grade 2 Workbook Answer Key Chapter 15 Multiplication Tables of 3 and 4 detailed solutions for the textbook questions.

Math in Focus Grade 2 Chapter 15 Answer Key Multiplication Tables of 3 and 4

Math Journal

These items are sold in a supermarket. Use the items to write a multiplication story.

Example
I want to buy 4 boxes of cereal.
I will have to give the cashier $16.

Story
__________________
Answer:

I want to buy cracked which costs $3

I want to buy cereal which costs $4.

Put On Your Thinking Cap!

Challenging Practice

Question 1.
Steve starts reading a book on page 7. He reads the book for 4 days. He reads 3 pages each day. Which page will Steve stop at on the 4th day?
(Hint: Use a diagram to help you solve.)
Answer:

Given,

Steve starts reading a book on page 7.

He reads the book for 4 days.

He reads 3 pages each day.

So, 4 x 3 = 12

12 + 7 = 19

Therefore, on the 4th day, steve will stop on the 19th page.

Question 2.
The music teacher is selecting children to sit in the front row at a concert. 100 children are given numbers 1 to 100. The teacher first picks the child with the number 3. He then skip-counts by tens to pick the other children. What are the numbers of the other children who are picked?
The numbers are ___________________
Answer:

Given,

The music teacher is selecting children to sit in the front row at a concert.

100 children are given numbers 1 to 100.

The teacher first picks the child with the number 3.

He then skip-counts by tens to pick the other children.

Put On Your Thinking Cap!

Problem Solving

Solve the riddle.

Question 1.
I am a two-digit number. I am more than 20 but less than 30. I can be found in both the multiplication tables of 3 and 4. What number am I?
Answer:

Given,

I am a two-digit number.

I am more than 20 but less than 30.

I can be found in both the multiplication tables of 3 and 4.

Let the number be a

20 < a > 30

the numbers that are both multiple of 3 and 4 and between 20 and 30 is are 24 only ( 3 x 8 = 4 x 6 )

Therefore, the number is 24.

Chapter Review/Test

Vocabulary

Fill in the blanks with words from the box.

skip-counting
dot paper
related multiplication facts

Question 1.

____________ is fun!
Answer:

Question 2.
are examples of _____________.
Answer:

Concepts and Skills

Skip count to find the missing numbers.

Question 3.
9 × 3 = ____________
Answer:

Question 4.
___________ × 3 = 24
Answer:

Question 5.
_________ × 4 = 16
Answer:

Question 6.
_________ × 4 = 36
Answer:

Find the missing numbers.

Question 7.
8 groups of 3 = __________ × 3
= ___________
Answer:

Question 8.
7 groups of 4 = ___________ × 4
= ___________
Answer:

Use dot paper to find the missing numbers.

Question 9.
6 × 4 = 5 groups of 4 + ___________ group of 4
= ___________ + 4
= ___________
Answer:

Problem Solving

Use skip-counting or dot paper to solve.

Question 10.
Caleb ties sets of 3 medals with a piece of ribbon. He ties 10 sets of medals. How many medals does Caleb have in all?
Answer:

Use related multiplication facts to solve.

Question 11.
Gail has 32 star-shaped key chains. She puts 4 key chains equally into some boxes. How many boxes are there?
Answer:

Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 1 Lesson 1.3 Introducing Irrational Numbers to finish your assignments.

Math in Focus Grade 7 Course 2 A Chapter 1 Lesson 1.3 Answer Key Introducing Irrational Numbers

Math in Focus Grade 7 Chapter 1 Lesson 1.3 Guided Practice Answer Key

Hands-On Activity

Materials:

• paper
• ruler
• scissors

Find the value of \(\sqrt{2}\) using a square.

Work in pairs.

Step 1.
Draw a square that has a length of 2 inches on a piece of paper. Then cut out the square.

Step 2.
Find the area of the square (square A).

Step 3.
Fold the four vertices of square A towards the center to form square B as shown below.

Step 4.
State how the areas of square A and square B are related. State the area of square B. How can you represent the length of a side of square B?

Step 5.
Using your answer in step 4, find the length of a side of square B with a calculator. Round your answer to 2 decimal places.

Math Journal
Place an edge of square B alongsi& a ruler to measure its length. Explain why the reading from the ruler is different from the answer in step 5.

Copy and complete.

Question 1.
Graph \(\sqrt{5}\) on the number line using rational approximations.
Which two whole numbers is \(\sqrt{5}\) between? Justify your reasoning. Using a calculator, \(\sqrt{5}\) = .
Graph an interval where \(\sqrt{5}\) is located.
The value of \(\sqrt{5}\) with two decimal places is
is closer to than to . So, \(\sqrt{5}\) is located closer to .

By using an approximate value of \(\sqrt{5}\), locate \(\sqrt{5}\) on the number line.

Answer:
The \(\sqrt{5}\) is between two whole numbers. The two whole numbers are 2 and 3.
By using calculator \(\sqrt{5}\) = 2.236067977….
The value of \(\sqrt{5}\) with two decimal places is 2.24.
The decimal 2.24 is closer to 2.2 than to 2.3.
So, \(\sqrt{5}\) is located closer to 2.2.

By using an approximate value of \(\sqrt{5}\),  located  \(\sqrt{5}\) on the number line as we can observe in the below image.

Copy and complete.

Question 2.
Graph –\(\sqrt{2}\) on the number line using rational approximations.
Which two integers is –\(\sqrt{2}\) between? Justify your reasoning. Using a calculator, –\(\sqrt{2}\) = .
Graph an interval where –\(\sqrt{2}\) is located.
The value of –\(\sqrt{2}\) with two decimal places is ? .
is closer to than to . So, –\(\sqrt{2}\) is located closer to ?

By using an approximate value of –\(\sqrt{2}\), locate –\(\sqrt{2}\) on the number line.

Answer:
The –\(\sqrt{2}\) is between two whole numbers. The two whole numbers are -1 and -2.
By using calculator –\(\sqrt{2}\) = -1.414213562…..
The value of –\(\sqrt{2}\) with two decimal places is -1.41.
The decimal -1.41 is closer to -1.4 than to -1.5.
So, –\(\sqrt{2}\) is located closer to -1.4.

By using an approximate value of –\(\sqrt{2}\),  located  –\(\sqrt{2}\) on the number line as we can observe in the below image.

Solve.

Question 3.
Graph –\(\sqrt{7}\) on the number line using rational approximations.
Answer:
The –\(\sqrt{7}\) is between two whole numbers. The two whole numbers are -2 and -3.
By using calculator –\(\sqrt{7}\) = -2.645751311…..
The value of –\(\sqrt{7}\) with two decimal places is -2.64.
The decimal -2.64 is closer to -2.6 than to -2.7.
So, –\(\sqrt{7}\) is located closer to -2.6.
By using an approximate value of –\(\sqrt{7}\),  located  –\(\sqrt{7}\) on the number line as we can observe in the below image.

Math in Focus Course 2A Practice 1.3 Answer Key

Locate each positive irrational number on the number line using rational approximations. First tell which two whole numbers the square root is between.

Question 1.
\(\sqrt{3}\)
Answer:
The \(\sqrt{3}\) is between two whole numbers. The two whole numbers are 1 and 2.
By using calculator \(\sqrt{3}\) = 1.732050807….
The value of \(\sqrt{3}\) with two decimal places is 1.73.
The decimal 1.73 is closer to 1.7 than to 1.8.
So, \(\sqrt{3}\) is located closer to 1.7.

By using an approximate value of \(\sqrt{3}\),  the positive irrational number \(\sqrt{3}\) is located on the number line as we can observe in the above image.

Question 2.
\(\sqrt{7}\)
Answer:
The \(\sqrt{7}\) is between two whole numbers. The two whole numbers are 2 and 3.
By using calculator \(\sqrt{7}\) = 2.645751311….
The value of \(\sqrt{7}\) with two decimal places is 2.64.
The decimal 2.64 is closer to 2.6 than to 2.7.
So, \(\sqrt{7}\) is located closer to 2.6.

By using an approximate value of \(\sqrt{7}\),  the positive irrational number \(\sqrt{7}\) is located on the number line as we can observe in the above image.

Question 3.
\(\sqrt{11}\)
Answer:
The \(\sqrt{11}\) is between two whole numbers. The two whole numbers are 3 and 4.
By using calculator \(\sqrt{11}\) = 3.316624790….
The value of \(\sqrt{11}\) with two decimal places is 3.31.
The decimal 3.31 is closer to 3.3 than to 3.4.
So, \(\sqrt{11}\) is located closer to 3.3.

By using an approximate value of \(\sqrt{11}\),  the positive irrational number \(\sqrt{11}\) is located on the number line as we can observe in the above image.

Question 4.
\(\sqrt{26}\)
Answer:
The \(\sqrt{26}\) is between two whole numbers. The two whole numbers are 5 and 6.
By using calculator \(\sqrt{26}\) = 5.099019513….
The value of \(\sqrt{26}\) with two decimal places is 5.09.
The decimal 5.09 is closer to 5.1 than to 5.0.
So, \(\sqrt{26}\) is located closer to 5.1.

By using an approximate value of \(\sqrt{26}\),  the positive irrational number \(\sqrt{26}\) is located on the number line as we can observe in the above image.

Question 5.
\(\sqrt{34}\)
Answer:
The \(\sqrt{34}\) is between two whole numbers. The two whole numbers are 5 and 6.
By using calculator \(\sqrt{34}\) = 5.830951894….
The value of \(\sqrt{34}\) with two decimal places is 5.83.
The decimal 5.83 is closer to 5.8 than to 5.9.
So, \(\sqrt{34}\) is located closer to 5.8.

By using an approximate value of \(\sqrt{34}\),  the positive irrational number \(\sqrt{34}\) is located on the number line as we can observe in the above image.

Question 6.
\(\sqrt{48}\)
Answer:
The \(\sqrt{48}\) is between two whole numbers. The two whole numbers are 6 and 7.
By using calculator \(\sqrt{48}\) = 6.928203230….
The value of \(\sqrt{48}\) with two decimal places is 6.92.
The decimal 6.92 is closer to 6.9 than to 7.0.
So, \(\sqrt{48}\) is located closer to 6.9.

By using an approximate value of \(\sqrt{48}\),  the positive irrational number \(\sqrt{48}\) is located on the number line as we can observe in the above image.

Locate each negative irrational number on the number line using rational approximations. First tell which two integers the square root is between.

Question 7.
–\(\sqrt{5}\)
Answer:
The –\(\sqrt{5}\) is between two integers. The two integers are -2 and -3.
By using calculator –\(\sqrt{5}\) = -2.236067977…..
The value of –\(\sqrt{5}\) with two decimal places is -2.23.
The decimal -2.23 is closer to -2.2 than to -2.3.
So, –\(\sqrt{5}\) is located closer to -2.2.

By using an approximate value of –\(\sqrt{5}\), the negative irrational number –\(\sqrt{5}\) is located on the number line as we can observe in the above image.

Question 8.
–\(\sqrt{6}\)
Answer:
The –\(\sqrt{6}\) is between two integers. The two integers are -2 and -3.
By using calculator –\(\sqrt{6}\) = -2.449489742…..
The value of –\(\sqrt{6}\) with two decimal places is -2.44.
The decimal -2.44 is closer to -2.4 than to -2.5.
So, –\(\sqrt{6}\) is located closer to -2.4.

By using an approximate value of –\(\sqrt{6}\), the negative irrational number –\(\sqrt{6}\) is located on the number line as we can observe in the above image.

Question 9.
–\(\sqrt{17}\)
Answer:
The –\(\sqrt{17}\) is between two integers. The two integers are -4 and -5.
By using calculator –\(\sqrt{17}\) = -4.123105625…..
The value of –\(\sqrt{17}\) with two decimal places is -4.12.
The decimal -4.12 is closer to -4.1 than to -4.2.
So, –\(\sqrt{17}\) is located closer to -4.1.

By using an approximate value of –\(\sqrt{17}\), the negative irrational number –\(\sqrt{17}\) is located on the number line as we can observe in the above image.

Question 10.
–\(\sqrt{26}\)
Answer:
The –\(\sqrt{26}\) is between two integers. The two integers are -5 and -6.
By using calculator –\(\sqrt{26}\) = -5.099019513….
The value of –\(\sqrt{26}\) with two decimal places is -5.09.
The decimal -5.09 is closer to -5.1 than to -5.0.
So, –\(\sqrt{26}\) is located closer to -5.1.

By using an approximate value of –\(\sqrt{26}\), the negative irrational number –\(\sqrt{26}\) is located on the number line as we can observe in the above image.

Question 11.
–\(\sqrt{53}\)
Answer:
The –\(\sqrt{53}\) is between two integers. The two integers are -7 and -8.
By using calculator –\(\sqrt{53}\) = -7.280109889….
The value of –\(\sqrt{53}\) with two decimal places is -7.28.
The decimal -7.28 is closer to -7.3 than to -7.2.
So, –\(\sqrt{53}\) is located closer to -7.3.

By using an approximate value of –\(\sqrt{53}\), the negative irrational number –\(\sqrt{53}\) is located on the number line as we can observe in the above image.

Question 12.
–\(\sqrt{80}\)
Answer:
The –\(\sqrt{80}\) is between two integers. The two integers are -8 and -9.
By using calculator –\(\sqrt{80}\) = -8.944271909….
The value of –\(\sqrt{80}\) with two decimal places is -8.94.
The decimal -8.94 is closer to -8.9 than to -9.0.
So, –\(\sqrt{80}\) is located closer to -8.9.

By using an approximate value of –\(\sqrt{80}\), the negative irrational number –\(\sqrt{80}\) is located on the number line as we can observe in the above image.

Use a calculator. Locate each irrational number to 3 decimal places on the number line using rational approximations.

Question 13.
\(\sqrt{47}\)
Answer:
By using calculator \(\sqrt{47}\) = 6.855654600….
The value of \(\sqrt{47}\) with three decimal places is 6.855.
The decimal 6.855 is closer to 6.86 than to 6.85.
So, \(\sqrt{47}\) is located closer to 6.86.

The given irrational number \(\sqrt{47}\) is located on the number line by using rational approximation as we can observe in the above image.

Question 14.
–\(\sqrt{15}\)
Answer:
By using calculator –\(\sqrt{15}\) = –3.872983346….
The value of –\(\sqrt{15}\) with three decimal places is –3.872.
The decimal -3.872 is closer to –3.87 than to –3.88.
So, –\(\sqrt{15}\) is located closer to -3.87.

The given irrational number –\(\sqrt{15}\) is located on the number line by using rational approximation as we can observe in the above image.

Question 15.

Answer:
By using calculator = 4.54683594….
The value of with three decimal places is 4.546.
The decimal 4.546 is in between 4.5 and 4.6.
So, is located on 4.55.

The given irrational number is located on the number line by using rational approximation as we can observe in the above image.

Locate each irrational number on the number line using rational approximations.

Question 16.
\(\sqrt{101}\)
Answer:
By using calculator \(\sqrt{101}\) = 10.049875….
The value of \(\sqrt{101}\) with two decimal places is 10.04.
The decimal 10.04 is closer to 10 than to 10.1.
So, \(\sqrt{101}\) is located closer to 10.

The given irrational number \(\sqrt{101}\) is located on the number line by using rational approximation as we can observe in the above image.

Question 17.
–\(\sqrt{132}\)
Answer:
By using calculator –\(\sqrt{132}\) = – 11.489125….
The value of –\(\sqrt{132}\) with two decimal places is –11.48.
The decimal -11.48 is closer to –11.5 than to –11.4.
So, –\(\sqrt{132}\) is located closer to –11.5.

The given irrational number –\(\sqrt{132}\) is located on the number line by using rational approximation as we can observe in the above image.

Question 18.
\(\sqrt{2,255}\)
Answer:
By using calculator \(\sqrt{2,255}\) = 47.4868….
The value of \(\sqrt{2,2551}\) with two decimal places is 47.48.
The decimal 47.48 is closer to 47.5 than to 47.4.
So, \(\sqrt{2,255}\) is located closer to 47.5.

The given irrational number \(\sqrt{2,255}\) is located on the number line by using rational approximation as we can observe in the above image.

Solve.

Question 19.
Locate the value of the constant, π, on the number line using rational numbers.
Answer:
We know that π = 3.14159265

In the above image we can observe the value of the constant, π, is located on the number line using rational numbers.

Question 20.
3.1416 and \(\frac{22}{7}\) are two rational approximate values of π.

a) Graph 3.1416, \(\frac{22}{7}\), and π on the number line.
b) Which of the two rational approximate values is closer to π?
Answer:
a)We know that 22/7 = 3.1428, π = 3.14159

In the above image we can observe 3.1416, 22/7 and π on the number line.
b) The two rational approximate values closer to π are  3.1416 and 22/7.

Question 21.
A triangle is cut from a square as shown in the diagram. The area of the square is 59 square inches. Approximate the height of the triangle to 3 decimal places.

Answer:

Question 22.
Math Journal When do you need to approximate an irrational number with a rational value? Explain and illustrate with an example.
Answer:

Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 1 Lesson 1.2 Writing Rational Numbers as Decimals to finish your assignments.

Math in Focus Grade 7 Course 2 A Chapter 1 Lesson 1.2 Answer Key Writing Rational Numbers as Decimals

Math in Focus Grade 7 Chapter 1 Lesson 1.2 Guided Practice Answer Key

Using long division, write each rational number as a terminating decimal.

Question 1.
\(\frac{7}{8}\)
Answer:
7/8

Explanation:
A Decimal Number that contains a finite number of digits next to the decimal point is called a Terminating Decimal. Perform division operation on given rational number. By using long division divide 7 by 8 the quotient is 0.875 which is a terminating decimal.

Question 2.
\(\frac{19}{4}\)
Answer:

Explanation:
Perform division operation on given rational number. By using long division divide 19 by 4 the quotient is 4.75 which is a terminating decimal.

Question 3.
\(\frac{52}{40}\)
Answer:

Explanation:
Perform division operation on given rational number. By using long division divide 52 by 40 the quotient is 1.3 which is a terminating decimal.

Question 4.
10\(\frac{13}{25}\)
Answer:
10(13/25)
= (250 + 13)/25
= 263/25

Explanation:
Perform division operation on given rational number. The mixed fraction 10(13/25) in fraction form as 263/25. By using long division divide 263 by 25 the quotient is 10.52 which is a terminating decimal.

Using long division, write each rational number as a repeating decimal.

Question 5.
\(\frac{2}{9}\)
Answer:

A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. Perform division operation on given rational number. By using long division divide 2 by 9 the quotient is 0.222… which is a repeating decimal.

Question 6.
\(\frac{11}{6}\)
Answer:

Explanation:
A repeating decimal is decimal representation of a number whose digits are periodic and the infinitely repeated portion is not zero. Perform division operation on given rational number. By using long division divide 11 by 6 the quotient is 1.8333… which is a repeating decimal.

Using a calculator, write each rational number as a repeating decimal.

Question 7.
\(\frac{23}{24}\)
Answer:
23/24
= 0.958333…
Explanation:
Perform division operation on given rational number. By using calculator divide 23 by 24 the quotient is 0.958333… which is a repeating decimal.

Question 8.
\(\frac{78}{37}\)
Answer:
78/37
= 2.108108….
Explanation:
Perform division operation on given rational number. By using calculator divide 78 by 37 the quotient is 2.108108… which is a repeating decimal.

Using long division, write each rational number as a repeating decimal. Use bar notation to indicate the repeating digits.

Question 9.
\(\frac{5}{6}\)
Answer:

Explanation:
Perform division operation on given rational number. By using long division divide 5 by 6 the quotient is 0.8333… which is a repeating decimal. The repeating digits are denoted by this ¯¯¯ symbol as we can observe in the above  image.

Question 10.
\(\frac{17}{12}\)
Answer:

Explanation:
Perform division operation on given rational number. By using long division divide 17 by 12 the quotient is 1.41666… which is a repeating decimal. The repeating digits are denoted by this ¯¯¯ symbol as we can observe in the above  image.

Technology Activity

Materials:

• spreadsheet software

Classify rational numbers in decimal form

Work in pairs.

Step 1.
On a spreadsheet, label four columns with the following column heads.

Step 2.
Enter each rational number below in the first column, labeled “Rational Numbers in Decimal Form”. Make sure that the cells in this column are formatted to display decimals up to 8 decimal places.
\(\frac{5}{16}\), \(\frac{141}{25}\), –\(\frac{40}{111}\), –\(\frac{15}{16}\), \(\frac{14}{5}\), \(\frac{1}{8}\), –\(\frac{9}{44}\), \(\frac{2}{11}\), \(\frac{5}{4}\) and –\(\frac{40}{9}\).
For example, if you enter into the spreadsheet, the entry will show the decimal form of this fraction.

Step 3.
Determine whether the decimal ¡s terminating, repeating, or neither. Enter either “Terminating”, “Repeating”, or “Neither” in the second column.

Step 4.
If the decimal terminates, record the number of decimal digits in the third column. If the decimal repeats, record the repeating digits in the fourth column.
Example:

Math Journal
Did you find any decimals that neither terminated nor repeated? What can you conclude about the decimal form of a rational number?

Compare the positive rational numbers using the symbols < or >. Use a number line to help you.

Question 11.
\(\frac{7}{10}\) ? \(\frac{13}{16}\)
Answer:
7/10 < 13/16

Explanation:
In the above number line we can observe the given positive rational numbers. The positive rational number 7/10 is less than 13/16.

Question 12.
\(\frac{24}{7}\) ? \(\frac{10}{3}\)
Answer:
24/7 > 10/3

Explanation:
In the above number line we can observe the given positive rational numbers 24/7 and 10/3. The positive rational number 24/7 is greater than 10/3.

Compare the negative rational numbers using the symbols < or >. Use a number line to help you.

Question 13.
–\(\frac{3}{5}\) ? –\(\frac{4}{5}\)
Answer:
-3/5  > -4/5

Explanation:
In the above number line we can observe the given negative rational numbers -3/5 and -4/5. The negative rational number -3/5 is greater than -4/5.

Question 14.
-10\(\frac{3}{4}\) ? –\(\frac{41}{5}\)
Answer:
-10(3/4)
= -(40 + 3)/4
= -43/4
-10(3/4) < – 41/5

Explanation:
In the above number line we can observe the given negative rational numbers -10(3/4) and -41/5. The negative rational number -10(3/4) is less than -41/5.

Question 15.
-4.063 ? -4\(\frac{1}{6}\)
Answer:
-4(1/6)
= – (24 + 1)/6
= -25/6
-4.063 > -4(1/6)

In the above number line we can observe the given negative rational numbers -4.063 and -4(1/6). The negative rational number -4.063 is greater than -4(1/6).

Math in Focus Course 2A Practice 1.2 Answer Key

Using long division, write each rational number as a terminating decimal.

Question 1.
76\(\frac{1}{2}\)
Answer:
76(1/2)
= 153/2

Explanation:
A Decimal Number that contains a finite number of digits next to the decimal point is called a Terminating Decimal. Perform division operation on given rational number. The mixed fraction 76(1/2) in fraction form is 153/2. By using long division divide 153 by 2 the quotient is 76.5 which is a terminating decimal.

Question 2.
-39\(\frac{2}{5}\)
Answer:
-39(2/5)
= -(195 + 2)/5
= -197/5

Explanation:
Perform division operation on given rational number. The mixed fraction -39(2/5) in fraction form is -197/5. By using long division divide -197 by 5 the quotient is -39.4 which is a terminating decimal.

Question 3.
–\(\frac{47}{10}\)
Answer:
-47/10

Explanation:
Perform division operation on given rational number. By using long division divide -47 by 10 the quotient is -4.7 which is a terminating decimal.

Question 4.
\(\frac{5}{16}\)
Answer:
5/16

Explanation:
Perform division operation on given rational number. By using long division divide 5 by 16 the quotient is 0.3125 which is a terminating decimal.

Question 5.
\(\frac{7}{20}\)
Answer:
7/20

Explanation:
Perform division operation on given rational number. By using long division divide 7 by 20 the quotient is 0.35 which is a terminating decimal.

Question 6.
\(\frac{7}{8}\)
Answer:
7/8

Explanation:
Perform division operation on given rational number. By using long division divide 7 by 8 the quotient is 0.875 which is a terminating decimal.

Simplify each rational number. Then use long division to write each rational number as a terminating decimal.

Question 7.
\(\frac{99}{36}\)
Answer:
99/36
= 11/4

Explanation:
The given ration number is 99/36. The simplified form of a given rational number is 11/4. Perform division operation on simplified rational number. By using long division divide 11 by 4 the quotient is 2.75 which is a terminating decimal.

Question 8.
\(\frac{12}{15}\)
Answer:
12/15
= 4/5

Explanation:
The given ration number is 12/15. The simplified form of a given rational number is 4/5. Perform division operation on simplified rational number. By using long division divide 4 by 5 the quotient is 0.8 which is a terminating decimal.

Question 9.
\(\frac{9}{48}\)
Answer:
9/48
= 3/16

Explanation:
The given ration number is 9/48. The simplified form of a given rational number is 3/16. Perform division operation on simplified rational number. By using long division divide 3 by 16 the quotient is 0.1875 which is a terminating decimal.

Question 10.
–\(\frac{132}{8}\)
Answer:
-132/8
= -33/2

Explanation:
The given ration number is -132/8. The simplified form of a given rational number is -33/2. Perform division operation on simplified rational number. By using long division divide -33 by 2 the quotient is -16.5 which is a terminating decimal.

Question 11.
–\(\frac{48}{50}\)
Answer:
-48/50
= -24/25

Explanation:
The given ration number is -48/50. The simplified form of a given rational number is -24/25. Perform division operation on simplified rational number. By using long division divide -24 by 25 the quotient is -0.96 which is a terminating decimal.

Question 12.
–\(\frac{14}{128}\)
Answer:
-14/128
= -7/64

Explanation:
The given ration number is -14/128. The simplified form of a given rational number is -7/64. Perform division operation on simplified rational number. By using long division divide -7 by 64 the quotient is -0.109375 which is a terminating decimal.

Using long division, write each rational number as a repeating decimal with 3 decimal places. Identify the pattern of repeating digits using bar notation.

Question 13.
\(\frac{5}{6}\)
Answer:

Explanation:
Perform division operation on given rational number. By using long division divide 5 by 6 the quotient is 0.83333… which is a repeating decimal. The repeating decimal with 3 decimal places is denoted as 0.833 bar for the number 3 on last. The repeating digits are denoted by this ¯¯¯ symbol as we can observe in the above  image.

Question 14.
-8\(\frac{2}{3}\)
Answer:
-8(2/3)
= -(24+2)/3
= -26/3

Explanation:
The mixed fraction -8(2/3) in fraction form is -26/3. Perform division operation on fraction. By using long division divide -26 by 3 the quotient is -8.66666… which is a repeating decimal. The repeating decimal with 3 decimal places is denoted as -8.666 bar for the number 6 on last. The repeating digits are denoted by this ¯¯¯ symbol as we can observe in the above  image.

Write each rational number as a repeating decimal using bar notation. You may use a calculator.

Question 15.
\(\frac{8}{55}\)
Answer:
8/55
= 0.1454545…
=
Explanation:
Perform division operation on given rational number. By using calculator divide 8 by 55 the quotient is 0.1454545… which is a repeating decimal. The repeating decimal 45 is represented by bar notation as we can observe in the answer.

Question 16.
\(\frac{456}{123}\)
Answer:
456/123
= 3.7073170731….
=
Explanation:
Perform division operation on given rational number. By using calculator divide 456 by 123 the quotient is 3.7073170731… which is a repeating decimal. The repeating decimal 70731 is represented by bar notation as we can observe in the answer.

Question 17.
–\(\frac{987}{110}\)
Answer:
-987/110
= -8.9727272….
=
Explanation:
Perform division operation on given rational number. By using calculator divide -987 by 110 the quotient is -8.9727272… which is a repeating decimal. The repeating decimal 72 is represented by bar notation as we can observe in the answer.

Question 18.
\(\frac{11}{14}\)
Answer:
11/14
= 0. 7857142857142….
=

Explanation:
Perform division operation on given rational number. By using calculator divide 11 by 14 the quotient is 0.7857142857142… which is a repeating decimal. The repeating decimal 857142 is represented by bar notation as we can observe in the answer.

Question 19.
–\(\frac{10}{13}\)
Answer:
-10/ 13
= – 0. 769230769230….
=

Explanation:
Perform division operation on given rational number. By using calculator divide -10 by 13 the quotient is -0.769230769230… which is a repeating decimal. The repeating decimal 769230 is represented by bar notation as we can observe in the answer.

Question 20.
\(\frac{4,005}{101}\)
Answer:
4,005/101
= 39.65346534….
=

Explanation:
Perform division operation on given rational number. By using calculator divide 4,005 by 101 the quotient is 39.65346534… which is a repeating decimal. The repeating decimal 6534 is represented by bar notation as we can observe in the answer.

Refer to the list of rational numbers below for questions 21 to 23, You may use a calculator.

–\(\frac{23}{32}\), \(\frac{7}{15}\), –\(\frac{368}{501}\), –\(\frac{19}{26}\), \(\frac{37}{44}\)

Question 21.
Write each rational number as a decimal with at most 6 decimal places.
Answer:
Given rational numbers are -23/32, 7/15, -368/501, -19/26, 37/44.
The given rational numbers in a decimal form with at most 6 decimal places.
-0.71875, 0.466667, -0.734531, -0.730769, 0.840909

Question 22.
Using your answers in 21 list the numbers from least to greatest using the symbol <. Graph a number line between —1 and 1 with 0 in the middle. Then, place each rational number on the number line.
Answer:

Explanation:
From the answer 21 the numbers from least to greatest are -368/501, -19/26, -23/32, 7/15, 37/44. In the above image we can observe the above given rational numbers on the number line.

Question 23.
Math Journal Margo tries to compare –\(\frac{2}{3}\) and –\(\frac{5}{8}\) using absolute values. She finds their decimal equivalents to be –\(0 . \overline{6}\) and —0.625, and she knows |-\(0 . \overline{6}\)| |-0.625|. Explain why she must reverse the inequality in her final answer, –\(\frac{2}{3}\) < –\(\frac{5}{8}\)
Answer:
The greater the absolute value of a number the farther that number is from 0.
So, -2/3 is farther to the left of 0 than -5/8.
A number that is to the left of another number on the number line is less than that number. So, -2/3 < -5/8.

Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 1 Lesson 1.1 Representing Rational Numbers on the Number Line to finish your assignments.

Math in Focus Grade 7 Course 2 A Chapter 1 Lesson 1.1 Answer Key Representing Rational Numbers on the Number Line

Math in Focus Grade 7 Chapter 1 Lesson 1.1 Guided Practice Answer Key

Solve.

Question 1.
Find the absolute values of 3\(\frac{2}{7}\) and –\(\frac{18}{5}\)
Answer:
3(2/7) = (21+2)/7 = 23/7
The simplified form of 3(2/7) is 23/7
The absolute value of |3(2/7)| is 3(2/7)
The absolute value of |-(18/5)| is 18/5

Question 2.
Graph the two numbers on a number line and indicate their distances from 0. Which number is farther from 0?
Answer:

The number -18/5 is farther from 0.
Explanation:
In the above image we can observe a number line. On the number line the two numbers 3(2/7) and -18/5 are indicated. The two numbers distance from 0 are graphed. The number -18/5 is farther from 0.

Write each number in \(\frac{m}{n}\) form where m and n are integers.

Question 3.
11\(\frac{1}{6}\)
Answer:
11(1/6)
= (66 + 1)/6
= 67/6
The number 11(1/6) in m/n form is 67/6.
Here m = 67 and n= 6

Question 4.
48
Answer:
48 = 48/1
The number 48 in m/n form is 48/1.
Here m = 48 and n = 1

Question 5.
-5\(\frac{4}{12}\)
Answer:
-5(4/12)
= – (60 + 4)/12
= -64/12
= -16/3
The number -5(4/12) in m/n form is -16/3.
Here m = -16 and n = 3

Question 6.
–\(\frac{25}{10}\)
Answer:
-25/10 = -5/2
The given number -25/10 is already in m/n form.

Write each decimal as \(\frac{m}{n}\) where m and n are integers with n ≠ 0.

Question 7.
11.5
Answer:
11.5 = 23/2
The given decimal number 11.5 is represented in m/n form. The m/n form of 11.5 is 23/2.

Question 8.
-7.8
Answer:
-7.8 = -78/10
The given decimal number -7.8 is represented in m/n form. The m/n form of -7.8 is -78/10.

Question 9.
0.36
Answer:
0.36 = 36/100
The given decimal number 0.36 is represented in m/n form. The m/n form of 0.36 is 36/100.

Question 10.
-0.125
Answer:
-0.125 = – 125/1000
The given decimal number -0.125 is represented in m/n form. The m/n form of -0.125 is 125/1000.

Copy and complete.

Question 11.
Locate the rational numbers -1.5 and \(\frac{15}{4}\) on the number line.
STEP 1
Find the integers that the rational number lies between.
\(\frac{15}{4}\) can be written as a mixed number, 3\(\frac{3}{4}\), and 3\(\frac{3}{4}\) lies between 3 and 4. The negative decimal -1.5 lies between —2 and —1.
STEP 2
Graph a number line and label the integers.

Answer:

The integers are labeled on a number line.
STEP 3
Divide the distance between the integers into equal segments.
You divide the distance between —2 and —1 into segments and the distance between 3 and 4 into segments.

Answer:

Divide the distance between —2 and —1 into 1 segments and the distance between 3 and 4 into 3 segments.
STEP4
Use the segments to locate -1.5 and 3\(\frac{3}{4}\).

Answer:

Located the rational numbers -1.5 and 15/4 on the number line.

Locate the following rational numbers on the number line.

Question 12.
\(\frac{1}{6}\) and \(\frac{15}{3}\)
Answer:
1/6 and 15/3

Explanation:
First we have to find the integers that where the rational number lies between on the number line.
The fraction 1/6 lies between 0 and 1. The simplified form of 15/3 is 5. The fraction 15/3 lies on number 5.
Next we have to label the integers and locate the rational numbers on a number line.
In the above image we can observe the rational numbers 1/6 and 15/3 are located on the number line.

Question 13.
-0.4 and \(\frac{11}{5}\)
Answer:
-0.4 and 11/5

Explanation:
First we have to find the integers that where the rational number lies between on the number line.
The negative decimal -0.4 lies between —1 and 0.The fraction 11/5 lies between 2 and 3.
Next we have to label the integers and locate the rational numbers on a number line.
Divide the distance between —1 and 0 into 4 segments and the distance between 2 and 3 into 4 segments.
In the above image we can observe the rational numbers -0.4 and 11/5 are located on the number line.

Question 14.
\(\frac{12}{15}\) and -1.8
Answer:
12/15 and -1.8

Explanation:
First we have to find the integers that where the rational number lies between on the number line.
The negative decimal -1.8 lies between —2 and -1.The fraction 12/15 lies between 0 and 1.
Next we have to label the integers and locate the rational numbers on a number line.
Divide the distance between —2 and -1 into 4 segments and the distance between 0 and 1 into 4 segments.
In the above image we can observe the rational numbers -1.8 and 12/15 are located on the number line.

Question 15.
\(-\frac{5}{15}\) and \(-\frac{25}{30}\)
Answer:
-5/15 and 25/30

Explanation:
First we have to find the integers that where the rational number lies between on the number line.
The negative fractions -25/30 and -5/15 lies between —1 and 0.
Next we have to label the integers and locate the rational numbers on a number line.
In the above image we can observe the rational numbers -25/30 and -5/15 are located on the number line.

Math in Focus Course 2A Practice 1.1 Answer Key

Find the absolute value of each fraction. Use a number line to show how far the fraction is from 0. Write fractions in simplest form.

Question 1.
\(\frac{7}{10}\)
Answer:
7/10

The absolute value of above fraction is 7/10.
Explanation:
First we have to find where the fraction lies between on the number line.
The fraction 7/10 lies between 0 and 1.
Next we have to label the fraction on a number line.
In the above image we can observe the fraction is 7/10 units far from the 0 on the number line.

Question 2.
\(\frac{18}{8}\)
Answer:
The absolute value of 18/8 is 18/8.
18/8 = 9/4
The simplest form of 18/8 is 9/4.

Explanation:
First we have to find where the fraction lies between on the number line.
The fraction 18/8 lies between 2 and 3.
Next we have to label the fraction on a number line.
In the above image we can observe the fraction is 18/8 units far from the 0 on the number line.

Question 3.
–\(\frac{5}{13}\)
Answer:
The absolute value of -5/13 is 5/13.

Explanation:
First we have to find where the fraction lies between on the number line.
The fraction -5/13 lies between -1 and 0.
Next we have to label the fraction on a number line.
In the above image we can observe the fraction is -5/13 units far from the 0 on the number line.

Question 4.
–\(\frac{48}{15}\)
Answer:
-48/15
The absolute value of -48/15 is 48/15.

Explanation:
First we have to find where the fraction lies between on the number line.
The fraction -48/15 lies between -3 and 0.
Next we have to label the fraction on a number line.
In the above image we can observe the fraction is -48/15 units far from the 0 on the number line.

Write each integer or fraction as \(\frac{m}{n}\) in simplest form where m and n are integers.

Question 5.
67
Answer:
67
= 67/1
The number 67 in m/n form is 67/1.
Here m = 67 and n= 1

Question 6.
-345
Answer:
-345
= -345/1
The number -345 in m/n form is -345/1.
Here m = -345 and n= 1

Question 7.
\(\frac{25}{80}\)
Answer:
25/80
= 5/16
The simplest form of 25/80 is 5/16.
The fraction 25/80 in m/n form is 5/16.
Here m = 5 and n= 16

Question 8.
–\(\frac{264}{90}\)
Answer:
-264/90
= -44/15
The simplest form of -264/90 is -44/15.
The fraction -264/90 in m/n form is -44/15.
Here m = -44 and n= 15

Question 9.
–\(\frac{14}{70}\)
Answer:
-14/70
= -1/5
The simplest form of -14/70 is -1/5.
The fraction -14/70 in m/n form is -1/5.
Here m = -1 and n= 5

Question 10.
\(\frac{600}{480}\)
Answer:
600/480
= 50/40
= 5/4
The simplest form of 600/480 is 5/4.
The fraction 600/480 in m/n form is 5/4.
Here m =5 and n = 4

Write each mixed number or decimal \(\frac{m}{n}\) as in simplest form where m and n are integers.

Question 11.
7\(\frac{7}{9}\)
Answer:
7(7/9)
= (63 + 7)/9
= 70/9
The simplest form of the mixed number 7(7/9) is 70/9.
Here m = 70 and n = 9 both are integers.

Question 12.
-5\(\frac{1}{10}\)
Answer:
-5(1/10)
= -(50 + 1)/10
= -51/10
The simplest form of the mixed number -5(1/10) is -51/10.
Here m = -51 and n = 10 both are integers.

Question 13.
2\(\frac{5}{12}\)
Answer:
2(5/12)
= (24 + 5)/12
= 29/12
The simplest form of the mixed number 2(5/12) is 29/12.
Here m = 29 and n = 12 both are integers.

Question 14.
-10\(\frac{11}{36}\)
Answer:
-10(11/36)
=-(360 + 11)/36
= -371/36
The simplest form of the mixed number-10(11/36) is -371/36.
Here m =-371 and n = 36 both are integers.

Question 15.
0.4
Answer:
0.4
= 4/10
= 2/5
The simplest form of the decimal number 0.4 is 2/5.
Here m = 2 and n = 5 both are integers.

Question 16.
-0.625
Answer:
-0.625
= -625/1000
= -5/8
The simplest form of the decimal number -0.625 is -5/8.
Here m = -5 and n = 8 both are integers.

Question 17.
5.80
Answer:
5.80
= 29/5
The simplest form of the decimal number 5.80 is 29/5.
Here m = 29 and n = 5 both are integers.

Question 18.
9.001
Answer:
9.001
= 9001/1000
The simplest form of the decimal number 9.001 is 9001/1000.
Here m = 9001 and n =1000 both are integers.

Question 19.
-10.68
Answer:
-10.68
= -267/25
The simplest form of the decimal number -10.68 is -267/25.
Here m = -267 and n = 25 both are integers.

Copy and complete.

Question 20.
Locate the following rational numbers correctly on the number line.
–\(\frac{1}{4}\), -1.5, 0.8, \(\frac{5}{2}\)

Answer:

Explanation:
First we have to find where the given rational numbers lies between on the number line.
The negative decimal -1.5 lies between -2 and -1.
The negative fraction -1/4 lies between -1 and 0.
The decimal 0.8 lies between 0 and 1.
The fraction 5/2 lies between 2 and 3.
The above given rational numbers are located correctly on the number line.

Question 21.
Locate the following rational numbers correctly on the number line.
1\(\frac{7}{10}\), –\(\frac{13}{5}\), 2.25, -0.7

Answer:

Explanation:
First we have to find where the given rational numbers lies between on the number line.
The negative fraction -13/5 lies between -3 and -2
The negative decimal -0.7 lies between -1 and 0.
The mixed fraction 1(7/10) in fraction as 17/10 lies between 1 and 2.
The decimal 2.25 lies between 2 and 3.
The above given rational numbers are located correctly on the number line.

Graph each rational number on a separate number line.

Question 22.
67\(\frac{1}{8}\)
Answer:
67(1/8)
= (536 + 1)/8
= 537/8

Explanation:
First we have to find where the given rational number lies between on the number line.
The mixed fraction 67(1/8) in fraction as 537/8 lies between 67 and 68.
The above given rational number is drawn correctly on the number line.

Question 23.
\(\frac{305}{20}\)
Answer:
305/20

Explanation:
First we have to find where the given rational number lies between on the number line.
The fraction 305/20 lies between 15 and 16.
The above given rational number is drawn correctly on the number line.

Question 24.
\(\frac{98}{28}\)
Answer:
98/28

Explanation:
First we have to find where the given rational number lies between on the number line.
The fraction 98/28 lies between 3 and 4.
The above given rational number is drawn correctly on the number line.

Question 25.
–\(\frac{21}{12}\)
Answer:
-21/12

Explanation:
First we have to find where the given rational number lies between on the number line.
The fraction -21/12 lies between -2 and -1.
The above given rational number is correctly drawn on the number line.

Question 26.
-25.8
Answer:

Explanation:
First we have to find where the given rational number lies between on the number line.
The decimal lies between -26 and -25.
The above given rational number is  drawn correctly on the number line.

Question 27.
-45.3
Answer:

Explanation:
First we have to find where the given rational number lies between on the number line.
The decimal lies between -46 and -45.
The above given rational number is correctly drawn on the number line.

A video game gives you 10 minutes to find a treasure. The results of your first 8 games show the amount of time left unused when you have found the treasure. A negative time means you have gone beyond the 10 minutes allotted. Use these data for questions 28 to 35.

\(\frac{23}{8}\), 0, -7\(\frac{1}{5}\), 6, –\(\frac{17}{4}\), 8, 7.8, -9.1

Question 28.
Order the times left from most to least time using the symbol >.
Answer:
The time left from most to least are 8, 7.8, 6, 23/8, 0, -17/4, -7(1/5), -9.1.

Question 29.
Write the absolute value of each number.
Answer:
23/8, 0, -7(1/5), 6 , -17/4, 8, 7.8, -9.1
The absolute value of 23/8 is 23/8.
The absolute value of 0 is 0.
The absolute value of -7(1/5) is 7(1/5) or 36/5.
The absolute value of 6 is 6.
The absolute value of -17/4 is 17/4.
The absolute value of 8 is 8.
The absolute value of 7.8 is 7.8.
The absolute value of -9.1 is 9.1.

Question 30.
Which number has the greatest absolute value?
Answer:
The decimal number – 9.1 has the greatest absolute value.

Question 31.
Order the absolute values from least to greatest. Use the symbol <.
Answer:
The absolute values from least to greatest are 0 < 23/8 < 17/4 < 6 < 7(1/5) < 7.8 < 8 < 9.1.

Question 32.
Graph the original numbers on a number line.
Answer:
23/8, 0, -7(1/5), 6 , -17/4, 8, 7.8, -9.1

The original numbers on a number line is drawn on the graph.

Question 33.
Which negative number in the list is farthest from 0?
Answer:
The negative number –9.1 in the given list is farthest from 0.

Question 34.
Which positive number in the list is closest to 10?
Answer:
The positive number 8 in the given list is closest to 10.

Question 35.
Which time is closest to —5 minutes?
Answer:
The time -17/4 is closest to – 5 minutes.