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