Math in Focus

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 5 Practice 3 Simplifying Algebraic Expressions to finish your assignments.

Math in Focus Grade 5 Chapter 5 Practice 3 Answer Key Simplifying Algebraic Expressions

Simplify each expression.

Example
c + c + c + c = 4c

Question 1.
6p + 3 p =
Answer:
6p + 3 p = 9p
Explanation:
The given expression is 6p + 3p. Add 6p with 3p the sum is 9p.

Question 2.
b + 3 b + 5b =
Answer:
b + 3b + 5b = 9b
Explanation:
The given expression is b + 3b + 5b. Add b with 3b and 5b the sum is 9b.

Question 3.
10k – 3k =
Answer:
10k – 3k = 7k
Explanation:
The given expression is 10k – 3k. Subtract 3k from 10k the difference is 7k.

Question 4.
12p – 12p =
Answer:
12p – 12p = 0
Explanation:
The given expression is 12p – 12p. Subtract 12p from 12p the difference is 0.

Question 5.
6p – 2p – 3p =
Answer:
6p – 2p – 3p = 6p – 5p = 1p
Explanation:
The given expression is 6p – 2p – 3p. First add 2p and 3p the sum is 5p. Subtract 5p from 6p the difference is 1p.

Question 6.
10a – a + 2a =
Answer:
10a – a + 2a = 9a + 2a = 11a
Explanation:
The given expression is 10a – a + 2a. First subtract a from 10a the difference is 9a. Now add 9a with 2a the sum is 11a.

Question 7.
4c + c – 5c =
Answer:
4c + c – 5c = 5c – 5c = 0
Explanation:
The given expression is 4c + c – 5c. First add 4c with c the sum is 5c. Subtract 5c from 5c the difference is 0.

Question 8.
10f – 4f + f =
Answer:
10f – 4f + f = 6f + f = 7f
Explanation:
The given expression is 10f – 4f + f. First subtract 4f from 10f the difference is 6f. Add 6f with f the sum is 7f.

Simplify each expression.

Example
5x + 2x + 4 = 7x + 4

Question 9.
x + 5x – 9 =
Answer:
x + 5x – 9 = 6x – 9
Explanation:
The given expression is x + 5x – 9. Add x with 5x the sum is 6x. The simplified expression is 6x – 9.

Question 10.
2m + 4 + 6m =
Answer:
2m + 4 + 6m = 8m + 4
Explanation:
The given expression is 2m + 4 + 6m. Add 2m with 6m the sum is 8m. The simplified expression is 8m + 4.

Question 11.
10p – 4p – 5 =
Answer:
10p – 4p – 5 = 6p – 5
Explanation:
The given expression is 10p – 4p – 5. Subtract 4p from 10p the difference is 6p. The simplified expression is 6p – 5.

Question 12.
4 + 5k – 4k =
Answer:
4 + 5k – 4k = 4 + k
Explanation:
The given expression is 4 + 5k – 4k . Subtract 4k from 5k the difference is k. The simplified expression is 4 + k.

Question 13.
2 + 6b – 1 + 4b =
Answer:
2 + 6b – 1 + 4b = 1 +10b
Explanation:
The given expression is 2 + 6b – 1 + 4b. Subtract 1 from 2 the difference is 1. Add 6b with 4b the sum is 10b. The simplified expression is 1 + 10b.

Question 14.
5c + 3 – 2c + 5 =
Answer:
5c + 3 – 2c + 5 = 3c + 8
Explanation:
The given expression is 5c + 3 – 2c + 5. Subtract 2c from 5c the difference is 3c. Add 3 with 5 the sum is 8. The simplified expression is 3c + 8.

Question 15.
9e – 2e + 3 + 5e =
Answer:
9e – 2e + 3 + 5e = 7e + 5e + 3 = 12e + 3
Explanation:
The given expression is 9e – 2e + 3 + 5e. Subtract 2e from 9e the difference is 7e. Add 7e with 5e the sum is 12e. The simplified expression is 12e + 3.

Question 16.
6h + 12 + 2h – 6 =
Answer:
6h + 12 + 2h – 6 = 8h + 6
Explanation:
The given expression is 6h + 12 + 2h – 6. Subtract 6 from 12 the difference is 6. Add 6h with 2h the sum is 8h. The simplified expression is 8h + 6.

Write an algebraic expression for each situation.

Question 17.
The length of a piece of fabric is 8y yards. London cuts 7 yards from it to make some cushion covers. He then cuts another 3y yards to make a curtain. The remaining material is cut into 4 equal pieces. How long is each piece?
Answer:
The length of a piece of fabric is 8y yards. London cuts 7 yards from it to make some cushion covers.
(8y – 7) yards
He then cuts another 3y yards to make a curtain.
(8y – 7 – 3y) yards
The remaining material is cut into 4 equal pieces.
(8y – 7 – 3y)/4 yards
(5y – 7)/4 yards

Question 18.
Ling has 4m pounds of flour. She buys another 2 packages of flour, each weighing m pounds. How much flour does Ling have now in terms of m?
Answer:
The algebraic expression is 4m + 2m = 6m.
Explanation:
Ling has 4m pounds of flour. She buys another 2 packages of flour, each weighing m pounds. The 2 packages of flour is represented as 2m. Add 4m with 2m the sum is 6m. Ling have 6m pounds of flour.

Question 19.
On Monday, Linus made 5k paper cranes and gave 2k paper cranes to his friends. On Tuesday, he made another 4k paper ‘ cranes. His friend gave him 5 paper cranes. How many paper cranes does he have now in terms of k?
Answer:
On Monday, Linus made 5k paper cranes and gave 2k paper cranes to his friends.
5k – 2k = 3k
On Tuesday, he made another 4k paper ‘ cranes. His friend gave him 5 paper cranes.
4k + 5k = 9k
3k + 9k = 12k
Now, he have 12k paper cranes.

Question 20.
At the market, a pear costs b cents and an apple costs 7 cents less than a pear. Randy buys 4 pears and an apple. How much does Randy pay in terms of b?
Answer:
The cost of pears is b cents.
The cost of an apple is 7 cents less than a pear = b – 7
Randy buys 4 pears and an apple.
4b + b – 7 = 5b – 7
At the market, Randy pays 5b -7.

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 10 Percent to score better marks in the exam.

Math in Focus Grade 5 Chapter 10 Answer Key Percent

Math Journal

Arnold had dinner at a restaurant with his family. The dinner cost $72. In addition, he paid 7% meals tax on the dinner. How much did Arnold pay for the dinner?

Tyrone worked out the answer using his calculator like this:
93% × $72 = $66.96
Brandon worked out the answer using his calculator like this:
107% × $72 = $77.04
Whose answer is correct? Explain why his answer is correct.
Answer:
Brandon answer is correct
Explanation:
Arnold paid
7% of tax and 100% of his bill
107% × $72 = $77.04
or
Arnold paid
$72 + $7% = $72 + $5.04 = $77.04

Put on Your Thinking Cap! 

Challenging Practice

Solve. Show your work.

Question 1.
Mr. Stanton bought a cell phone at 80% of the regular price. The regular price of the phone was $450. Mr. Wilson bought the same cell phone but paid $500 for it. How much more did Mr. Wilson pay than Mr. Stanton?
Answer:
140 more did Mr. Wilson pay than Mr. Stanton
Explanation:
Cell phone regular price is $450
Mr. Stanton paid 80% of 450 = $360
80% x $450= $360
Mr. Wilson paid $500
500 – 360 = 140
Mr. Wilson pay 140 more than Mr. Stanton.

Question 2.
Helen has 30 tickets. Gina has 20 more tickets than Helen. What percent of her tickets must Gina give Helen so that both of them have the same number of tickets?
Answer: 20%
Explanation:
Helen has 30 tickets.
Gina has 20 more tickets than Helen = 30 + 20 = 50 tickets
20 percent of her tickets must Gina give Helen so that both of them have the same number of tickets
such that both can have 40 tickets
Gina has 50 tickets
if she give 10 tickets to Helen ,now both are 40 tickets
20% of 50 is 10

Put on Your Thinking cap!

Problem Solving

Solve. Show your work.

Michelle collects U.S., Canadian, and Mexican stamps. In her collection, 80% of the stamps are U.S. and Mexican stamps. There are 3 times as many U.S. stamps as Mexican stamps. What percent of Michelle’s collection is made up of U.S. stamps?
Answer:
53.4%
Explanation:
100% of U.S. stamps + Canadian stamps + Mexican stamps
80% of the stamps are U.S. stamps + Mexican stamps
20% Canadian stamps
let Mexican stamp is x then
U.S stamps 3x
What percent of Michelle’s collection is made up of U.S. stamps?
80%  —– 3X
?       —– X
26.6 % Mexican
80% – 26.6% = 53.4%

This handy Math in Focus Grade 5 Workbook Answer Key Chapter 12 Practice 2 Angles at a Point provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 12 Practice 2 Answer Key Angles at a Point

In each figure, the rays meet at a point. Use a protractor to find unknown angle measures.

Question 1.

m∠a = ___
m∠b = ___
m∠c = ____
m∠a + m∠b + m∠c = ___ + ___ + ___
= ____
Answer:
m∠a = 120°
m∠b = 90°
m∠c = 150°
m∠a + m∠b + m∠c = 120° + 90° + 150° = 360°
Explanation:
Angle less than 180° is obtuse angle.
m∠a = 120°
m∠c = 150°
Angle 90° is Right angle triangle.
m∠b = 90°
Add all the angles to get a complete angle.
m∠a + m∠b + m∠c = 120° + 90° + 150° = 360°

Question 2.

m∠AOB = ___
m∠BOC = ___
m∠COD = ____
m∠DOE = _____
m∠AOE = ____
m∠AOB + m∠BOC + m∠COD + m∠DOE + m∠AOE
= ___ + ___ + ___ + ___ + ____
= ____
Answer:
m∠AOB = 140°
m∠BOC = 40°
m∠COD = 50°
m∠DOE = 100°
m∠AOE = 30°
m∠AOB + m∠BOC + m∠COD + m∠DOE + m∠AOE
= 140°+40°+50°+100°+30°= 360° is called a complete angle.
Explanation:

m∠AOB = 140°
m∠DOE = 100°
Angle less than 180° is obtuse angle.
m∠BOC = 40°
m∠COD = 50°
m∠AOE = 30°
Angle 90° is Right angle triangle.
Add all the angles to show complete angle.
m∠AOB + m∠BOC + m∠COD + m∠DOE + m∠AOE
= 140°+40°+50°+100°+30°= 360°

Name the angles at a point.

Question 3.

Answer:
∠a = 120°
∠b= 80°
∠c = 160°
∠a + ∠b + ∠c = 120° + 80° + 160° = 360°
Explanation:
∠a = 120° and ∠c = 160° are obtuse angles.
∠b = 80° is acute angle.
∠a + ∠b + ∠c = 120° + 80° + 160° = 360°

Question 4.

Answer:
m∠XOW = 40°
m∠ZOW = 90°
m∠ZOY = 140°
m∠XOY=90°
m∠XOY + m∠XOW + m∠ZOW + m∠ZOY + m∠XOY
= 40° + 90° + 140° + 90° = 360°
Explanation:

In the above picture
m∠ZOW = 90° and m∠XOY=90° are right angles.
m∠XOW = 40° is acute angle as the angle is less than 90°
m∠ZOY = 140° is obtuse angle as the angle is less than 180°
Add all the angles to get complete angle.
m∠XOY + m∠XOW + m∠ZOW + m∠ZOY + m∠XOY
= 40° + 90° + 140° + 90° = 360°

Question 5.

Answer:
∠a = 60°
∠b= 120°
∠c = 60°
∠d= 120°
∠a + ∠b + ∠c +∠d = 60°+ 120° + 60° + 120° = 360°
Explanation:

As shown in the above picture
∠a + ∠c= 60° are acute angles as the angle is less than 90°
∠b  and ∠d = 120° are obtuse angles as the angle is less than 180°
Add all the angles to get complete angle.
∠a + ∠b + ∠c +∠d = 60°+ 120° + 60° + 120° = 360°

Question 6.

Answer:
∠e = 90°
∠f  = 90°
∠g = 30°
∠h = 100°
∠k = 50°
∠e + ∠f + ∠g +∠h + ∠k =  90° + 90°+ 30° + 100° + 50° = 360°
Explanation:

As shown in the above picture
∠g = 30° and ∠k= 50° are acute angles as the angle is less than 90°
∠e = 90° and ∠f= 90° are right angles as the angle is 90°
∠h = 100° is obtuse angle as the angle is less than 180°
Add all the angles to get complete angle.
∠e + ∠f + ∠g +∠h + ∠k =  90° + 90°+ 30° + 100° + 50° = 360°

Find the unknown angle measures.

Question 7.
Find the measure of ∠AOB.

Answer: 114°
Explanation:
complete angle is 360°
∠AOC +∠COB = 104° + 142° = 246°
∠AOB = 360° – 246° = 114°

Question 8.
Find the measure of ∠a.

Answer: 270°
Explanation:
complete angle is 360°
360°- 90° = 270°

Question 9.
Find the measure of ∠b.

Answer: 50°
Explanation:
complete angle is 360°
360°- 310° = 50°

Question 10.
Find the measure of ∠c.

Answer: 294°
Explanation:
complete angle is 360°
given information
40°+ 26° = 66°
360°- 66° = 294°

Find the unknown angle measures.

Question 11.
Find the measure of ∠q.

Answer: 150°
Explanation:
complete angle is 360°
given information
90°+37°+ 83° = 210°
360°- 210° = 150°

Question 12.
Find the measure of ∠r.

Answer: 68°
Explanation:
complete angle is 360°
given information
90°+90°+ 112° = 292°
360°- 292° = 68°

Question 13.
Find the measure of ∠a.

Answer: 106°
Explanation:
complete angle is 360°
given information
90°+164° = 254°
360°- 292° = 106°

Question 14.
\(\overleftrightarrow{P R}\) and \(\overleftrightarrow{T U}\) meet at Q. Find the measures of ∠PQSand ∠TQR.

Answer:
m∠PQS = 54°
m∠TQR = 105°
Explanation:
complete angle is 360°
given information
∠PQT = 75° = ∠UQR
∠PQS = 180° – 51° + 75° = 54°
∠TQR = 180° – 75° = 105°

This handy Math in Focus Grade 3 Workbook Answer Key Chapter 16 Time and Temperature provides detailed solutions for the textbook questions.

Math in Focus Grade 3 Chapter 16 Answer Key Time and Temperature

Math Journal

Example

Question 1.
Here are the steps to do this subtraction exercise:
4 h 30 min – 2 h 45 min
Step 1: Regroup the 4 h to 3 h 60 min.
Step 2: Add 60 min to 30 min to get 90 min.
Step 3: Subtract 45 min from 90 min to get 45 min.
Step 4: Subtract 2 h from 3 h to get 1 h.
Step 5: Add 1 h and 45 min to get 1 h 45 min.

The steps to express time in hours and minutes are not in order.
Fill in the blanks.
320 min _____ h _____ min
Order the steps by writing the step numbers ¡n the boxes.
320 min is 5 h 20 min.
Subtract 300 min from 320 min to get 20 min.
Think 1 h = 60 mm, 5 h = 300 min. So, regroup 300 min to 5 h.
Answer:
320 can be written as 300 and 20
300 min to hours=300/60=5
5 h 20 min.
Ordered in steps:
Step 1: Think 1 h = 60 mm, 5 h = 300 min. So, regroup 300 min to 5 h.
Step 2: Subtract 300 min from 320 min to get 20 min.
Step 3: 320 min is 5 h 20 min.

Question 2.
David wanted to find out how much time Garrett took to make a kite. Garrett started at 2:20 P.M. and ended at 5:05 P.M. David drew this timeline to help him find how much time had passed:

The time line did not help him. Can you improve the timeline so that it is easier for him to find how much time had passed?

Answer:
The started time =2:20 PM
The ending time=5:05 PM
The elapsed time =?
There might be a chance of 3 h 25 min.

Question 3.
Imagine you and your friends are outdoors. The temperature is 90°F. Describe two activities you and your friends might want to do and the clothes that all of you should wear. Explain your thinking.
Answer:
The temperature feels like 90°F then it is hot.
– Wear protective clothing. Lightweight, light-coloured and loose-fitting clothing helps protect against heat. Change clothing if it gets completed
– Stay hydrated. Drink plenty of fluids; drink about 16 ounces before starting and 5 to 7 ounces every 15 or 20 minutes.
– Avoid dehydrating liquids. Alcohol, coffee, tea and caffeinated soft drinks can hurt more than help.
– Schedule frequent breaks. Take time for rest periods and water breaks in a shaded or air-conditioned area.

Put on Your  Thinking Cap!

Challenging Practice

Solve.

Question 1.

Clock A is 25 minutes slow.
Clock B is 10 minutes fast.
a. What is the actual time?
Answer: 10:00

From 9:35 we need to calculate up to 25 min.
We need to count forward for 25 min.
The 25 min from 9:35 is 10:00.

b. What is the time shown on Clock B?

Answer: 9:25

The time is fast in the clock B.
We need to count back by 10 min.
So the time is 9:25.

Put On Your Thinking Cap!

Problem Solving

Scientists in Snowland found that it is warmer in January than in July. It is warmer in July than in June. October is warmer than July but colder than January. List these months in order from warmest to coldest.

Answer:
The months which are warmer: January, July, October.
The months which are coldest: July, June, October.
The months from warmest to coldest: January, July, June, October.

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Chapter 8 Practice 3 Subtracting Decimals to score better marks in the exam.

Math in Focus Grade 4 Chapter 8 Practice 3 Answer Key Subtracting Decimals

Fill in the blanks. Write each difference as a decimal.

Example
0.9 – 0.4 = 9 tenths – 4 tenths
= 5 tenths
= 0.5

Question 1.
1 – 0.3 = ___ tenths – ___ tenths
= ___ tenths
= ____
Answer:
1 – 0.3 = 0.7.

Explanation:
1 – 0.3 = 10 tenths – 3 tenths
= 7 tenths
= 0.7.

Question 2.
1.3 – 0.6 = ___ tenths – ___ tenths
= ___ tenths
= ____
Answer:
1.3 – 0.6 = 0.7.

Explanation:
1.3 – 0.6 = 13 tenths – 6 tenths
= 7 tenths
= 0.7.

Question 3.
1.8 – 0.9 = ___ tenths – ___ tenths
= ___ tenths
= ____
Answer:
1.8 – 0.9 = ___ tenths – ___ tenths
= ___ tenths
= ____

Explanation:
1.8 – 0.9 = 18 tenths – 9 tenths
= 9 tenths
= 0.9.

Fill in the blanks.
Question 4.
Step 1

You cannot subtract 7 tenths from 5 tenths. So, regroup 3 ones and 5 tenths. 3 ones and 5 tenths
= ___ ones and ___ tenths
Subtract the tenths.
___ tenths – 7 tenths = ____ tenths
Step 2

Subtract the ones.
___ ones – ___one
= ___ one
So, 3.5 – 1.7 = ____
Answer:
3.5 – 1.7 = 1.8.

Explanation:
Step 1 :

You cannot subtract 7 tenths from 5 tenths. So, regroup 3 ones and 5 tenths. 3 ones and 5 tenths
= 2 ones and 15 tenths
Subtract the tenths.
15 tenths – 7 tenths = 8 tenths.
Step 2 :

Subtract the ones.
2 ones – 1 one
= 1 one.
So, 3.5 – 1.7 = 1.8.

Subtract.
Question 5.

Answer:
4.6 – 2.2 = 2.4.

Explanation:
Step 1 :

Subtract the tenths :
6 tenths – 2 tenths = 4 tenths.

Step 2 :

Subtract the ones.
4 ones – 2 ones
= 2 ones.
So, 4.6 – 2.2 = 2.4.

Question 6.

Answer:
7.4 – 6.5 = 0.9.

Explanation:
Step 1 :

You cannot subtract 5 tenths from 4 tenths. So, regroup 7 ones and 4 tenths. 7 ones and 4 tenths
= 6 ones and 14 tenths.
Subtract the tenths.
14 tenths – 5 tenths = 9 tenths.
Step 2 :

Subtract the ones.
6 ones – 6 ones
= 0 ones.
So, 7.4 – 6.5 = 0.9.

Write in vertical form. Then subtract.
Question 7.
6.7 – 2.4 = ___
Answer:
6.7 – 2.4 = 4.3.

Explanation:

Question 8.
3 – 1.3 = ____
Answer:
3 – 1.3 = 1.7.

Explanation:

Fill in the blanks. Write each difference as a decimal.
Example
0.08 – 0.02 = 8 hundredths – 2 hundredths
= 6 hundredths
= 0.06

Question 9.
0.23 – 0.19 = ___ hundredths – ___ hundredths
= ___ hundredths
= ____
Answer:
0.23 – 0.19 = 0.04.

Explanation:
0.23 – 0.19 = 23 hundredths – 19 hundredths
= 4 hundredths
= 0.04.

Question 10.
0.1 – 0.06 = ___ hundredths – ___ hundredths
= ___ hundredths
= ____
Answer:
0.1 – 0.06 = 0.94.

Explanation:
0.1 – 0.06 = 100 hundredths – 6 hundredths
= 94 hundredths
= 0.94.

Fill in the blanks.
Question 11.
Step 1

You cannot subtract 4 hundredths from 3 hundredths. So, regroup 2 tenths 3 hundredths.
2 tenths 3 hundredths
= ___ tenth ___ hundredths
Subtract the hundredths.
___ hundredths – ___ hundredths
= ___ hundredths
Step 2

You cannot subtract 5 tenths from ___ tenth.
So, regroup 4 ones and ___ tenth.
4 ones and ___ tenth
= ___ ones and ___ tenths
Subtract the tenths.
___ tenths – 5 tenths = ___ tenths
Step 3

Subtract the ones.
___ ones – 1 one = ___ ones
So, 4.23 – 1.54 = ___

Answer:
4.23 – 1.54 = 2.69.

Explanation:
Step 1:

You cannot subtract 4 hundredths from 3 hundredths. So, regroup 2 tenths 3 hundredths.
2 tenths 3 hundredths
= 1 tenth 13 hundredths
Subtract the hundredths.
13 hundredths – 4 hundredths
= 9 hundredths.
Step 2:

You cannot subtract 5 tenths from 1 tenth.
So, regroup 4 ones and 1 tenth.
3 ones and 11 tenth
= 4 ones and 11 tenths
Subtract the tenths.
11 tenths – 5 tenths = 6 tenths.
Step 3:

Subtract the ones.
3 ones – 1 one = 2 ones.

Subtract.
Question 12.

Answer:
0.39 – 0.07 = 0.32.

Explanation:
Step 1:

Subtract the hundredths.
9 hundredths – 7 hundredths
= 2 hundredths.
Step 2:

Subtract the tenths.
3 tenths – 0 tenths = 3 tenths.
Step 3:

Subtract the ones.
0 ones – 0 one = 0 ones.

Question 13.

Answer:
0.51 – 0.36 = 0.15.

Explanation:
Step 1

You cannot subtract 6 hundredths from 1 hundredths. So, regroup 5 tenths 1 hundredths.
5 tenths 1 hundredths
= 5 tenth 1 hundredths.
Subtract the hundredths.
11 hundredths – 6 hundredths
= 5 hundredths.
Step 2:

Subtract the tenths.
4 tenths – 3 tenths = 2 tenths.
Step 3:

Subtract the ones.
0 ones – 0 one = 0 ones.

Question 14.

Answer:
2.35 – 0.48 = 1.87.

Explanation:
Step 1:

You cannot subtract 8 hundredths from 5 hundredths. So, regroup 3 tenths 5 hundredths.
= 2 tenth 15 hundredths
Subtract the hundredths.
15 hundredths – 8 hundredths
= 7 hundredths.
Step 2:

You cannot subtract 4 tenths from 2 tenth.
So, regroup 2 ones and 2 tenth.
1 ones and  12 tenth.
Subtract the tenths.
12 tenths – 4 tenths = 8 tenths.
Step 3:

Subtract the ones.
1 ones – 0 one = 1 ones.

Question 15.

Answer:
12.45 – 10.63 = 1.82.

Explanation:
Step 1:

Subtract the hundredths.
5 hundredths – 3 hundredths
= 2 hundredths.
Step 2:

You cannot subtract 6 tenths from 4 tenth.
So, regroup 2 ones and 4 tenth.
= 1 ones and 14 tenths
Subtract the tenths.
14 tenths – 6 tenths = 8 tenths.
Step 3:

Subtract the ones.
1 ones – 0 one = 1 ones.
Step 4:
Subtract the tens.
1 tens – 1 tens = 0 tens.

Question 16.

Answer:
10.13 – 7.18 = 2.95.

Explanation:
Step 1:

You cannot subtract 8 hundredths from 3 hundredths. So, regroup 1 tenths 3 hundredths.
0 tenths 13 hundredths.
Subtract the hundredths.
13 hundredths – 8 hundredths
= 5 hundredths.
Step 2:

You cannot subtract 1 tenths from 0 tenth.
So, regroup 0 ones and 0 tenth.
regroup 1 tens 0 tenths.
9 ones and 10 tenth.
= 9 ones and 10 tenths
Subtract the tenths.
10 tenths – 1 tenths = 9 tenths.
Step 3:

Subtract the ones.
9 ones – 7 one = 2 ones.
So, 4.23 – 1.54 = ___
Step 4:

Subtract the tens.
0 tens – 0 tens = 0 tens.

Question 17.

Answer:
20.00 – 14.56 = 5.44.

Explanation:
Step 1:

You cannot subtract 6  hundredths from 0 hundredths. So, regroup 0 tenths 0 hundredths. So, regroup 0 ones 0 hundredths. So, regroup 2 tens 0 ones.
So, 1 tens. So, 10 ones. So, 10 tenths. So, 10 hundredths.
9 tenths 10 hundredths
= 9 tenth 10 hundredths.
Subtract the hundredths.
10 hundredths – 6 hundredths
= 4 hundredths
Step 2:

Subtract the tenths.
9 tenths – 5 tenths = 4 tenths.
Step 3:

Subtract the ones.
9 ones – 4 one = 5 ones.
Step 4:

Subtract the tens .
1 ones – 1 one = 0 ones.

Write in vertical form. Then subtract.
Question 18.
5.38 – 2.73 = ____
Answer:
5.38 – 2.73 = 2.65.

Explanation:

Question 19.
1.06 – 0.38 = ___
Answer:
1.06 – 0.38 = 0.68.

Explanation:

Question 20.
5.6 – 1.72 = ___
Answer:
5.6 – 1.72 = 3.88.

Explanation:

Question 21.
3 – 0.42 = ___
Answer:
3 – 0.42 = 2.58.

Explanation:

This handy Math in Focus Grade 1 Workbook Answer Key Chapter 5 Practice 2 Exploring Plane Shapes detailed solutions for the textbook questions.

Math in Focus Grade 1 Chapter 5 Practice 2 Answer Key Exploring Plane Shapes

Read.
Then answer the questions.

Question 1.
Josh has a square piece of paper. He folds it and unfolds it. Then he draws a line along the fold. Now he has two new shapes, A and B.

Write yes or no.

a. Are Shape A and Shape B the same shape? ____
Answer:
Yes, shape A and shape B both are having the same shape.

b. Are Shape A and Shape B the same size? ____
Answer:
Yes, the shape A and shape B are the same size.

Count.

c. How many sides are there?
Shape A ___ Shape B ____
Answer:
Shape A has 2 sides and shape B has 2 sides.

d. How many corners are there?
Shape A ___ Shape B ____
Answer:
Shape A has 2 corners and shape B also have 2 corners.

Write yes or no.

e. Are Shape A and Shape B different?
No, the shape A and shape B both are same.

Josh then cuts out Shape A and Shape B.

f. Can Shape A fit exactly over Shape B? ________
Answer:
Yes, the shape A fits exactly over the shape B.

Are the shapes the same shape and size? Write yes or no.

Question 2.

Shapes C and D ____
Answer:
Here the shape C and shape D both are the same shapes.

Question 3.

Shapes E and F ____
Answer:
Here the shape E and shape F are in different shapes.

Go through the Math in Focus Grade 3 Workbook Answer Key Chapter 6 Practice 1 Multiplication Properties to finish your assignments.

Math in Focus Grade 3 Chapter 6 Practice 1 Answer Key Multiplication Properties

Look at each number line. Write the multiplication fact.

Question 1.

Answer:
5×5 = 25.

Explanation:
In the number line, we can see that 5 jumps of 5. So the multiplication fact is 5×5 which is 25.

Question 2.

Answer:
4×7 = 28.

Explanation:
In the number line, we can see that 4 jumps of 7. So the multiplication fact is 4×7 which is 28.

Question 3.

Answer:
2×8 = 16.

Explanation:
In the number line, we can see that 2 jumps of 8. So the multiplication fact is 2×8 which is 16.

Complete each multiplication fact. Then show on each number line.

Question 4.
4 × 5 = ____

Answer:
4 × 5 = 20.

Explanation:
We will represent in the number line by 4 jumps of 5 for 4 × 5 which is 20.

Question 5.
5 × 3 = ____

Answer:
5 × 3 = 15.

Explanation:
We will represent in the number line by 5 jumps of 3 for 5 × 3 which is 15.

Look at the dot paper. Write the multiplication fact.

Example

Question 6.

Answer:
3 × 4 = 12.

Explanation:
The multiplication between 3 and 4 is 3 × 4 which is 12.

Question 7.

Answer:
2 × 3 = 6.

Explanation:
The multiplication between 2 and 3 is 2 × 3 which is 6.

Look at the dot paper. Write the multiplication fact.

Question 7.

Answer:
1 × 5 = 5.

Explanation:
The multiplication between 1 and 5 is 1 × 5 which is 5.

Question 8.

Answer:
3 × 5 = 5 × 3 = 15.

Explanation:
The multiplication between 3 and 5 is 3 × 5 which is 15.

Complete the multiplication fact. Then show on each number line.

Question 9.

Answer:

Fill in the missing numbers.

Question 10.
2 × __ = 0 × ___
= ____
Answer:
2 × 0 = 0 × 2 = 0.

Explanation:
Here, if we multiply 0 with anything we will get the product as 0. So
2 × 0 = 0 × 2
= 0.
So the missing letter is 0.

Question 11.
0 × ___ = 4 × ___
= _____
Answer:
0 × 4 = 4 × 0 =0.

Explanation:
Here, if we multiply 0 with anything we will get the product as 0. So
0 × 4 = 4 × 0
= 0.
So the missing letter is 4.

Question 12.
5 × ___ = 1 × ___
= ___
Answer:
5 × 1 = 1 × 5 = 5.

Explanation:
Here the missing letter is 1, as
5 × 1 = 1 × 5
= 5.
So the missing letter is 1.

Question 13.
1 × ___ = 10 × ___
= ____
Answer:
1 × 10 = 10 × 1 = 10.

Explanation:
Here the missing letter is 1, as
1 × 10 = 10 × 1
= 10.
So the missing letter is 1.

Complete each multiplication fact. Then show on the number line.

Example
2 × 3 × 3 = ?

Question 14.
2 × 4 × 2 = ___ × ____
= _____

Answer:
2 × 4 × 2 = 16.

Explanation:
Here, in Step 1 we will multiply 2 × 4 which is 8,
and in step 2 we will multiply 8 × 2 which is 16,
So, 2 × 4 × 2 = 16

Go through the Math in Focus Grade 3 Workbook Answer Key Chapter 7 Multiplication to finish your assignments.

Math in Focus Grade 3 Chapter 7 Answer Key Multiplication

Math Journal

Write the steps to your answer.

Multiply 243 by 2.

Example
Step 1
Multiply 3 ones by 2.
2 × 3 ones = 6 ones

Step 2
Multiply 4 tens by 2.
2 × 4 tens = 8 tens

Step 3
Multiply 2 hundreds by 2.
2 × 2 hundreds = 4 hundreds
So, 2 × 243 = 486.

Multiply 323 by 3.
Step 1 _________________
_____________________
Step 2 _________________
_____________________
Step 3 _________________
_____________________

Answer:
323 × 3 = 969.

Explanation:
Step 1
Multiply 3 ones by 3.
3 × 3 ones = 9 ones

Step 2
Multiply 2 tens by 3.
2 × 3 tens = 6 tens

Step 3
Multiply 3 hundreds by 3.
3 × 3 hundreds = 9 hundreds

So 323 × 3 is 969.

Put On Your Thinking cap!

Challenging Practice

Fill in the missing numbers.

Question 1.

Answer:
The missing digit is 4.

Explanation:
As the product is 48 and the multiplier 2, to find the missing digit we will divide 48÷2 which is 24. So the missing digit is 4.

Question 2.

Answer:
The missing digit is 4.

Explanation:
As the product is 68 and the multiplicand is 17, to find the missing digit we will divide 68÷17 which is 4. So the missing digit is 4.

Question 3.

Answer:
The missing digit is 2.

Explanation:
As the product is 693 and the multiplier 3, to find the missing digit we will divide 693÷3 which is 231. So the missing digit is 2.

Question 4.

Answer:
The missing digit is 5.

Explanation:
As the product is 605 and the multiplicand is 121, to find the missing digit we will divide 605÷121 which is 5. So the missing digit is 5.

Question 5.

Answer:
The missing digit is 2.

Explanation:
As the product is 616 and the multiplicand is 308, to find the missing digit we will divide 616÷308 which is 2. So the missing digit is 2.

Question 6.

Answer:
The missing digit is 3.

Explanation:
As the product is 540 and the multiplier 4, to find the missing digit we will divide 540÷4 which is 135. So the missing digit is 3.

Question 7.

Answer:
The missing digit is 2.

Explanation:
As the product is 756 and the multiplier 3, to find the missing digit we will divide 756÷3 which is 252. So the missing digit is 2.

Question 8.

Answer:
The missing digit is 4.

Explanation:
As the product is 592 and the multiplier 4, to find the missing digit we will divide 592÷4 which is 148. So the missing digit is 4.

Put on Your Thinking Cap!

Problem Solving

Solve.
Frank has 100 geese and cows on his farm. The animals have a total of 340 legs. How many geese and cows does Frank have?

Frank has ___ geese and __ cows.

Answer:
Frank has 30 geese and 70 cows.

Explanation:
Given that Frank has 100 geese and cows on his farm and the animals have a total of 340 legs. So the number of geese and cows do Frank has is

Practice the problems of Math in Focus Grade 2 Workbook Answer Key Chapter 11 Practice 3 Real-World Problems: Money to score better marks in the exam.

Math in Focus Grade 2 Chapter 11 Practice 3 Answer Key Real-World Problems: Money

Solve.

Draw bar models to help you.

Question 1.
Maddy buys a pencil for 25¢ and an eraser for 17¢. She gives the cashier 50¢. How much change does she get?
Answer: 8¢
Explanation:
Given:
Maddy buys a pencil for 25¢
Maddy buys an eraser for 17¢
So, Total amount spent will be
25¢ + 17¢ = 42¢
She gives the cashier 50¢
Then the total change she has to get will be
50¢ – 42¢ = 8¢

Question 2.
The Lesters have $600. They spent $110 on food and $97 on electricity. How much do they have left?
Answer: $393
Explanation:
Given:
Amount spent on food = $110
Amount spent on electricity = $97
Total amount spent will be
$110 + $97 = $207
total amount Lester’s left with would be
$600 – $207 = $393

Question 3.
Walter buys a notebook for 50¢. He buys another notebook that costs 12¢ more. How much does Walter pay in all?
Answer:62¢
Explanation:
Given:
Cost for the first book = 50¢
Cost for the second book = 12¢
Total amount that Walter must pay will be
50¢ + 12¢ = 62¢

Solve.
Write your answers using $ or ¢.

Question 4.
Tyler buys a book and a pen. How much does he spend?
Answer:$1.80
Explanation:
Given:
Amount spent on pen = $1
Amount spent on book = 80¢
80¢ = $0.80
then we get
$1 + $0.80 = $1.80

Question 5.
Rosie buys a teddy bear. Pamela buys a pencil sharpener. How much do they spend?
Answer:
Explanation:
Given:
Amount spent on Teddy bear = 95¢
Amount spent on Sharpener = 65¢
Total amount they both combinedly spent will be
95¢ + 65¢ = 160¢

Question 6.
How much more is a pen than a pencil sharpener?
Answer: 35¢
Explanation:
Given:
$1 =100¢
so
100¢ – 65¢ =35¢

Question 7.
Jessie has a dollar bill and a quarter. She wants to buy a teddy bear and a book.

a. Does she have enough money?
Answer: No
Explanation:
Given:
Jessie has a dollar bill and a quarter
that is $1= 100¢
And a quarter = 25¢
100¢ + 25¢ = 125¢
which is not enough

b. If not, how much more does she need?
Answer: 50¢ more
Explanation:
Given:
Jessie has a dollar bill and a quarter
that is $1= 100¢
And a quarter = 25¢
100¢ + 25¢ = 125¢
But for teddy and book she needs
95¢ + 80¢ = 175¢
so
175¢ – 150¢ = 50¢ more is needed

Question 8.
Henry has a $10 bill. He buys a teddy bear, a book, and a pen. How much does he have left?
Answer: $7 and 25¢
Explanation:
Given:
Amount for teddy bear = 95¢
Amount for book = 80¢
Amount for pen = $1 =100¢
100¢ + 80¢ + 95¢ = 275¢
$10 = 1000¢
so
1000¢ -275¢ =$7 and 25¢