Hillary

Go through the Math in Focus Grade 2 Workbook Answer Key Chapter 2 Practice 8 Addition with Regrouping in Ones and Tens to finish your assignments.

Math in Focus Grade 2 Chapter 2 Practice 8 Answer Key Addition with Regrouping in Ones and Tens

Solve.

Question 1.
On Wednesday, 487 people visit the zoo. On Thursday, 135 more people visit the zoo than on Wednesday. How many people visit the zoo on Thursday?
___ people visit the zoo on Thursday.
Answer:
616 people visit the zoo on Thursday.
Explanation:
On Wednesday, 487 people visit the zoo.
On Thursday, 135 more people visit the zoo than on Wednesday.
481 + 135 = 616 people visit the zoo on Thursday

Question 2.
After selling 694 books, Mr. Brown has 276 books left. How many books did he have at first?
He had ___ books at first.
Answer:
He had 970 books at first.
Explanation:
After selling 694 books,
Mr. Brown has 276 books left.
694 + 276 = 970 books that he have at first

Question 3.
A toy company gives away 111 toys in a contest There are 177 toys left. How many toys are there at first?

There are ___ toys at first.
Answer:
There are 288 toys at first.
Explanation:
A toy company gives away 111 toys in a contest
There are 177 toys left.
111 + 177 = 288 toys are there at first

Question 4.
There are 167 dolls in a toy store. The owner buys 533 more dolls. How many dolls are there now?

There are ___ dolls now.
Answer:
There are 700 dolls now.
Explanation:
There are 167 dolls in a toy store.
The owner buys 533 more dolls.
167 + 533 = 700 dolls are there now

Question 5.
Sunshine Camp has 324 boys.
There are 379 girls.
How many campers are at Sunshine Camp?
There are ___ campers at Sunshine Camp.
Answer:
There are 703 campers at Sunshine Camp.
Explanation:
Sunshine Camp has 324 boys.
There are 379 girls.
324 + 379 = 703 campers are at Sunshine Camp

Question 6.
Luke has 548 coins in his collection. Luke has 276 fewer coins than Sam. How many coins does Sam have?

Sam has ___ coins in his collection.
Answer:
Sam has 824 coins in his collection.
Explanation:
Luke has 548 coins in his collection.
Luke has 276 fewer coins than Sam.
548 + 276 = 824 coins that Sam have

Go through the Math in Focus Grade 4 Workbook Answer Key Chapter 3 Practice 2 Multiplying by a 2-Digit Number to finish your assignments.

Math in Focus Grade 4 Chapter 3 Practice 2 Answer Key Multiplying by a 2-Digit Number

Example

15 × 10 = 150 63 × 10 = 630

Question 1.
5 × 60 = 5 × ___ tens
= ____ tens
= ____
Answer:
5 × 60 = 30.

Explanation:
Given that 5 × 60 which is
5 × 60 = 5 ×6 tens
= 3 tens
= 300.

Question 2.
16 × 20 = 16 × ___ tens
= ___ tens
= ___
Answer:
16 × 20 = 320.

Explanation:
Given that 16 × 20 which is
16 × 20 = 16 × 2 tens
= 32 tens
= 320.

Question 3.
33 × 40 = 33 × ___ tens
= ___ tens
= ___
Answer:
33 × 40 = 1320.

Explanation:
Given that 33 × 40 which is
33 × 40 = 33 × 4 tens
= 132 tens
= 1,320.

Question 4.
29 × 30 = 29 × ___ tens
= ___ tens
= ___
Answer:
29 × 30 = 870.

Explanation:
Given that 29 × 30 which is
29 × 30 = 29 × 3 tens
= 87 tens
= 870.

Question 5.
41 × 60 = 41 × ___ × 10
= ___ × 10
= ___
Answer:
41 × 60 = 2,460.

Explanation:
Given that 41 × 60 which is
41 × 60 = 41 × 6 × 10
= 246 × 10
= 2,460.

Question 6.
96 × 40 = 96 × ___ × 4
= ___ × 4
= ___
Answer:
96 × 40 = 3,840.

Explanation:
Given that 96 × 40 which is
96 × 40 = 96 × 10 × 4
= 960 × 4
= 3,840.

Question 7.
618 × 50
= 618 × ___ × 10
= ___ × 10
= ___
Answer:
618 × 50 = 30,900.

Explanation:
Given that 618 × 50 which is
= 618 × 5 × 10
= 3,090 × 10
= 30,900.

Question 8.
752 × 70
= 752 × ___ × 7
= ___ × 7
= ___
Answer:
752 × 70 = 52,640.

Explanation:
Given that 752 × 70 which is
= 752 × 10 × 7
= 7,520 × 7
= 52,640.

What is the French word that has the same meaning as ‘hello’? Match the letters to the products below to find out.

Find each product.

Question 9.
42 × 1o = ________
Answer:
42 × 1o = 420.

Explanation:
The multiplication of 42 × 1o is 420.

Question 10.
786 × 1o = ____
Answer:
786 × 1o = 7,860.

Explanation:
The multiplication of 786 × 1o is 7,860.

Question 11.
16 × 5 = ____
16 × 50 = ___
Answer:
16 × 5 = 80,
16 × 50 = 800.

Explanation:
The multiplication of 16 × 5 is 80 and 16 × 50 is 800.

Question 12.
137 × 6 = ___
137 × 60 = ___
Answer:
137 × 6 = 822,
137 × 60 = 8,220.

Explanation:
The multiplication of 137 × 6 is 822 and 137 × 60 which is 8,220.

Question 13.
23 × 4 = _________
23 × 40 = ___
Answer:
23 × 4 = 92,
23 × 40 = 920.

Explanation:
The multiplication of 23 × 4 is 92 and 23 × 40 which is 920.

Question 14.
405 × 9 = ___
405 × 90 = ___
Answer:
405 × 9 = 3,645,
405 × 90 = 36,450.

Explanation:
The multiplication of 405 × 9 is 3,645 and 405 × 90 which is 36,6450.

Find each product.

Question 15.
70 × 800
7 × 8 = ______
7 × 80 = ______
7 × 800 = _______
So, 700 × 800 = ___
Answer:
7 × 8 = 56,
7 × 80 = 560,
7 × 800 = 5,600,
70 × 800 = 56,000,
700 × 800 = 5,60,000.

Explanation:
The multiplication of 7 × 8 which is 56,so 70 × 800 is 56,000
7 × 80 = 560,
7 × 800 = 5,600,
700 × 800 = 5,60,000.

Question 16.
300 × 90
__________
__________
__________
__________
Answer:
3 × 9 = 27,
3 × 90 = 270,
3 × 900 = 2,700,
30 × 90 = 2,700,
300 × 90 = 27,000.

Explanation:
The multiplication of 300 × 90 which is 27,000. So
3 × 9 = 27,
3 × 90 = 270,
3 × 900 = 2,700,
30 × 90 = 2,700.

Multiply. Find the missing numbers.

Example

Question 17.

Answer:
61 × 86 = 5,246.

Explanation:
The multiplication of 61 × 86 is 5,246.

Question 18.

Answer:
872 × 62 = 54,064.

Explanation:
The multiplication of 872 × 62 is 54,064.

Question 19.

Answer:
709 × 49 = 34,741.

Explanation:
The multiplication of 709 × 49 is 34,741.

Estimate each product. Round each number to its greatest place value.

Example
67 × 35 is about 70 × 40.
70 × 40 = 2,800

Question 20.
61 × 86 is about _____ × ___.
__ × __ = ____
Answer:
Actual product is 61 × 86 = 5,246.
Estimated product is 60 × 90 = 5,400.

Explanation:
Given that 61 × 86 which is about 60 × 90,
60 × 90 = 5,400.

Question 21.
872 × 62 is about _____ × ____.
__ × __ = ___
Answer:
Actual product is 872 × 62 = 54,064.
Estimated product is 870 × 60 = 52,200.

Explanation:
Given that 872 × 62 which is about 870 × 60,
870 × 60 = 52,200.

Question 22.
709 × 49 is about ____ × ___.
__ × __ = ___
Answer:
Actual product is 709 × 49 = 34,741.
Estimated product is 710 × 50 = 35,500.

Explanation:
Given that 709 × 49 which is about 710 × 50,
710 × 50 = 35,500.

Multiply. Then estimate to check that your answers are reasonable. Round each number to its greatest place value.

Example

252 is close to 200, So, the answer is reasonable.

Question 23.
48 × 21 = ____
Answer:
Actual product is 48 × 21 = 1,008.
Esstimated product is 50 × 20 = 1,000.

Explanation:
Given that 48 × 21 which is about 50 × 20,
50 × 20 = 1,000.

Question 24.
196 × 34 = ___
Answer:
Actual product is 196 × 34 = 6,664.
Esstimated product is 200 × 30 = 6,000.

Explanation:
Given that 196 × 34 which is about 200 × 30,
200 × 30 = 6,000.

Question 25.
608 × 73 = ___
Answer:
Actual product is 608 × 73 = 44,384.
Esstimated product is 610 × 20 = 12,200.

Explanation:
Given that 608 × 73 which is about 610 × 20,
610 × 20 = 12,200.

Question 26.
721 × 54 = ___
Answer:
Actual product is 721 × 54 = 38,934.
Esstimated product is 720 × 50 = 36,000.

Explanation:
Given that 721 × 54 which is about 720 × 50,
720 × 50 = 36,000.

Go through the Math in Focus Grade 4 Workbook Answer Key Chapter 3 Practice 3 Modeling Division with Regrouping to finish your assignments.

Math in Focus Grade 4 Chapter 3 Practice 3 Answer Key Modeling Division with Regrouping

Lisa cannot remember the steps to divide.
Help her complete the steps.

Question 1.

Answer:

Question 2.

Answer:

Divide. Then use the quotients to complete the number puzzle.

Down

Question 3.

Answer:
798 ÷ 2 = 399.

Explanation:
The quotient of 798 ÷ 2 is 399.

Question 4.

Answer:
849 ÷ 3 = 283.

Explanation:
The quotient of 849 ÷ 3 is 283.

Question 5.

Answer:
696 ÷ 4 = 174.

Explanation:
The quotient of 696 ÷ 4 is 174.

Across

Question 6.

Answer:
695 ÷ 5 = 139.

Explanation:
The quotient of 695 ÷ 5 is 139.

Question 7.

Answer:
754 ÷ 2 = 377.

Explanation:
The quotient of 754 ÷ 2 is 377.

Question 8.

Answer:
372 ÷ 4 = 93.

Explanation:
The quotient of 372 ÷ 4 is 93.

Divide. Then solve the riddle.

Question 9.

Which pet makes the loudest noise?
Match the letters to the quotients below to find out.

Answer:
The pet that makes loudest noise is Trumpet.

Explanation:

Divide.

Question 10.
516 ÷ 10 = ____
Answer:
516 ÷ 10 = 51 R 16.

Explanation:
By dividing 516 ÷ 10 we will get quotient as 51 with remainder 6.

Question 11.
144 ÷ 3 = ____
Answer:
144 ÷ 3 = 48.

Explanation:
By dividing 144 ÷ 3 we will get quotient as 48.

Question 12.
396 ÷ 4 = ____
Answer:
396 ÷ 4 = 99.

Explanation:
By dividing 396 ÷ 4 we will get quotient as 99.

Question 13.
885 ÷ 5 = ____
Answer:
885 ÷ 5 = 177.

Explanation:
By dividing 885 ÷ 5 we will get quotient as 177.

Look at the steps for dividing a 3-digit number by a 1-digit number.

Example

This shows the steps in division.

Write a number for each instruction box to match the instruction with the correct step for division. The first one has been done for you.

Complete the division.

Question 14.

Then write the steps, using the exercise on page 53 as a guide.
Step 1
___________________
Step 2
___________________
Step 3
___________________
Step 4
___________________
Step 5
___________________
Answer:
752 ÷ 4 = 188.

Explanation:
By dividing 752 ÷ 4 we will get the remainder as 188.

Go through the Math in Focus Grade 4 Workbook Answer Key Chapter 3 Practice 5 Real-World Problems: Multiplication and Division to finish your assignments.

Math in Focus Grade 4 Chapter 3 Practice 5 Answer Key Real-World Problems: Multiplication and Division

Solve. Show your work.

Example
A company has 4,059 people. Their names are listed in alphabetical order and then divided into groups of 5.
How many groups of 5 names are there and how many names are left?
4,059 ÷ 5 = 811R 4
There are 811 groups of 5 names, and 4 names are left.
If the number of men in the company is 600 times the number of names left, how many men are there in the company?
600 × 4 = 2,400
There are 2,400 men in the company.

Question 1.
Factory A produces 326 sweaters in a day. Factory B produces 1 07 more sweaters a day than Factory A.

a. How many sweaters does Factory B produce in a day?
Answer:
433 sweaters.

Explanation:
Given that Factory A produces 326 sweaters in a day and Factory B produces 107 more sweaters a day than Factory A. So the number of sweaters Factory B produce in a day is 326+107 which is 433 sweaters.

b. How many sweaters do the two factories produce in 68 days?

Answer:
The number of sweaters does the two factories produce in 68 days is 51,612 sweaters.

Explanation:
Factory A produces 326 sweaters in a day and Factory B produces 433 sweaters in a day. So the total number of sweaters Factory A and Factory B produce in a day is 326+433 which is 759 sweaters. So the number of sweaters the factories produce in 68 days is 759×68 which is 51,612 sweaters.

Question 2.
In her shop, Lee had a piece of fabric measuring 150 meters. A customer asked her to sew 10 cushion covers, each requiring 3 meters of fabric. Another customer bought 21 meters of the same fabric. How much fabric does Lee have left?
Answer:
The remaining amount left is 99 m.

Explanation:
Given that Lee had a piece of fabric measuring 150 meters and a customer asked her to sew 10 cushion covers and each requiring 3 meters of fabric. So for 10 covers 10×3 which is 30 m. And the amount remaining is 150-30-21 which is 99 m.

Question 3.
A bakery produces 3,000 loaves of bread. The bread is delivered to 75 stores. Of the 75 stores, 67 receive 2,000 loaves of bread altogether. The remaining stores receive an equal number of loaves of bread. How many loaves does each of the remaining stores receive?
Answer:
The remaining stores will receive 125 loaves for 8 stores.

Explanation:
Given that a bakery produces 3,000 loaves of bread and the bread is delivered to 75 stores. Of the 75 stores, 67 receive 2,000 loaves of bread altogether and the remaining loaf is 3,000-2,000 which is 1,000. The remaining stores will be 75-67 which is 8 stores. So the remaining loaves does each of the remaining stores receive will be 1,000÷8 which is 125 loaves.

Question 4.
Before lunch, Cindy packed 850 oranges, and Glen packed 470 fewer oranges than Cindy. Glen went home after lunch, but Cindy went back to work. That afternoon, Cindy packed 3 times as many oranges as Glen had packed in the morning.

a. How many oranges did Glen pack?
Answer:
Glen packed 370 oranges.

Explanation:
Given that before lunch, Cindy packed 850 oranges, and Glen packed 470 fewer oranges than Cindy which is 850-470 which is 370 oranges.

b. How many oranges did Cindy pack altogether?
Answer:
Cindy pack altogether is 1,960 oranges.

Explanation:
In the morning, Cindy packed 850 oranges and in the afternoon Cindy packed 3 times as many oranges as Glen had packed in the morning which is 3×370 which is 1,110 oranges. So Cindy pack altogether is 850+1,110 which is 1,960 oranges.

c. Cindy packed the oranges in bags of 5. How many bags of oranges did Cindy pack?

Answer:
Cindy packed 392 bags.

Explanation:
As Cindy packed the oranges in bags of 5, so the number of bags of oranges did Cindy packed is 1,960÷5 which is 392 bags.

Question 5.
Ms. Edstrom had a budget of $1500 to spend on a table and 6 chairs. The total price was $249 under her budget amount. The table cost 3 times as much as a chair.
Answer:
The table will be $417.

Explanation:
Given that Ms. Edstrom had a budget of $1500 to spend on a table and 6 chairs and the total price was $249 under her budget amount. Let X be the tables and Y be chairs. Then,
X = 3Y as the chairs are 3 times as much as a chair. So
X+6Y = 1,251
3Y+6Y = 1,251
9Y = 1,251
Y = 1,251÷9
= $139.
So the table will be 3×$139 =  $417.

Question 6.
Kamala had 5,026 grams of flour in a canister. She bought a 4,157-gram bag of flour. She poured some flour from the bag to the canister. As a result, the mass of the flour in the canister is now twice the mass of the flour left in the bag. How much flour is in the bag now?
Answer:
The flour left in the bag is 4,157-1,096 which is 3,061 grams.

Explanation:
Given that Kamala had 5,026 grams of flour in a canister and she bought a 4,157-gram bag of flour.
Let X be the number of grams of flour, so
5,026+X = 2(4,157-X)
5,026+X = 8,314 – 2X
2X+X = 8,314 – 5,026
3X = 3,288
X = 3,288÷3
X = 1,096.
So the flour left in the bag is 4,157-1,096 which is 3,061 grams.

Question 7.
Mr. Shea saved $2,500 in April. His monthly salary is twice the amount he saved in April. In May, he saved a certain amount of money. He spent $4,200 more than the amount he saved. How much did he save in May?
Answer:
The savings in the May will be $400.

Explanation:
Given that Mr. Shea saved $2,500 in April and his monthly salary is twice the amount he saved in April which is $2,500×2 which is $5,000. And in May, he saved a certain amount of money and he spent $4,200 more than the amount he saved. Let the savings in May be X, so the expenses in May will be X+4,200. So the amount he saved in May will be
(X)+(X+4,200) = $5,000
2X+4,200 = $5,000
2X = $5,000 – 4,200
2X = 800
X = 800÷2
= $400.
The savings in the May will be $400.

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Cumulative Review Chapters 7 and 8 to score better marks in the exam.

Math in Focus Grade 4 Cumulative Review Chapters 7 and 8 Answer Key

Concepts and Skills

write each fraction or mixed number as a decimal. (Lesson 7.1)

Question 1.
\(\frac{4}{10}\) = ____
Answer:
\(\frac{4}{10}\) =  0.4.

Explanation:
\(\frac{4}{10}\) = 4 ÷ 10 = 2 ÷ 5 = 0.4.

Question 2.
3\(\frac{3}{10}\) = ____
Answer:
3\(\frac{3}{10}\) = 0.9.

Explanation:
3\(\frac{3}{10}\) = 3(3 ÷ 10) = 3(0.3) = 0.9.

Question 3.
\(\frac{18}{10}\) = ____
Answer:
\(\frac{18}{10}\) = 1.8.

Explanation:
\(\frac{18}{10}\) = 18 ÷ 10 = 9÷ 5 = 1.8.

Write each decimal in tenths. (Lesson 7.1)
Question 4.
0.6 = ___ tenths
Answer:
0.6 = 6 tenths.

Explanation:

0.6 = 6 tenths.

Question 5.
1.7 = ___ tenths
Answer:
1.7 = 17 tenths.

Explanation:
1.7 = 17 tenths.

Question 6.
9.5 = ___ tenths
Answer:
9.5 = 95 tenths.

Explanation:
9.5 = 95 tenths.

Question 7.
4.2 = ___ tenths
Answer:
4.2 = 42 tenths.

Explanation:
4.2 = 42 tenths.

write each of these as a decimal. (Lesson 7.1)
Question 8.
3 ones and 4 tenths = ___
Answer:
3 ones and 4 tenths = 3.4.

Explanation:
3 ones and 4 tenths = 3.4.

Question 9.
8 ones and 1 tenth = ____
Answer:
8 ones and 1 tenth = 8.1.

Explanation:
8 ones and 1 tenth = 8.1.

Question 10.
77 tenths = ___
Answer:
77 tenths = 7.7.

Explanation:
77 tenths = 7.7.

Question 11.
19 tenths = ____
Answer:
19 tenths = 1.9.

Explanation:
19 tenths = 1.9.

Fill in the blanks. (Lesson 7.1)
Question 12.
22 tenths = 2 ones and ___ tenths
Answer:
22 tenths = 2 ones and  2 tenths.

Explanation:
22 tenths = 2 ones and 2 tenths.

Question 13.
3.2 = 3 ones and ___ tenths
Answer:
3.2 = 3 ones and 2 tenths.

Explanation:
3.2 = 3 ones and 2 tenths.

Write the correct decimal in each box. (Lesson 7.1)
Question 14.

Answer:

Explanation:
1. 1 tenths.
2.1 one.
3. 1 one 3 tenths.
4. 2 one o tenths.
5. 2 one 8 tenths.

Complete the expanded form of each decimal. (Lesson 7.1)
Question 15.
5.4 = 5 + ___
Answer:
5.4 = 5 + 4 tenths.

Explanation:
5.4 = 5 + 4 tenths.

Question 16.
7.1 = 7 + ___
Answer:
7.1 = 7 + 1 tenths.

Explanation:
7.1 = 7 + 1 tenths.

Question 17.
3.6 = 3 + __.
Answer:
3.6 = 3 + 6 tenths.

Explanation:
3.6 = 3 + 6 tenths.

Question 18.
10.2 = 10 + ___
Answer:
10.2 = 10 + 2 tenths.

Explanation:
10.2 = 10 + 2 tenths.

Fill in the blanks. (Lesson 7.1)
Question 19.
In 22.3, the digit 3 is in the ___ place. Its value is ____.
Answer:
In 22.3, the digit 3 is in the tenths place. Its value is 3 ÷ 10.

Explanation:
In 22.3,
the digit 3 is in the tenths place.
Its value is \(\frac{3}{10}\) = 3 ÷ 10.

Write each fraction or mixed number as a decimal. (Lesson 7.2)
Question 20.
\(\frac{9}{100}\) = ____
Answer:
\(\frac{9}{100}\) = 0.09.

Explanation:
\(\frac{9}{100}\) = 9 ÷ 100 = 0.09.

Question 21.
2\(\frac{26}{100}\) = ____
Answer:
2\(\frac{26}{100}\) = 0.52.

Explanation:
2\(\frac{26}{100}\) = 2(26 ÷ 100)
= 2 × 0.26
= 0.52.

Question 3.
\(\frac{105}{100}\) = ____
Answer:
\(\frac{105}{100}\) = 1.05.

Explanation:
\(\frac{105}{100}\) = 105 ÷ 100 = 1.05.

Write each decimal in hundredths. (Lesson 7.2)
Question 23.
0.06 = ___ hundredths
Answer:
0.06 = 6 hundredths.

Explanation:
0.06 = 6 hundredths.

Question 24.
1.33 = ___ hundredths
Answer:
1.33 = 133 hundredths.

Explanation:
1.33 = 133 hundredths.

Question 25.
2.5 = ___ hundredths
Answer:
2.5 = 250 hundredths.

Explanation:
2.5 = 250 hundredths.

Write each of these as a decimal. (Lesson 7.2)
Question 26.
2 ones and 6 hundredths = ____
Answer:
2 ones and 6 hundredths = 2.06.

Explanation:
2 ones and 6 hundredths = 2.06.

Question 27.
5 tenths 5 hundredths = ____
Answer:
5 tenths 5 hundredths = 0.55.

Explanation:
5 tenths 5 hundredths = 0.55.

Question 28.
7 ones and 3 tenths 4 hundredths = ___
Answer:
7 ones and 3 tenths 4 hundredths = 7.34

Explanation:
7 ones and 3 tenths 4 hundredths = 7.34.

Fill in the blanks. (Lesson 7.2)
Question 29.
16 hundredths = 1 tenth ___ hundredths
Answer:
16 hundredths = 1 tenth 6 hundredths.

Explanation:
16 hundredths = 1 tenth 6 hundredths.

Question 30.
0.45 = 4 tenths ___ hundredths
Answer:
0.45 = 4 tenths 5 hundredths.

Explanation:
0.45 = 4 tenths 5 hundredths.

Mark ✗ to show where each decimal is located on the number line. Label its value. (Lesson 7.2)

Question 31.
0.04
Answer:
0.04 = 4 hundredths.

Explanation:

Question 32.
0.15
Answer:
0.15 = 0 ones 1 tenths 5 hundredths.

Explanation:

Question 33.
0.26
Answer:
0.26 = 0 ones 2 tenths 6 hundredths.

Explanation:

Complete.
Question 34.
5.2 = __________ ones and __________ tenths
Answer:
5.2 = 5 ones and 2 tenths.

Explanation:
5.2 = 5 ones and 2 tenths.

Question 35.
0.86 = ___________ tenths ___________ hundredths
Answer:
0.86 = 8 tenths 6 hundredths.

Explanation:
0.86 = 8 tenths 6 hundredths.

Question 36.
3.7 = ___________ tenths
Answer:
3.7 = 7 tenths.

Explanation:
3.7 = 7 tenths.

Question 37.
0.93 = __________ hundredths
Answer:
0.93 = 3 hundredths.

Explanation:
0.93 = 3 hundredths.

Write each sum as a decimal. (Lesson 7.2)
Question 38.
7 + 0.6 + 0.02 = ___
Answer:
7 + 0.6 + 0.02 = 7.62.

Explanation:
7 + 0.6 + 0.02 = 7.6 + 0.02
= 7.62.

Question 39.
10 + 0.4 + 0.04 = ___
Answer:
10 + 0.4 + 0.04 = 10.44.

Explanation:
10 + 0.4 + 0.04 =  10.4 + 0.04
= 10.44.

Question 40.
5 + \(\frac{1}{10}\) + \(\frac{8}{100}\) = ___
Answer:
5 + \(\frac{1}{10}\) + \(\frac{8}{100}\) = 5.09.

Explanation:
5 + \(\frac{1}{10}\) + \(\frac{8}{100}\) = 5 + (1 ÷ 100) + (8 ÷ 100)
= 5 + 0.1 + 0.08
= 5.1 + 0.08
= 5.18.

Question 41.
9 + \(\frac{3}{10}\) + \(\frac{7}{100}\) = ___
Answer:
9 + \(\frac{3}{10}\) + \(\frac{7}{100}\) = 9.37.

Explanation:
9 + \(\frac{3}{10}\) + \(\frac{7}{100}\) = 9 + (3 ÷ 10) + (7 ÷ 100)
= 9 + 0.3 + 0.07
= 9.3 + 0.07
= 9.37.

Fill in the blanks. (Lesson 7.2)
Question 42.
In 14.68, the digit 8 is in the ___ place. Its value is ___.
Answer:
In 14.68, the digit 8 is in the hundredths place. Its value is 8 hundredths.

Explanation:
In 14.68,
the digit 8 is in the hundredths place. Its value is 8 hundredths.

Fill in the blanks. (Lesson 7.2)
Question 43.
$0.75 = ___ cents
Answer:
$0.75 = 75 cents.

Explanation:
Conversion: 1 dollar = 100 cents.
$0.75 = 100 × 0.75
= 75 cents.

Question 44.
$12.25 = ___ cents
Answer:
$12.25 = 1225 cents.

Explanation:
Conversion: 1 dollar = 100 cents.
$12.25 = 100 × 12.25
= 1225 cents.

Question 45.
$8.05 = ___ cents
Answer:
$8.05 = 805 cents.

Explanation:
Conversion: 1 dollar = 100 cents.
$8.05 = 100 × 8.05
= 805 cents.

Write each amount of money in decimal form. (Lesson 7.2)
Question 46.
65 cents = $___
Answer:
65 cents = $___

Explanation:
Conversion: 1 dollar = 100 cents.
65 cents = 65 ÷ 100
= $ 0.65.

Question 47.
10 dollars and 90 cents = $___
Answer:
10 dollars and 90 cents = $10.90.

Explanation:
Conversion: 1 dollar = 100 cents.
10 dollars and 90 cents = 10 + (90 ÷ 100)
= 10 + 0.90
= $10.90.

Question 48.
2 dollars and 5 cents = $____
Answer:
2 dollars and 5 cents = $2.05.

Explanation:
Conversion: 1 dollar = 100 cents.
2 dollars and 5 cents = 2 + (5 ÷ 100)
= 2 + 0.05
= $2.05.

Fill in the blanks. (Lesson 7.3)
Question 49.
0.1 more than 1.1 is ____
Answer:
0.1 more than 1.1 =  1.2.

Explanation:
0.1 more than 1.1 =  0.1 + 1.1 = 1.2.

Question 50.
0.2 less than 2 is ____
Answer:
0.2 less than 2 = 0.8.

Explanation:
0.2 less than 2 =  2 – 0.2 = 0.8.

Question 51.
0.01 less than 0.1 is ___
Answer:
0.01 less than 0.1 = 0.09.

Explanation:
0.01 less than 0.1 =  0.1 – 0.01 = 0.09.

Question 52.
0.03 more than 0.07 is ___
Answer:
0.03 more than 0.07 = 0.10.

Explanation:
0.03 more than 0.07 =  0.07 + 0.03 = 0.10.

Mark ✗ to show where each decimal is located on the number line. Label its value. (Lesson 7.3)

Question 53.
0.16
Answer:
0.16 = 0 ones 1 tenths 6 hundredths.

Explanation:

Question 54.
0.24
Answer:
0.24 = 0 ones 1 tenths 6 hundredths.

Explanation:

Compare. Write > or <. (Lesson 7.3)
Question 55.
4.1 0.41
Answer:
4.1 > 0.41.

Explanation:
4.1 is greater than 0.41 as its ones place number is greater in comparison.

Question 56.
0.73 0.70
Answer:
0.73 < 0.70.

Explanation:
0.73  is lesser than 0.70 as its hundredths place number in comparison comes first in comparison.

Circle the greatest decimal and underline the least. (Lesson 7.3)
Question 57.
3.04 3.4 0.34
Answer:

Explanation:
3.4 is comparatively greater than 3.04 and 0.34 as its tenths place number is greater.
0.34 is comparatively lesser than the 3.4 and 3.04 as its ones place number is less.

Question 58.
0.6 0.61 0.65
Answer:

Explanation:
0.6 is comparatively greater than 0.61 and 0.65 as its tenths place number comes first in number line.
0.65 is comparatively lesser than the 0.6 and 0.61 as its comes last in number line.

Fill in the blank. (Lesson 7.3)
Question 59.
Write a decimal that is greater than 0.9 but less than 1.0. ____
Answer:
A decimal that is greater than 0.9 but less than 1.0 is 0.987.

Explanation:
A decimal that is greater than 0.9 but less than 1.0 is 0.987.
The largest nearest number that can be approximated to 0.9 is 0.94999999999.
The lowest nearest number that can be approx. to 0.987 is 0.986500000000000000000
Hence, 0.987 is larger than 0.9.
Such problems are categorized under “ Number Theory”.

Round each decimal to the nearest whole number. (Lesson 7.4)
Question 60.
4.36 = ___
Answer:
4.36 = 4.0.

Explanation:
Rounding 4.36 to its nearest whole number = 4.0.

Question 61.
7.81 = ___
Answer:
7.81 = 8.0.

Explanation:
Rounding 7.81  to its nearest whole number = 8.0.

Question 62.
5.07 = ___
Answer:
5.07 = 5.0.

Explanation:
Rounding 5.07 to its nearest whole number = 5.0.

Round each decimal to the nearest tenth. (Lesson 7.4)
Question 63.
2.39 = ___
Answer:
2.39 = 2.50.

Explanation:
Rounding 2.39 to its nearest tenth = 2.50.

Question 64.
6.63 = ___
Answer:
6.63 = 7.0.

Explanation:
Rounding 6.63 to its nearest tenth = 7.0.

Question 65.
4.00 = ___
Answer:
4.00 = 4.0.

Explanation:
Rounding 4.00 to its nearest tenth = 4.0.

write each decimal as a fraction in simplest form. (Lesson 7.5)
Question 66.
0.6 =
Answer:
0.6 = 

Explanation:
simplest form of 0.6 = 6 ÷10.

Question 67.
0.55 =
Answer:
0.55 =

Explanation:
simplest form of  0.55 = 55 ÷ 100.

write each fraction or mixed number as a decimal. (Lesson 7.5)
Question 68.
\(\frac{1}{5}\) =
Answer:
\(\frac{1}{5}\) = 0.2.

Explanation:
\(\frac{1}{5}\) = 1 ÷ 5 = 0.2.

Question 69.
\(\frac{9}{20}\) =
Answer:
\(\frac{9}{20}\) = 0.45.

Explanation:
\(\frac{9}{20}\) = 9 ÷ 20 = 0.45.

Question 70.
\(\frac{5}{2}\) =
Answer:
\(\frac{5}{2}\) = 2.50.

Explanation:
\(\frac{5}{2}\) = 5 ÷ 2 = 2.50.

Question 71.
1\(\frac{3}{4}\) =
Answer:
1\(\frac{3}{4}\) = 1.75.

Explanation:
1\(\frac{3}{4}\) = 1 (3 ÷ 4)
= (4 + 3) ÷ 4
= 7 ÷ 4
= 1.75.

Question 72.
4\(\frac{2}{5}\) =
Answer:
4\(\frac{2}{5}\) = 4.4.

Explanation:
4\(\frac{2}{5}\) = 4 (2 ÷ 5)
= (20+2) ÷ 5
= 22 ÷ 5
= 4.4.

Question 73.
5\(\frac{1}{4}\) =
Answer:
5\(\frac{1}{4}\) = 5.25.

Explanation:
5\(\frac{1}{4}\) = 5 (1 ÷ 4)
= (20 + 1) ÷ 4
= 21 ÷ 4
= 5.25.

Find each sum or difference. (Lesson 8.1 and 8.2)

Question 74.

Answer:

Explanation:
6.74 + 2.17 = 8.91.

Question 75.

Answer:

Explanation:
3.28 + 0.91 = 4.19.

Question 76.

Answer:

Explanation:
5.76 + 4.26 = 10.02.

Question 77.

Answer:

Explanation:
7.05 – 1.33 = 5.72.

Question 78.

Answer:

Explanation:
8.72 – 3.43 = 5.29.

Question 79.

Answer:

Explanation:
6.36 – 5.79 = 0.57.

Problem Solving
Solve. Show your work. (Lesson 8.3)
Question 80.
Lina thinks of a number. When she adds 9.65 to it, she gets 20.7. What number is Lina thinking of?
Answer:
The number Lina thinks = 11.05.

Explanation:
When she adds 9.65 to it, she gets 20.7.
Let the number be X.
=> X + 9.65 = 20.7.
=> X = 20.7 – 9.65
=> X = 11.05.

Question 81.
Suri bought a skirt for $25.90 and a sweatshirt for $19.90. She paid the cashier $50. How much change did she receive?
Answer:
Amount of change she received = $4.2.

Explanation:
Cost of a skirt Suri bought = $25.90.
Cost of a sweatshirt Suri bought = $19.90.
Amount of money she paid to the cashier = $50.
Amount of change she received = Amount of money she paid to the cashier – (Cost of a skirt Suri bought + Cost of a sweatshirt Suri bought)
= $50 – ($25.90 + $19.90)
= $50 – $45.8
= $4.2.

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Chapter 9 Practice 3 Turns and Right Angles to score better marks in the exam.

Math in Focus Grade 4 Chapter 9 Practice 3 Answer Key Turns and Right Angles

Find the measure of each angle.

Question 1.

A \(\frac{1}{2}\)-turn is ____.
Answer:
180°.

Explanation:
Here, a \(\frac{1}{2}\)-turn is 180°.

Question 2.

A \(\frac{3}{4}\)-turn is ____.
Answer:
270°.

Explanation:
Here, a \(\frac{3}{4}\)-turn is 270°.

Fill in the blanks.

Question 3.

A ___ -turn is 90°
Answer:
\(\frac{1}{4}\).

Explanation:
Here, a \(\frac{1}{4}\)-turn is 90°.

Question 4.

A ___ -turn is 360°
Answer:
1 -turn.

Explanation:
Here, a 1 -turn is 360°.

Look at the three pairs of angle strips shown.

Which pair of angle strips shows

Question 5.
\(\frac{1}{2}\) turn? ___________
Answer:
∠c.

Explanation:
In the above images, ∠c is a \(\frac{1}{2}\) turn which is 180°.

Question 6.
a straight angle? ____
Answer:
∠c.

Explanation:
In the above images, ∠c is a \(\frac{1}{2}\) turn which is 180°.

Question 7.
a turn between \(\frac{1}{2}\)-turn and \(\frac{3}{4}\)-turn? ____
Answer:
225°.

Explanation:
a turn between \(\frac{1}{2}\)-turn and \(\frac{3}{4}\)-turn is 225°.

Look at the three pairs of angle strips shown.

Which pair of angle strips shows

Question 8.
360°? _________
Answer:
1 turn.

Explanation:
In the above images, ∠D is a 1 turn which is 360°.

Question 9.
an angle between 180° and 360°? ___________
Answer:
\(\frac{3}{4}\).

Explanation:
In the above images, ∠F is a \(\frac{3}{4}\) turn which is 270°.

Complete.

Question 10.
180° makes up ___ of a full turn.
Answer:
180° makes up half of a full turn.

Explanation:
Here, 180° makes up half of a full turn. As 360° makes a full turn.

Question 11.
Three right angles make up a __ -turn
Answer:
Three right angles make up a \(\frac{3}{4}\) -turn.

Explanation:
Here, three right angles make up a \(\frac{3}{4}\) -turn which is 270°.

Question 12.
105° is between a ___-turn and a ___-turn.
Answer:
105° is between a \(\frac{1}{4}\)-turn and a \(\frac{1}{2}\)-turn.

Explanation:
105° angle lies between a \(\frac{1}{4}\)-turn and a \(\frac{1}{2}\)-turn.

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

Math in Focus Grade 4 Chapter 8 Answer Key Adding and Subtracting Decimals

Put On Your Thinking Cap!

Challenging Practice

Question 1.
Miguel subtracts two numbers and gets the answer 4.95. The lesser of the two numbers is 3.4. What is the other number?
Answer:
The other number = 8.35.

Explanation:
Miguel subtracts two numbers and gets the answer 4.95.
Let the two number s be X and Y.
=> X – Y = 4.95.
The lesser of the two numbers is 3.4.
=> X – 3.4 = 4.95
=> X = 4.95 + 3.4
=> X = 8.35.

Question 2.
Julia subtracts two numbers and gets the answer 6.8. The greater of the two numbers is 10.55. What is the other number?
Answer:
The other number = 3.75.

Explanation:
Julia subtracts two numbers and gets the answer 6.8.
Let the two number s be X and Y.
=> X – Y = 6.8.
The greater of the two numbers is 10.55.
=> 10.55 – Y = 6.8
=> 10.55 = 6.8 + Y
=> 10.55 – 6.8 = Y
=> 3.75 = Y

Put On Your Thinking Cap!
Problem Solving
Question 1.
The number in each rectangle is the sum of the numbers in the two circles next to it. Find the numbers in the circles.

Answer:
A = 0.3.
B = 1.1
C = 0.6

Explanation:
The number in each rectangle is the sum of the numbers in the two circles next to it.
=> Equation 1: A + B = 1.4
=> Equation 2: A + C = 0.9
=> Equation 3: B + C = 1.7.
Equation 1 – Equation 2
=> (A + B) – (A + C ) = 1.4 – 0.9
=> A + B – A – C = 0.5
=> B – C = 0.5.
=> B = 0.5 + C.
Equation 3 – Equation 2:
(B + C) – (A + C ) =  1.7 – 0.9
=> B + C – A – C = 0.8
=> B – A = 0.8.
=> A = B – 0.8.
Substitute A and B in Equation:1.
=> A + B = 1.4
=> B – 0.8 + B = 1.4
=> 2B – 0.8 = 1.4
=> 2B = 1.4 + 0.8
=> 2B = 2.2
=> B = 2.2 ÷ 2
=> B = 1.1.
A = 1.1 – 0.8
=> A = 0.3.
Substitute A = 0.3 in Equation 2:
=> A + C = 0.9
=> 0.3 + C = 0.9
=> C = 0.9 – 0.3
=> C = 0.6.

Question 2.
Each week, Rena saves $5. Her brother saves $2.50 less each week, but he started saving 4 weeks earlier. After how many weeks will Rena’s savings be equal to her brother’s?
Answer:
Number of weeks Rena’s savings be equal to her brother’s = 2.

Explanation:
Amount of money Rena saves each week = $5.
Her brother saves $2.50 less each week, but he started saving 4 weeks earlier.
Amount of money her brother saves each week = Amount of money Rena saves each week – $2.50.
= $5 – $2.50
= $2.50.
Total amount of money her brother saves for 4 weeks =  4 × Amount of money her brother saves each week
= 4 × $2.50
= $10.
Number of weeks Rena’s savings be equal to her brother’s =  Total amount of money her brother saves for 4 weeks ÷ Amount of money Rena saves each week
= $10 ÷ $5
= 2.

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Chapter 9 Angles to score better marks in the exam.

Math in Focus Grade 4 Chapter 9 Answer Key Angles

Math Journal

Question 1.
Which statements are wrong? Explain your answer.

a. Two right angles form a \(\frac{1}{2}\)-turn.
Answer:
Yes.

Explanation:
Yes, two right angles form a \(\frac{1}{2}\)-turn.

b. The measure of an angle is a fraction of a \(\frac{3}{4}\)-turn.
Answer:

c. An acute angle has a measure greater than 90°.
Answer:
Wrong.

Explanation:
No, because the acute angle will be less than 90°. So the statement is wrong.

d. A \(\frac{1}{4}\)-turn is 90°.
Answer:
Yes.

Explanation:
Yes, a \(\frac{1}{4}\)-turn is 90°.

e. A straight angle has a measure of 180°.
Answer:
Yes.

Explanation:
Yes, a straight angle has a measure of 180°.

f. 150° is between a \(\frac{1}{4}\) -turn and a \(\frac{1}{2}\)-turn.
Answer:
Yes.

Explanation:
Yes, 150° is between a \(\frac{1}{4}\) -turn and a \(\frac{1}{2}\)-turn.

Complete.

Question 2.
Conrad named the angle as shown. Is he correct? Explain your answer.

The names of the angle are ∠EFG, ∠FGE, and ∠F.
Answer:
Wrong.

Explanation:
The names of the angle ∠FGE, and ∠F are wrong because the middle point must be a vertex.

Put On Your Thinking cap!

Challenging Practice

Look at the clock. The hour hand and minute hand were at the position as shown in figure A. Figure B shows the position of the hour hand and minute hand after some time.

What fraction of a turn did the minute hand move? Explain your answer.

Answer:
The fraction will be \(\frac{1}{4}\).

Explanation:
Here, the fraction of a turn did the minute hand move is \(\frac{1}{4}\).

Put on Your Thinking Cap!

Problem Solving

Look at the diagram.
Tom walks from J to K and at that point makes a \(\frac{1}{4}\)-turn to his right.
Then, he walks to H and at that point, makes a \(\frac{1}{2}\)-turn before walking on to the end of that line.
Where will he be?

Answer:
Tom will be on G.

Explanation:
Here, Tom walks from J to K and at that point makes a \(\frac{1}{4}\)-turn to his right which is 90°, and then he walks to H, and at that point, makes a \(\frac{1}{2}\)-turn which is 180° before walking on to the end of that line. So he will be at point G.

This handy Math in Focus Grade 4 Workbook Answer Key Chapter 12 Practice 5 Using Formulas for Area and Perimeter detailed solutions for the textbook questions.

Math in Focus Grade 4 Chapter 12 Practice 5 Answer Key Using Formulas for Area and Perimeter

Solve. Show your work.

Example

The floor of a patio measuring 8 feet by 7 feet is tiled with 1 -foot square tiles. The shaded area in the figure is tiled in black, and the unshaded area is tiled in white. What is the area tiled in white?

Area of patio = 8 × 7
= 56 ft²
Shaded area = 6 × 4
= 24 ft²
Area of patio – shaded area
= 56 – 24
= 32 ft²
The area tiled in white is 32 square feet.

Question 1.
The floor of Mr. Jones’ living room is in the shape shown below.

a. Estimate, in square yards, the area of his living room.
Answer:
We can calculate the living rom by making the room into two shapes where area of them can be easily find.
Area of the living room = area of the triangle + area of the rectangle
= 1/2 × 3 × 2 + 4 × 3
= 3 + 12
= 15
The estimated area of Mr. Jones’ living room is 15 square yards.

b. Mr. Jones wants to carpet his living room. If a roll of carpet is 3 yards wide, what is the smallest length of carpet Mr. Jones should buy?
Answer:
Area of the carpet required is 15 square yards.
As carpet will be in rectangular shape, so length x width = 15
As given, width is 3 yards. So 3 × 5 = 15
The smallest length of carpet Mr. Jones should buy is 5 yards.

Solve. Show your work.

Question 2.
The figure shows a small rectangle and a large rectangle. Find the area of the shaded part of the figure.

Area of large rectangle = ___________ × ___________
= ______________ ft²
Area of small rectangle = ___________ × ___________
= ________ ft²
Area of shaded part area of large rectangle – area of small rectangle
= ________ ft²
The area of the shaded part is __________ square feet.
Answer:
Area of large rectangle = 18ft × 16ft
= 288 ft²
Area of small rectangle = 9ft × 6ft
= 54 ft²
Area of shaded part area of large rectangle – area of small rectangle
= 288 ft² – 54 ft²
= 234 ft²
The area of the shaded part is 234 square feet.

Solve. Show your work.

Question 3.
The figure shows a small rectangle and a large rectangle. Find the area of the shaded part of the figure.

Area of large rectangle = ___________ × ___________
= ______________ in.²
Area of small rectangle = ___________ × ___________
= ________ in.²
Area of shaded part area of large rectangle – area of small rectangle
= ________ in.²
The area of the shaded part is __________ square inches.
Answer:
Area of large rectangle = 15 in × 11 in
= 165 in.²
Area of small rectangle = 4 in × 3 in
= 12 in.²
Area of shaded part area of large rectangle – area of small rectangle
= 165 – 12
=153 in.²
The area of the shaded part is 153 square inches.

Example

A rug is centered on a rectangular floor as shown in the diagram. Find the area of the rug.

Length of rug = 9 – 1 – 1
= 7 m
Width of rug = 6 – 1 – 1
= 4 m
Area of rug = 7 × 4
= 28 m²
The area of the rug is 28 square meters.

Solve. Show your work.

Question 4.
A rectangular pool is surrounded by a 2-yard-wide deck as shown in the diagram. Find the area of the deck.

Answer:
Total area = 22yd × 12yd
= 264 yd²
Area of the pool = 18yd × 8yd
= 144 yd²
Area of the deck = Total area – area of the pool
= 264 – 144
= 120 yd²
The area of the deck is 120 square yards.

Question 5.
A rectangular picture frame measures 25 centimeters by 1 5 centimeters. It has a wooden border 3 centimeters wide. To fit the picture frame, how large should a picture be?

Answer:
Length of picture  = 25 – 3 – 3
= 19 cm
Width of picture = 15 – 3 – 3
= 9 m
Area of picture = 19 × 9
= 171 cm²
The area of the picture is 171 square centimeters.

Solve. Show your work.

Question 6.
Renee has a piece of rectangular cardboard measuring 90 centimeters by 80 centimeters. She cuts out a small rectangular piece measuring 15 centimeters by 20 centimeters.

a. Find the area of the remaining piece of cardboard.
Answer:
Area of larger rectangular cardboard = 90 cm × 80 cm  = 7,200 cm²
Area of smaller rectangular cardboard = 20 cm × 15 cm  = 300 cm²
Area of the remaining piece of cardboard = Area of larger rectangular cardboard – area of smaller rectangular cardboard
= 7,200 – 300
= 6,900 cm²
Area of remaining piece of cardboard is 6,900 square centimeters.

b. Find the perimeter of the remaining piece of cardboard.
Answer:
Even if we remove a rectangular piece of cardboard at the edge of larger cardboard, the perimeter remains same.
Perimeter of larger rectangular cardboard = 90 cm + 80 cm + 90 cm+ 80 cm  = 340 cm
Perimeter of remaining piece of cardboard is 340 centimeters.

c. Compare the perimeter of the remaining piece of cardboard with that of the original piece of cardboard. Which one is greater?
Answer:
Perimeter of remaining piece of cardboard is 340 centimeters.
Perimeter of original piece of cardboard is 340 centimeters.
Perimeter of original piece of cardboard is equal to perimeter of remaining piece of cardboard.

Solve. Show your work.

Question 7.
Melanie makes a path 1 yard wide around her rectangular patch of land as shown in the diagram. Find the perimeter and area of the patch of land.

Answer:
Length of patch of land  = 20 – 1 – 1
= 18 yards
Width of patch of land = 12 – 1 – 1
= 10 yards
Area of patch of land = 18 × 10
= 180 yd²
The area of the patch of land is 180 square yards.
Perimeter of the patch of land = 18 + 10 + 18 + 10
= 56 yards

Question 8.
A rectangular piece of paper measuring 15 centimeters by 7 centimeters is folded along the dotted lines to form the figure shown.

Find the area of the figure formed.
Answer:
Area of the triangle = 1/2 × b × h
= 1/2 × 7 × 7
= 49/2 square centimeters
Area of the rectangle = length × width
= 7 cm × 1 cm
= 7 square centimeters
Area of the triangle = 1/2 × b × h
= 1/2 × 7 × 7
= 49/2 square centimeters
Area of the figure = Area of the triangle + Area of the rectangle + Area of the triangle
= 49/2 + 7 + 49/2
= 56 square centimeters
Area of the figure formed is 56 square centimeters

This handy Math in Focus Grade 4 Workbook Answer Key Chapter 12 Practice 3 Rectangles and Squares detailed solutions for the textbook questions.

Math in Focus Grade 4 Chapter 12 Practice 3 Answer Key Rectangles and Squares

Find the area of each figure.

Example

Area of the rectangle = 12 × 6
= 72 ft²
The area of the rectangle is 72 square feet.

Question 1.

Area of the square = _________ × __________
= __________ cm²
The area of the square is _____________ square centimeters.
Answer:
Area of the square = 9 cm × 9 cm
= 81 cm²
The area of the square is 81 square centimeters.

Solve. Show your work.

Example

The area of a rectangular hall is 78 square yards. Its width is 6 yards. Find the length.

Length × width = area
Length × 6 = 78 yd²
Length = 78 ÷ 6
= 13 yd
The length of the hall is 13 yards.

Question 2.
A rectangle has an area of 56 square centimeters. Its length is 8 centimeters. Find the width.

The width of the rectangle is ___________ centimeters.
Answer:
Length = 8 cm
width = ?
Area of the rectangle = 56 cm²
Area of the rectangle = length × width
56 cm² = 8 cm x width
56 cm²  ÷ 8 cm = width
7 cm = width 
The width of the rectangle is 7 centimeters.

Solve. Show your work.

Question 3.
The area of a rectangular carpet is 84 square meters. Its width is 7 meters.

a. Find the length.
Answer:
Length = ?
width = 7 m
Area of the rectangular carpet = 84 m²
Area of the rectangular carpet = length × width
84 m² = length x 7 m
84 m²  ÷ 7 m = length
12 m = length
The length of the rectangular carpet is 12 meters.

b. Find the perimeter of the carpet.
Answer:
Perimeter of the carpet = 7 m + 12 m + 7 m + 12 m
= 38 m
Perimeter of the carpet is 38 meters.

Question 4.
The area of a square is 64 square inches. Find the length of one side of the square.
(Hint: What number multiplied by itself is equal to 64?)

Answer:
Area = side × side = s²
Where $s$ is the length of the side of the square.
Area of a square is 64 square inches.
64 in²$\mathrm{=\; s2}$(8 in)$2$= $\mathrm{s2}$8 inches = s
The length of one side of the square is 8 inches.

Question 5.
The area of a square garden is 100 square meters.
a. Find the length of each side of the garden.

Answer:
A square is a regular polygon with four sides.
Area = width × height
But since the width and height are by definition the same, the formula is usually written as
Area = side × side = s²
where s is the length of one side.
To find the length of each side of the garden we know that the area is 100  applying the area formula and solving for s, the length of one side, we get that
100 m²= s²
(10 m)² = s²
10 m = s
The length of each side of the garden is 10 m.

b. Find the perimeter of the garden.
Answer:
In the case of a square, all four sides are the same length, so the perimeter is four times the length of a side.
We find that the length of each side is 10 m. Therefore, the perimeter is
Perimeter = 4 × s
= 4 x 10 m
= 40 m
where s is the length of any one side.
The perimeter of the garden is 40 m.

Solve. Show your work.

Question 6.
The area of a rectangular recreation area is 45 square miles. Its width is 5 miles.

a. Find the length.
Answer:
Length = ?
width = 5 mi
Area of the rectangular recreation = 45 mi²
Area of the rectangular recreation = length × width
45 mi² = length x 5 mi
45 mi²  ÷ 5 mi = length
9 mi = length
The length of the rectangular recreation is 9 miles.

b. Find the perimeter.
Answer:
Perimeter of the rectangular recreation = 9 mi + 5 mi + 9 mi + 5 mi
= 28 miles
Perimeter of the rectangular recreation is 28 miles.

Question 7.
The perimeter of a rectangular poster is 156 inches. Its width is 36 inches.

a. Find the length.
Answer:
Length = ?
width = 36 in
perimeter  of a rectangular poster = 156 in
Perimeter of the rectangular poster = length + width + length + width
156 in = l + 36 in + l + 36 in
156 in = 2l + 72 in
156 in – 72 in = 2l
84 in = 2l
42 in = l
The length of the rectangular poster is 42 inches.

b. Find the area.
Answer:
Length = 42 inches
width = 36 inches
Area of the rectangular poster = length x width
= 42 inches x 36 inches
= 1,512 in² 
Area of the rectangular poster is 1,512 square inches.