## Everyday Mathematics 4th Grade Answer Key Unit 3 Fractions and Decimals

### Everyday Math Grade 4 Home Link 3.1 Answer Key

**Sharing Equally**

Use drawings to help you solve the problems. Solve each problem in more than one way. Show your work.

Question 1.

Four friends shared 5 pizzas equally. How much pizza did each friend get?

____ pizzas

One way:

Another way:

Answer:

Explanation :

First Way :

Number of Pizzas = 5

Number of people = 4

Each Person take a pizza, number of pizzas taken = 4 pizzas

Number of pizzas left = 1

Fraction of pizza each person get = \(\frac{1}{4}\).

Fraction of pizza each person get = 1 + \(\frac{1}{4}\) = \(\frac{5}{4}\) .

Second Way :

Number of Pizzas = 5

Number of people = 4

Each pizza is divided into 4 parts .

Each person takes 1 pizza slice .

Fraction of each pizza slice = \(\frac{1}{4}\)

Total Fraction of 5 pizza slices = 5 × \(\frac{1}{4}\) = \(\frac{5}{4}\)

Therefore , Each person gets \(\frac{5}{4}\) fraction of pizza that means each person gets 1 slice from 5 pizzas .

it is represented in above figure with different colors .

Question 2.

Five kittens are sharing 6 cups of milk equally. How much milk does each kitten get?

____ cups of milk

One way:

Another way:

Answer:

One Way :

Number of Kittens = 5

Number of cups of milk = 6

Each kittens gets 1 cup that means 5 cups of milk is given to 5 kittens .

1 cup of milk is left which is shared by 5 kittens .

Fraction of milk given to each kitten in 1 cup = number of cups ÷ number of kittens = 1 ÷ 5 =

Total cups of milk given each kitten = 1 + \(\frac{1}{5}\) = \(\frac{5}{5}\) + \(\frac{1}{5}\) = \(\frac{6}{5}\) cups .

Another Way :

Number of Kittens = 5

Number of cups of milk = 6

Each cup of milk is divided into 5 parts .

Each kitten is given \(\frac{1}{5}\) cup of milk

As there are 6 cups Each kitten gets 6 × \(\frac{1}{5}\) cup of milk = \(\frac{6}{5}\) cups of milk .

Therefore each kitten gets \(\frac{6}{5}\) cups of milk .

**Practice**

Question 3.

Name the next 4 multiples of 7. 7, ___, ___, ___, ___

Answer:

The next 4 multiples of 7 are :

7, 14, 21, 28 .

Question 4.

List all the factors of 18. ____

Answer:

All factors of 18 are : 1, 2, 3, 6, 9 , 18 .

Question 5.

List all the factors of 18 that are prime.

Answer:

All factors of 18 are : 1, 2, 3, 6, 9 , 18 .

All factors of 18 that are prime : 1, 2, 3 .

Explanation :

A number that is divisible only by itself and 1 (e.g. 2, 3, 5, 7, 11).

Question 6.

List all the factor pairs of 40.

___ and ___; ___ and ; ___

___ and ___; ___ and ; ___

Answer:

The pair factorsof40are (1,40), (2, 20), (4, 10), and (5, 8).

### Everyday Math Grade 4 Home Link 3.2 Answer Key

**Fraction Circles**

Question 1.

Divide into 4 equal parts. Shade \(\frac{1}{4}\).

Answer:

Explanation :

Circle is divided into 4 parts . Each part is a fraction of \(\frac{1}{4}\) and and 1 part is shaded .

Question 2.

Divide into 8 equal parts. Shade \(\frac{2}{8}\).

Answer:

Explanation :

Circle is divided into 8 parts . Each part is a fraction of \(\frac{1}{8}\) and and 2 parts are shaded .

Question 3.

Divide into 12 equal parts. Shade \(\frac{3}{12}\).

Answer:

Explanation :

Circle is divided into 12 parts . Each part is a fraction of \(\frac{1}{12}\) and and 3 parts are shaded .

Question 4.

Create your own. Divide into equal parts and shade a portion. Record the amount you shaded.

Answer:

Explanation :

Circle is divided into 2 parts . Each part is a fraction of \(\frac{1}{2}\) and 1 part is shaded which is a fraction of \(\frac{1}{2}\) .

Question 5.

What patterns do you notice in Problems 1 through 3?

Answer:

The pattern we notice in problem 1 through 3 is equivalent fraction .

\(\frac{1}{4}\) = \(\frac{2}{8}\) = \(\frac{3}{12}\) .

**Practice**

Question 6.

List the next 4 multiples of 5. 20, __, ___, ___, ___

Answer:

4 multiples of 5 are from 20 , 25, 30, 35, 40 .

Question 7.

List all the factors of 48. __________

Answer:

All Factors of 48 are : 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Question 8.

List the factors of 48 that are composite. __________

Answer:

All Factors of 48 are : 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

composite numbers are : 4, 6, 8, 12, 16, 24 and 48.

Explanation :

Acomposite number is a natural number or a positive integer which has more than two factors. For example, 15 has factors 1, 3, 5 .

### Everyday Math Grade 4 Home Link 3.3 Answer Key

**Finding Equivalent Fractions**

Use the number lines to help you answer the following questions

1 . Fill in the blank with = or ≠ .

a. \(\frac{2}{3}\) __ \(\frac{1}{3}\)

Answer:

\(\frac{2}{3}\) > \(\frac{1}{3}\)

Explanation :

1. A fractionis larger if it’s farther from 0 on thenumber line.

2. A fraction is smaller if it’s closer to 0 on the number line.

\(\frac{2}{3}\) is farther from 0 so, it is greater number .

Therefore, \(\frac{2}{3}\) > \(\frac{1}{3}\) .

b. \(\frac{2}{6}\) ____ \(\frac{1}{3}\)

Answer:

\(\frac{2}{6}\) = \(\frac{1}{3}\)

Explanation :

\(\frac{2}{6}\) = \(\frac{1}{3}\) as both locate at the same point as shown in above figure .

c. \(\frac{2}{6}\) __ \(\frac{2}{5}\)

Answer:

\(\frac{2}{5}\) > \(\frac{2}{6}\)

Explanation :

1. A fractionis larger if it’s farther from 0 on thenumber line.

2. A fraction is smaller if it’s closer to 0 on the number line.

\(\frac{2}{5}\) is farther from 0 than \(\frac{2}{6}\) so, it is a greater number

Therefore, \(\frac{2}{5}\) > \(\frac{2}{6}\) .

d. \(\frac{1}{5}\) ___ \(\frac{2}{10}\)

Answer:

Explanation :

\(\frac{2}{6}\) = \(\frac{1}{3}\) as both locate at the same point as shown in above figure .

Question 2.

Fill in the missing numbers.

a.

Answer:

\(\frac{1}{5}\) = \(\frac{2}{10}\)

Explanation :

The fraction \(\frac{1}{5}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 1 by 2, the result is 2. When you multiply the denominator 5 by 2, the result is 10.

\(\frac{1 \times 2}{5 \times 2}\) = \(\frac{2}{10}\)

This results in the number sentence \(\frac{1}{5}\) = \(\frac{2}{10}\).

b.

Answer:

\(\frac{4}{12}\) = \(\frac{1}{3}\)

Explanation :

The fraction \(\frac{4}{12}\) can be renamed as an infinite number of equivalent fractions.

When you divide the numerator 4 by 4, the result is 1. When you divide the denominator 12 by 4, the result is 3.

\(\frac{4 ÷ 4 }{12 ÷ 4 }\)= \(\frac{1}{3}\)

This results in the number sentence \(\frac{4}{12}\) = \(\frac{1}{3}\).

c.

Answer:

\(\frac{5}{10}\) = \(\frac{1}{2}\)

Explanation :

The fraction \(\frac{5}{10}\) can be renamed as an infinite number of equivalent fractions.

When you divide the numerator 5 by 5, the result is 1. When you divide the denominator 10 by 5, the result is 2.

\(\frac{5 ÷ 5 }{10 ÷ 5 }\)= \(\frac{1}{2}\)

This results in the number sentence \(\frac{5}{10}\) = \(\frac{1}{2}\).

d.

Answer:

\(\frac{3}{6}\) = \(\frac{6}{12}\)

Explanation :

The fraction \(\frac{3}{6}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 3 by 2, the result is 6. When you multiply the denominator 6 by 2, the result is 12.

\(\frac{3 \times 2}{6 \times 2}\) = \(\frac{6}{12}\)

This results in the number sentence \(\frac{3}{6}\) = \(\frac{6}{12}\).

e.

Answer:

\(\frac{4}{6}\) = \(\frac{2}{3}\)

Explanation :

The fraction \(\frac{4}{6}\) can be renamed as an infinite number of equivalent fractions.

When you divide the numerator 4 by 2, the result is 2. When you divide the denominator 6 by 2, the result is 3.

\(\frac{4 ÷ 2 }{6 ÷ 2 }\)= \(\frac{2}{3}\)

This results in the number sentence \(\frac{4}{6}\) = \(\frac{2}{3}\).

Question 3.

Circle the number sentences that are NOT true.

a. \(\frac{3}{12}\) = \(\frac{1}{4}\)

Answer:

Yes, it is true

\(\frac{3}{12}\) = \(\frac{1}{4}\)

Explanation :

The fraction \(\frac{3}{12}\) can be renamed as an infinite number of equivalent fractions.

When you divide the numerator 3 by 3, the result is 1. When you divide the denominator 12 by 3, the result is 4.

\(\frac{3 ÷ 3 }{12 ÷ 3 }\)= \(\frac{1}{4}\)

This results in the number sentence \(\frac{3}{12}\) = \(\frac{1}{4}\).

b. \(\frac{1}{2}\) = \(\frac{5}{10}\)

Answer:

Yes, it is true

\(\frac{1}{2}\) = \(\frac{5}{10}\)

Explanation :

The fraction \(\frac{1}{2}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 1 by 5, the result is 5. When you multiply the denominator 2 by 5, the result is 10.

\(\frac{1 \times 5}{2 \times 5}\) = \(\frac{5}{10}\)

This results in the number sentence \(\frac{1}{2}\) = \(\frac{5}{10}\).

c. \(\frac{2}{6}\) = \(\frac{2}{5}\)

Answer:

No it is not true \(\frac{2}{6}\) can’t be equal to \(\frac{2}{5}\)

d. \(\frac{7}{10}\) = \(\frac{4}{6}\)

Answer:

No it is not true \(\frac{7}{10}\) can’t be equal to \(\frac{4}{6}\)

e. \(\frac{9}{10}\) = \(\frac{11}{12}\)

Answer:

No it is not true \(\frac{9}{10}\) can’t be equal to \(\frac{11}{12}\)

**Practice**

Solve using U.S. traditional addition or subtraction.

Question 4.

____ = 989 + 657

Answer:

1646 = 989 + 657

Explanation :

Step 1

Add the 1s: 9 + 7 = 16.

16 ones = 1 ten and 6 ones

Write 1 in the 6s place below the line.

Write 1 above the digits in the 10s place.

Step 2

Add the 10s: 8 + 5 + 1 = 14

14 tens = 1 hundred + 4 tens

Write 4 in the 10s place below the line.

Write 1 above the digits in the 100s place.

Step 3

Add the 100s: 9 + 6 + 1 = 16

16 hundreds = 1 thousand + 6 hundred

Write 6 in the 100s place below the line.

Write 1 above the digits in the 1000s place.

No values to add in the thousand’s place so write 1 below the line in 1000s place .

Question 5.

3,314 + 4,719 = ____

Answer:

3,314 + 4,719 = 8033

Explanation :

Step 1

Add the 1s: 4 + 9 = 13.

13 ones = 1 ten and 3 ones

Write 3 in the 1s place below the line.

Write 1 above the digits in the 10s place.

Step 2

Add the 10s: 1 + 1 + 1 = 3

Write 3 in the 10s place below the line.

Step 3

Add the 100s: 3 + 7 = 10

10 hundreds = 1 thousand + 0 hundred

Write 0 in the 100s place below the line.

Write 1 above the digits in the 1000s place.

Step 4

Add the 1000s: 3 + 4 + 1 = 8

Write 8 in the 1000s place below the line.

Question 6.

5,887 – 3,598 = ___

Answer:

5,887 – 3,598 = 2289

Question 7.

____ = 2,004 – 1,716

Answer:

288= 2,004 – 1,716

### Everyday Math Grade 4 Home Link 3.4 Answer Key

**Finding Equivalent Fractions**

Family Note Today students learned about an Equivalent Fractions Rule, which can be used to rename any fraction as an equivalent fraction. The rule for multiplication states that if the numerator and denominator are multiplied by the same nonzero number, the result is a fraction that is equivalent to the original fraction.

For example, the fraction \(\frac{1}{2}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 1 by 5, the result is 5. When you multiply the denominator 2 by 5, the result is 10.

\(\frac{1 \times 5}{2 \times 5}\) = \(\frac{5}{10}\)

This results in the number sentence \(\frac{1}{2}\) = \(\frac{5}{10}\). If you multiplied both the numerator and denominator in \(\frac{1}{2}\) by 3, the result would be \(\frac{3}{6}\), which is also equal to \(\frac{1}{2}\).

Fill in the boxes to complete the equivalent fractions.

Example:

Question 1.

Answer:

\(\frac{1}{2}\) = \(\frac{6}{12}\)

Explanation :

The fraction \(\frac{1}{2}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 1 by 6, the result is 6. When you multiply the denominator 2 by 6, the result is 12.

\(\frac{1 \times 6}{2 \times 6}\) = \(\frac{6}{12}\)

This results in the number sentence \(\frac{1}{2}\) = \(\frac{6}{12}\).

Question 2.

Answer:

\(\frac{1}{4}\) = \(\frac{3}{12}\)

Explanation :

The fraction \(\frac{1}{4}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 1 by 3, the result is 3. When you multiply the denominator 4 by 3, the result is 12.

\(\frac{1 \times 3}{4 \times 3}\) = \(\frac{3}{12}\)

This results in the number sentence \(\frac{1}{4}\) = \(\frac{3}{12}\).

Question 3.

Answer:

\(\frac{1}{3}\) = \(\frac{2}{6}\)

Explanation :

The fraction \(\frac{1}{3}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 1 by 2, the result is 2. When you multiply the denominator 3 by 2, the result is 6.

\(\frac{1 \times 2}{3 \times 2}\) = \(\frac{2}{6}\)

This results in the number sentence \(\frac{1}{3}\) = \(\frac{2}{6}\).

Question 4.

Answer:

\(\frac{2}{3}\) = \(\frac{8}{12}\)

Explanation :

The fraction \(\frac{2}{3}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 2 by 4, the result is 8. When you multiply the denominator 3 by 4, the result is 12.

\(\frac{2 \times 4}{3 \times 4}\) = \(\frac{8}{12}\)

This results in the number sentence \(\frac{2}{3}\) = \(\frac{8}{12}\).

Question 5.

Answer:

\(\frac{1}{5}\) = \(\frac{2}{10}\)

Explanation :

The fraction \(\frac{1}{5}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 1 by 2, the result is 2. When you multiply the denominator 5 by 2, the result is 10.

\(\frac{1 \times 2}{5 \times 2}\) = \(\frac{2}{10}\)

This results in the number sentence \(\frac{1}{5}\) = \(\frac{2}{10}\).

Question 6.

Answer:

\(\frac{2}{5}\) = \(\frac{4}{10}\)

Explanation :

The fraction \(\frac{2}{5}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 2 by 2, the result is 4. When you multiply the denominator 5 by 2, the result is 10.

\(\frac{2 \times 2}{5 \times 2}\) = \(\frac{4}{10}\)

This results in the number sentence \(\frac{2}{5}\) = \(\frac{4}{10}\).

Question 7.

Answer:

\(\frac{3}{4}\) = \(\frac{9}{12}\)

Explanation :

The fraction \(\frac{3}{4}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 3 by 3, the result is 9. When you multiply the denominator 4 by 3, the result is 12.

\(\frac{3 \times 3}{4 \times 3}\) = \(\frac{9}{12}\)

This results in the number sentence \(\frac{3}{4}\) = \(\frac{9}{12}\).

Question 8.

Answer:

\(\frac{5}{6}\) = \(\frac{10}{12}\)

Explanation :

The fraction \(\frac{5}{6}\) can be renamed as an infinite number of equivalent fractions.

When you multiply the numerator 5 by 2, the result is 10. When you multiply the denominator 6 by 2, the result is 12.

\(\frac{5 \times 2}{6 \times 2}\) = \(\frac{10}{12}\)

This results in the number sentence \(\frac{5}{6}\) = \(\frac{10}{12}\).

Question 9.

Answer:

\(\frac{6}{9}\) = \(\frac{2}{3}\)

Explanation :

The fraction \(\frac{6}{9}\) can be renamed as an infinite number of equivalent fractions.

When you divide the numerator 6 by 3, the result is 2. When you divide the denominator 9 by 3, the result is 3.

\(\frac{6 ÷ 3 }{9 ÷ 3 }\)= \(\frac{2}{3}\)

This results in the number sentence \(\frac{2}{3}\) = \(\frac{6}{9}\).

Question 10.

Answer:

\(\frac{4}{6}\) = \(\frac{8}{12}\)

Explanation :

The fraction \(\frac{8}{12}\) can be renamed as an infinite number of equivalent fractions.

When you divide the numerator 8 by 2, the result is 4. When you divide the denominator 12 by 2, the result is 6.

\(\frac{8 ÷ 2 }{12 ÷ 2 }\)= \(\frac{4}{6}\)

This results in the number sentence \(\frac{4}{6}\) = \(\frac{8}{12}\).

Question 11.

Name 3 equivalent fractions for \(\frac{1}{2}\). ___

Answer:

The fraction \(\frac{8}{12}\) can be renamed as an infinite number of equivalent fractions.

The 3 equivalent fractions for \(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{3}{6}\) = \(\frac{4}{8}\) .

**Practice**

Question 12.

List all the factors of 56.

Answer:

Factors of 56: 1, 2, 4, 7, 8, 14, 28 and56

Question 13.

Write the factor pairs for 30.

___ and ___, ____ and ___, ___ and, ___.

___ and ____

Answer:

The factor pairs for 30 are 2 and 15, 3 and 10, 5 and 6 , 1 and 30 .

Question 14.

Is 30 prime or composite? ____

Answer:

30 is a Composite .

Explanation :

Acompositenumber is a number that can be divided evenly by more numbers than 1 and itself. It is the opposite of aprimenumber. The number30can be evenly divided by 1 2 3 5 6 10 15 and30, with no remainder. Since30cannot be divided by just 1 and30, it is acompositenumber.

### Everyday Math Grade 4 Home Link 3.5 Answer Key

**Sharing Veggie Pizza**

Question 1.

Karen and her 3 friends want to share 3 small veggie pizzas equally. Karen tried to figure out how much pizza each of the 4 children would get. She drew this picture and wrote two answers.

a. Which of Karen’s answers is correct? ___

b. Draw on Karen’s diagram to make it clear how the pizza should be distributed among the 4 children.

Answer:

a. \(\frac{3}{4}\) is the correct answer .

b.

Number of children = 4

Number of pizzas = 3

Each Pizza is divided into 4 parts. Each children get \(\frac{1}{4}\) part of pizza .

Fraction of pizza received by each children from 3 pizzas= 3 × \(\frac{1}{4}\) part of pizza . = \(\frac{3}{4}\)

Each children get respective number written on pizzas as shown in below diagram .

Question 2.

Erin and her 7 friends want to share 6 small veggie pizzas equally. How much pizza will each of the 8 children get ? ___

Answer:

Erin and here7 friends are sharing pizza

⇒8 people are sharing pizza.

6pizzas divided among8 people:

Fraction of pizza each children get = \(\frac{6 pizzas }{8 people}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\) .

That means 4 children share 3 pizzas .

Each Pizza is divided into 4 parts. Each children get \(\frac{1}{4}\) part of pizza .

Fraction of pizza received by each children from 3 pizzas= 3 × \(\frac{1}{4}\) part of pizza . = \(\frac{3}{4}\)

Each children get respective number written on pizzas as shown in below diagram .

Question 3.

Who will get more pizza, Karen or Erin? ____ Explain or show how you know.

Answer :

Both Karen and Erin gets same amount of Pizza that is \(\frac{3}{4}\) of the pizza .

**Practice**

Question 4.

List all the factors of 50. __________

Answer:

Factors of 50 : 1, 2, 5, 10 and 50 .

Question 5.

Is 50 prime or composite? __________

Answer:

50 is a composite number .

Explanation :

Acomposite numberis anumberthat can be divided evenly by morenumbersthan 1 and itself. … Thenumber 50can be evenly divided by 1, 2, 5, 10, 25 and50, with no remainder. Since50cannot be divided by just 1 and50, it is acomposite number

Question 6.

Write the factor pairs for 75.

___ and ___

___ and ___

___ and ___

Answer :

The factor pairs for 75 are

3 and 25.

5 and 15.

1 and 75 .

### Everyday Math Grade 4 Home Link 3.6 Answer Key

**Solving Fraction Comparison Number Stories**

Solve the problems below.

Question 1.

Tenisha and Christa were each reading the same book. Tenisha said she was \(\frac{3}{4}\) of the way done with it, and Christa said she was \(\frac{6}{8}\) of the way finished. Who has read more, or have they read the same amount? Ho w do you know?

Answer:

Fraction of book read by Tenisha = \(\frac{3}{4}\)

Fraction of book read by christa = \(\frac{6}{8}\) = \(\frac{3}{4}\) .

\(\frac{3}{4}\) = \(\frac{6}{8}\)

Explanation :

The fraction \(\frac{6}{9}\) can be renamed as an infinite number of equivalent fractions.

When you divide the numerator 6 by 2, the result is 3. When you divide the denominator 8 by 2, the result is 4.

\(\frac{6 ÷ 2 }{8 ÷ 2 }\)= \(\frac{3}{4}\)

This results in the number sentence \(\frac{3}{4}\) = \(\frac{6}{8}\).

Question 2.

Heather and Jerry each bought an ice cream bar. Although the bars were the same size, they were different flavors. Heather ate \(\frac{5}{8}\) of her ice cream bar, and Jerry ate \(\frac{5}{10}\) of his.

Who ate more, or did they eat the same amount? ___

Write a number sentence to show this. ___

Answer :

Explanation :

Fraction of ice cream ate by Heather = \(\frac{5}{8}\)

Fraction of ice cream ate by Jerry = \(\frac{5}{10}\)

Both the ice creams bar are represented in the above figure .

from the above figure we notice that \(\frac{5}{8}\) > \(\frac{5}{10}\) that means Jerry ate more ice cream bar than Heather .

Question 3.

Howard’s baseball team won \(\frac{7}{10}\) of its games. Jermaine’s team won \(\frac{2}{5}\) of its games. They both played the same number of games.

Whose team won more games, or did they win the same amount? ___

How do you know? __________

Answer:

Fraction of games won by Howard’s = \(\frac{7}{10}\)

Fraction of games won by Jermaine’s = \(\frac{2}{5}\)

\(\frac{7}{10}\) >\(\frac{2}{5}\) that means Howard won more games than Jermaine as it shown in the above figure .

Question 4.

Write your own fraction number story. Ask someone at home to solve it.

Answer:

Cristine had 4/5 m of cloth. She used 3/4 of it to make handkerchiefs. How much cloth had she left?

Explanation :

Fraction of total cloth with Cristine = \(\frac{4}{5}\)m

Fraction of cloth used = \(\frac{3}{4}\) m

Fraction of cloth left = \(\frac{4}{5}\) – \(\frac{3}{4}\) m =\(\frac{16}{20}\) – \(\frac{15}{20}\) = \(\frac{1}{20}\) m .

Therefore, Fraction of cloth left = \(\frac{1}{20}\) m .

**Practice**

Write T for true or F for false.

Question 5.

1,286 + 2,286 = 3,752 ___

Answer:

1,286 + 2,286 = 3,752 is not true as

Explanation :

1,286 + 2,286 = 3,572

Question 6.

9,907 – 9,709 = 200 ___

Answer:

9,907 – 9,709 = 200 is not true as 9,907 – 9,709 = 198 .

Explanation :

Question 7.

2,641 + 4,359 = 2,359 + 4,641 ___

Answer:

2,641 + 4,359 = 2,359 + 4,641 yes, it is true .

Explanation :

Question 8.

2,345 – 198 = 2,969 – 822 ____

Answer:

2,345 – 198 = 2,969 – 822 Yes, it is true .

Explanation :

### Everyday Math Grade 4 Home Link 3.7 Answer Key

**Comparing and Ordering Fractions**

Write the fractions from smallest to largest, and then justify your conclusions by placing the numbers in the correct places on the number lines.

Question 1.

Answer:

Explanation :

1. A fractionis larger if it’s farther from 0 on thenumber line.

2. A fraction is smaller if it’s closer to 0 on the number line.

\(\frac{5}{6}\) is farther from 0 so, it is greater number .

\(\frac{2}{6}\) is closer to 0 so, it is smaller number .

Therefore, \(\frac{2}{6}\) < \(\frac{4}{6}\) < \(\frac{5}{6}\) .

Question 2.

Answer:

Explanation :

1. A fractionis larger if it’s farther from 0 on thenumber line.

2. A fraction is smaller if it’s closer to 0 on the number line.

\(\frac{9}{10}\) is farther from 0 so, it is greater number .

\(\frac{1}{4}\) is closer to 0 so, it is smaller number .

Therefore, \(\frac{1}{4}\) < \(\frac{5}{12}\) < \(\frac{3}{5}\) < \(\frac{9}{10}\) .

Question 3.

Answer:

Explanation :

1. A fractionis larger if it’s farther from 0 on thenumber line.

2. A fraction is smaller if it’s closer to 0 on the number line.

\(\frac{2}{3}\) is farther from 0 so, it is greater number .

\(\frac{1}{6}\) is closer to 0 so, it is smaller number .

Therefore, \(\frac{1}{6}\) < \(\frac{4}{10}\) < \(\frac{1}{2}\) < \(\frac{7}{12}\) < \(\frac{2}{3}\) .

**Practice**

Question 4.

___ = 5,494 + 3,769

Answer:

9263 = 5,494 + 3,769

Explanation :

Question 5.

5,853 + 4,268 = ___

Answer:

5,853 + 4,268 = 10,121

Explanation :

Question 6.

__ = 8,210 – 6,654

Answer:

1556 = 8,210 – 6,654

Explanation :

Question 7.

7,235 – 5,906 = ___

Answer:

7,235 – 5,906 = 1329

Explanation :

### Everyday Math Grade 4 Home Link 3.8 Answer Key

**Names for Fractions and Decimals**

Question 1.

Fill in the blanks in the table below.

Answer:

Question 2.

Name two ways you might see decimals used outside of school.

Answer:

The Two ways we see decimals used outside of school are Money and to represent Weight .

Question 3.

What decimal is represented by the tick mark labeled M?

Answer:

The M and P are marked as per given table which in the fractions of 10 .

The fraction of tick Mark labeled M = \(\frac{5}{10}\) = 0.5

Question 4.

What fraction is represented by the tick mark labeled M?

Answer:

The fraction of tick Mark labeled M = \(\frac{5}{10}\)

Question 5.

What decimal is represented by the tick mark labeled P?

Answer:

The M and P are marked as per given table which in the fractions of 10 .

The fraction of tick Mark labeled P = \(\frac{9}{10}\) = 0.9

Question 6.

What fraction is represented by the tick mark labeled P?

Answer:

The fraction of tick Mark labeled P = \(\frac{9}{10}\)

**Practice**

Question 7.

List all the factors of 100.

Answer:

The Factors of 100 : 1, 2, 4, 5, 10, 20, 25, 50, and100

Question 8.

List the factors of 100 that are prime.

Answer:

The Factors of 100 : 1, 2, 4, 5, 10, 20, 25, 50, and100

where 2 and 5 are theprimenumbers.

Explanation :

Prime numbersare specialnumbers, greater than 1, that have exactly twofactors, themselves and 1.

Question 9.

Write the factor pairs for 42.

___ and ___ ___and ___

___ and ___ ___and ___

Answer :

The factor pairs for 42 are

2 and 21.

3 and 14 .

6 and 7 .

### Everyday Math Grade 4 Home Link 3.9 Answer Key

**Representing Fractions and Decimals**

If the grid is the whole, then what part of each grid is shaded?

Write a fraction and a decimal below each grid.

Question 1.

fraction: __________

decimal: __________

Answer:

Total Number of boxes = 100

Number of boxes shaded = 30 .

Fraction = Number of boxes shaded by Total Number of boxes in a grid .

fraction: \(\frac{30}{100}\)

decimal: 0.30

Explanation :

Division by 10,100,1000, etc. Shift thedecimal point to the left by as many digits as there are zeroes in the divisor.

Question 2.

fraction: __________

decimal: __________

Answer:

Total Number of boxes = 100

Number of boxes shaded = 9 .

Fraction = Number of boxes shaded by Total Number of boxes in a grid .

fraction: \(\frac{9}{100}\)

decimal: 0.09

Explanation :

Division by 10,100,1000, etc. Shift thedecimal point to the left by as many digits as there are zeroes in the divisor.

Question 3.

fraction: __________

decimal: __________

Answer:

Total Number of boxes = 100

Number of boxes shaded = 65 .

Fraction = Number of boxes shaded by Total Number of boxes in a grid .

fraction: \(\frac{65}{100}\)

decimal: 0.65

Explanation :

Division by 10,100,1000, etc. Shift thedecimal point to the left by as many digits as there are zeroes in the divisor.

Question 4.

Color 0.8 of the grid.

Answer:

Explanation :

decimal: 0.8

Multiplying by 100 to numerator and denominator we get fraction as \(\frac{80}{100}\)

Total Number of boxes = 100

Number of boxes shaded = 80 .

Fraction = Number of boxes shaded by Total Number of boxes in a grid .

fraction: \(\frac{80}{100}\)

Question 5.

Color 0.04 of the grid.

Answer:

Explanation :

0.04

Multiplying by 100 to numerator and denominator we get fraction as \(\frac{80}{100}\)

Total Number of boxes = 100

Number of boxes shaded = 4 .

Fraction = Number of boxes shaded by Total Number of boxes in a grid .

fraction: \(\frac{4}{100}\)

Question 6.

Color 0.53 of the grid.

Answer:

Explanation :

decimal: 0.53

Multiplying by 100 to numerator and denominator we get fraction as \(\frac{80}{100}\)

Total Number of boxes = 100

Number of boxes shaded = 53 .

Fraction = Number of boxes shaded by Total Number of boxes in a grid .

fraction: \(\frac{53}{100}\)

**Practice**

Question 7.

The numbers 81, 27, and 45 are all multiples of 1, ___, and ___.

Answer:

The numbers 81, 27, and 45 are all multiples of 1, 3, and 9 .

Question 8.

List the first ten multiples of 6.

___, ___, ___, ___, ___, ___, ___, ___, ___, ___.

Answer :

The first ten multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 , 66 .

### Everyday Math Grade 4 Home Link 3.10 Answer Key

**Tenths and Hundredths**

Family Note Your child continues to work with decimals. Encourage him or her to think about ways to write money amounts. This is called dollars-and-cents notation. For example, $0.07 (7 cents), $0.09 (9 cents), and so on.

Write the decimal numbers that represent the shaded part in each diagram .

Question 1.

__ hundredths

__ tenths __ hundredths

Answer:

Total Number of boxes = 100

Number of boxes shaded = 57 .

Fraction = Number of boxes shaded by Total Number of boxes in a grid .

fraction: \(\frac{57}{100}\)

decimal = 0.53 .

5 tenths 7 hundredths.

57 hundredths

Explanation :

To the right of thedecimalpoint are thetenths and hundredths, where you put digits that represent numbers that are fractional parts of one, numbers that are more than zero and less than one

Question 2.

__ hundredths

__ tenths __ hundredths

Answer:

Total Number of boxes = 100

Number of boxes shaded = 70 .

Fraction = Number of boxes shaded by Total Number of boxes in a grid .

fraction: \(\frac{70}{100}\)

decimal = 0.70 .

7 tenths 0 hundredths.

0 hundredths

Explanation :

To the right of thedecimalpoint are thetenths and hundredths, where you put digits that represent numbers that are fractional parts of one, numbers that are more than zero and less than one

Question 3.

__ hundredths

__ tenths __ hundredths

Answer:

Total Number of boxes = 100

Number of boxes shaded = 4 .

Fraction = Number of boxes shaded by Total Number of boxes in a grid .

fraction: \(\frac{4}{100}\)

decimal = 0.04 .

0 tenths 4 hundredths.

4 hundredths .

Explanation :

To the right of thedecimalpoint are thetenths and hundredths, where you put digits that represent numbers that are fractional parts of one, numbers that are more than zero and less than one

Write the words as decimal numbers.

Question 4.

twenty-three hundredths ___

Answer:

twenty-three hundredths = 0.23

Explanation :

23 hundredths wouldbewrittenas .23as a decimal.23 hundredthsis the same as the fraction23/100, or23out of 100 parts.

Question 5.

eight and four-tenths

______

Answer:

eight and four-tenths = 8.4

Question 6.

thirty and twenty-hundredths

____

Answer:

thirty and twenty-hundredths = 30.20

Question 7.

five-hundredths

______

Answer :

five-hundredths = 0.05

Continue each pattern.

Question 8.

0.1, 0.2, 0.3, ____, ___, ___, ___, ____, ___

Answer:

0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9

Question 9.

0.01, 0.02, 0.03, ____, ___, ___, ___, ____, ___

Answer:

0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09

**Practice**

Question 10.

Round 7,604 to the nearest thousand. ______

Answer:

7,604 to the nearest thousand is 8000 .

Question 11.

Round 46,099 to the nearest thousand. ____

Answer:

46,099 to the nearest thousand is 46,000

Question 12.

Round 8,500,976 three ways: nearest thousand, hundred-thousand, and million.

_____ ____ ____

Answer:

8,500,976 three ways: nearest

thousand = 8,501,000

hundred-thousand = 8,500,000

million = 9,000,000

### Everyday Math Grade 4 Home Link 3.11 Answer Key

**Practice with Decimals**

Fill in the missing numbers.

Question 1.

Answer:

Question 2.

Answer:

Follow these directions on the ruler below.

Question 3.

Make a dot at 7 cm and label it with the letter A.

Answer:

Question 4.

Make a dot at 90 mm and label it with the letter B.

Answer:

Explanation :

1cm = 10mm

9 cm = 90 mm

Question 5.

Make a dot at 0.13 m and label it with the letter C.

Answer:

Explanation :

1m = 100 cm

0.13 m = 13 cm

Question 6.

Make a dot at 0.06 m and label it with the letter D.

Answer:

Explanation :

1m = 100 cm

0.06 m = 6 cm

Question 7.

Write <, >, or =.

a. 1.2 ___ 0.12

Answer:

1.2 > 0.12

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

b. 0.3 __ 0.38

Answer:

0.3 < 0.38

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

c. 0.80 __ 0.08

Answer:

0.80 > 0.08

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Question 8.

Complete.

Answer :

**Practice**

Question 9.

6,366 + 7,565 = ____

Answer:

6,366 + 7,565 = 13,931

Question 10.

3,238 + 29,784 = ___

Answer:

3,238 + 29,784 = 33022

Question 11.

9,325 – 7,756 = ___

Answer:

9,325 – 7,756 = 1569

Explanation :

Question 12.

14,805 – 2,927 = ___

Answer:

14,805 – 2,927 = 11878

### Everyday Math Grade 4 Home Link 3.12 Answer Key

**Measuring Centimeters and Millimeters **

Question 1.

Find 6 objects in your home to measure. Use the ruler from the bottom of the page to measure them, first in centimeters and then in millimeters. Record your objects and their measurements.

Answer :

Fill in the tables.

Question 2.

Answer:

Explanation :

1 cm is 10 mm

multiply the given cm value with 10 to get the value in mm .

Respective given values are converted into mm and written in the above tabular column .

Question 3.

Answer:

Explanation :

1 cm is 10 mm

multiply the given cm value with 10 to get the value in mm .

divide the given mm value with 10 to get the value in cm .

Respective given values are converted into mm and cm , written in the above tabular column .

**Practice**

Question 4.

List the factors for 63. ________

Answer:

The factorsof63are 1, 3, 7, 9, 21 and63

Question 5.

Write the factor pairs for 60.

Answer:

The factor pairs for 60 are

1 and 60

2 and 30

3 and 20

4 and 15

5 and 12

6 and 10

### Everyday Math Grade 4 Home Link 3.13 Answer Key

**Comparing Decimals**

Family Note Ask your child to read the decimal numerals aloud. Encourage your child to use the following method:

- Read the whole-number part.
- Say and for the decimal point.
- Read the digits after the decimal point as though they form their own number.
- Say tenths or hundredths, depending on the placement of the right-hand digit. Encourage your child to exaggerate the -ths sound. For example, 2.37 is read as “two and thirty-seven hundredths.”

Write >, <, or =.

Question 1.

2.35 ___ 2.57

Answer:

2.35 < 2.57

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Question 2.

1.08 __ 1.8

Answer:

1.08 < 1.8

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Question 3.

0.64 __ 0.46

Answer:

0.64 > 0.46

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Question 4.

0.90 ___ 0.9

Answer:

0.90 = 0.9

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Question 5.

42.1 ___ 42.09

Answer:

42.1 > 42.09

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Question 6.

7.09 __ 7.54

Answer:

7.09 < 7.54

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Question 7.

0.4 __ 0.40

Answer:

0.4 = 0.40

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Question 8.

0.26 __ 0.21

Answer:

0.26 > 0.21

Explanation :

when decimals are compared start with tenths place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.

Question 9.

The 9 in 4.59 stands for 9 ___ or ____.

Answer:

The 9 in 4.59 stands for 9 Hundredths or 0.09 .

Question 10.

The 3 in 3.62 stands for 3 ___ or ___.

Answer :

The 3 in 3.62 stands for 3 Ones or 3 .

Continue each number pattern.

Question 11.

6.56, 6.57, 6.58, ___, ___, ___

Answer:

6.56, 6.57, 6.58, 6.59, 6.60, 6.61

Explanation :

0.01 more

Question 12.

0.73, 0.83, 0.93, __, ___, ___

Answer :

0.73, 0.83, 0.93, 1.03, 1.13, 1.23

Explanation :

0.10 more

Write the number that is 0.1 more.

Question 13.

4.3 ___

Answer:

4.3 + 0.1 = 4.4

Question 14.

4.07 ___

Answer:

4.07 + 0.1 = 4.17

Write the number that is 0.1 less.

Question 15.

8.2 ___

Answer:

8.2 – 0.1 = 8.1

Question 16.

5.63 ___

Answer :

5.63 – 0.1 =5.53

**Practice**

Question 17.

43,589 + 12,641 = ____

Answer:

43,589 + 12,641 = 56230

Explanation :

Question 18.

63,274 + 97,047 = ____

Answer:

63,274 + 97,047 = 1,60,321

Explanation :

Question 19.

41,805 – 26,426 = ____

Answer:

41,805 – 26,426 = 15379

Explanation :

Question 20.

82,004 – 11,534 = ___

Answer:

82,004 – 11,534 = 70,470

Explanation :