## Everyday Mathematics 5th Grade Answer Key Unit 5 Operations with Fractions

### Everyday Mathematics Grade 5 Home Link 5.1 Answers

**Using Equivalent Fractions to Solve Problems**

Question 1.

Fill in the equivalent fractions in the table below.

Answer:

Estimation:

Filled in the equivalent fractions in the table above as

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

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

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

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

\(\frac{2}{3}\) X 6 = \(\frac{12}{18}\),

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

\(\frac{3}{4}\) X 5 = \(\frac{15}{20}\).

Estimate. Then solve by finding fractions with a common denominator. Write a number sentence to show which fractions you used.

Example: \(\frac{1}{3}\) + \(\frac{7}{12}\) = ?

Estimate: close to 1, because \(\frac{1}{3}\) is less than \(\frac{1}{2}\), and \(\frac{7}{12}\) is a little more than \(\frac{1}{2}\).

Common denominator: 12

Number sentence: \(\frac{4}{12}\) + \(\frac{7}{12}\) = ?

Answer:

\(\frac{11}{12}\),

Explanation:

Given to find \(\frac{1}{3}\) + \(\frac{7}{12}\) = ,

As both denominators are different first we need to

make common denominators means we need to multiply

numerator and denominator by 4 as

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

\(\frac{4}{12}\) now we add as

\(\frac{4}{12}\) + \(\frac{7}{12}\) as

denominators are common as 12 we add numerators as

\(\frac{4 + 7}{12}\) = \(\frac{11}{12}\),

therefore common denominator is 12 and

Number sentence: \(\frac{4}{12}\) + \(\frac{7}{12}\) =

\(\frac{11}{12}\).

Question 2.

\(\frac{6}{8}\) – \(\frac{1}{2}\) = ?

Common denominator: _____8_____

Number sentence: _____\(\frac{6}{8}\) – \(\frac{1}{2}\) = \(\frac{2}{8}\),

Answer:

Common denominator: 8,

Number sentence: \(\frac{6}{8}\) – \(\frac{1}{2}\) = \(\frac{2}{8}\),

Explanation:

Given to find \(\frac{6}{8}\) – \(\frac{1}{2}\) = ,

As both denominators are different first we need to

make common denominators means we need to multiply

numerator and denominator by 4 as

\(\frac{1}{2}\) X 4 = \(\frac{1 X 4}{2 X 4}\) =

\(\frac{4}{8}\) now we subtract as

\(\frac{6}{8}\) – \(\frac{4}{8}\) as

denominators are common as 8 we subtract numerators as

\(\frac{6 – 4}{8}\) = \(\frac{2}{8}\),

therefore common denominator is 8 and

Number sentence: \(\frac{6}{8}\) – \(\frac{4}{8}\) =

\(\frac{2}{8}\).

Question 3.

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

Common denominator: ____6______

Number sentence: ____\(\frac{1}{6}\) + \(\frac{2}{3}\) = \(\frac{5}{6}\)_____

Answer:

Common denominator: 6

Number sentence: \(\frac{1}{6}\) + \(\frac{2}{3}\) = \(\frac{5}{6}\),

Explanation:

Given to find \(\frac{1}{6}\) + \(\frac{2}{3}\) = ,

As both denominators are different first we need to

make common denominators means we need to multiply

numerator and denominator by 2 as

\(\frac{2}{3}\) X 2 = \(\frac{2 X 2}{3 X 2}\) =

\(\frac{4}{6}\) now we add as

\(\frac{1}{6}\) + \(\frac{4}{6}\) as

denominators are common as 6 we add numerators as

\(\frac{1 + 4}{6}\) = \(\frac{5}{6}\),

therefore common denominator is 6 and

Number sentence: \(\frac{1}{6}\) + \(\frac{4}{6}\) =

\(\frac{5}{6}\).

**Practice**

Estimate. Then solve using U.S. traditional multiplication.

Show your work on the back of this page.

Question 4.

723 ∗ 89 = __64,347________

Estimate: ___723 X 89 = 64,347_______

Answer:

723 X 89 = 64,347,

Estimate : 723 X 89 =64,347,

Explanation:

Estimate : 723 X 89 = 64,347,

So 723 X 89 =

723

X 89

6507

57840

64,347

Question 5.

1,20 7 ∗ 54 = ___65,178_______

Estimate: ___1,20 7 ∗ 54 = 65,178_______

Answer:

1,207 X 54 = 65,178,

Estimate: 1,20 7 ∗ 54 = 65,178,

Explanation:

Estimate : 1,207 X 54 =65,178,

So 723 X 89 =

1,207

X 54

4828

60350

65,178

### Everyday Math Grade 5 Home Link 5.2 Answer Key

**Using a Common Denominator**

Question 1.

For each pair of fractions in the table, find a common denominator. Then rewrite the two fractions as equivalent fractions with a common denominator. Write > or < in the space provided to create a true number sentence.

Remember the three strategies you have learned:

- List equivalent fractions.
- Check to see if one denominator is a multiple of the other denominator.
- Multiply denominators to get a quick common denominator.

Answer:

Explanation:

For each pair of fractions in the table, found a common denominator.

Then rewrote the two fractions as equivalent fractions with a common denominator. Wrote > or < in the space provided to create a true number sentence as shown above as

a. Given \(\frac{4}{7}\) , \(\frac{3}{5}\)

As both denominators are different first we need to

make common denominators 35 means we need to multiply

numerator and denominator by 5 for \(\frac{4}{7}\) and

by 7 for \(\frac{3}{5}\) we get \(\frac{20}{35}\) and

\(\frac{21}{35}\), Now if we compare we get

\(\frac{20}{35}\) < \(\frac{21}{35}\), so

\(\frac{4}{7}\) < \(\frac{3}{5}\).

b. Given \(\frac{5}{9}\) , \(\frac{2}{3}\)

As both denominators are different first we need to

make common denominators 9 means we need to multiply

numerator and denominator by 3 for \(\frac{2}{3}\) we get \(\frac{6}{9}\),Now if we compare we get

\(\frac{5}{9}\) < \(\frac{6}{9}\),

\(\frac{5}{9}\) < \(\frac{2}{3}\).

c. Given \(\frac{1}{4}\) , \(\frac{2}{10}\)

As both denominators are different first we need to

make common denominators 20 means we need to multiply

numerator and denominator by 5 for \(\frac{1}{4}\) and

by 2 for \(\frac{2}{10}\) we get \(\frac{5}{20}\) and

\(\frac{4}{20}\), Now if we compare we get

\(\frac{5}{20}\) > \(\frac{4}{20}\), so

\(\frac{1}{4}\) < \(\frac{2}{10}\).

d. Given \(\frac{7}{9}\) , \(\frac{5}{6}\)

As both denominators are different first we need to

make common denominators 18 means we need to multiply

numerator and denominator by 2 for \(\frac{7}{9}\) and

by 3 for \(\frac{5}{6}\) we get \(\frac{14}{18}\) and

\(\frac{15}{18}\), Now if we compare we get

\(\frac{14}{18}\) < \(\frac{15}{18}\), so

\(\frac{7}{9}\) < \(\frac{5}{6}\).

e. Given \(\frac{5}{12}\) , \(\frac{3}{8}\)

As both denominators are different first we need to

make common denominators 24 means we need to multiply

numerator and denominator by 2 for \(\frac{5}{12}\) and

by 3 for \(\frac{3}{8}\) we get \(\frac{10}{24}\) and

\(\frac{9}{24}\), Now if we compare we get

\(\frac{10}{24}\) > \(\frac{9}{24}\), so

\(\frac{5}{12}\) > \(\frac{3}{8}\).

Use the table to help you rewrite the problems with

common denominators. Then solve.

Question 2.

\(\frac{3}{5}\) – \(\frac{4}{7}\) = _________ – ________ = __________

Answer:

\(\frac{3}{5}\) – \(\frac{4}{7}\) =\(\frac{21}{35}\) – \(\frac{20}{35}\) =\(\frac{1}{35}\),

Explanation:

Used the table to help me to rewrite the problems with

common denominators as given

\(\frac{3}{5}\) – \(\frac{4}{7}\) =

As both denominators are different first we need to

make common denominators 35 means we need to multiply

numerator and denominator by 7 for \(\frac{3}{5}\)

and by 5 for \(\frac{4}{7}\) we get \(\frac{21}{35}\) and

\(\frac{20}{35}\), Now we subtract we get

\(\frac{21}{35}\) – \(\frac{20}{35}\), as we have

common denominators we subtract denominators as

\(\frac{21-20}{35}\) =\(\frac{1}{35}\).

Question 3.

\(\frac{1}{4}\) + \(\frac{2}{10}\) = _________ – ________ = __________

Answer:

\(\frac{1}{4}\) + \(\frac{2}{10}\) =

\(\frac{5}{20}\) + \(\frac{4}{20}\) =\(\frac{9}{20}\),

Explanation:

Used the table to help me to rewrite the problems with

common denominators as given

\(\frac{1}{4}\) +\(\frac{2}{10}\) =

As both denominators are different first we need to

make common denominators 20 means we need to multiply

numerator and denominator by 5 for \(\frac{1}{4}\) and

by 2 for \(\frac{2}{10}\) we get \(\frac{5}{20}\) and

\(\frac{4}{20}\), Now we add numerators as we have common

denominators we get \(\frac{5 + 4}{20}\) = \(\frac{9}{20}\).

Question 4.

\(\frac{5}{9}\) + \(\frac{2}{3}\) = _________ – ________ = __________

Answer:

\(\frac{5}{9}\) + \(\frac{2}{3}\) =

\(\frac{5}{9}\) + \(\frac{6}{9}\) =

\(\frac{11}{9}\) or 1\(\frac{2}{9}\),

Explanation:

Used the table to help me to rewrite the problems with

common denominators as given

\(\frac{5}{9}\) +\(\frac{2}{3}\) =

As both denominators are different first we need to

make common denominators 9 means we need to multiply

numerator and denominator by 3 for \(\frac{2}{3}\)

we get \(\frac{6}{9}\), Now we add numerators as we have common denominators as \(\frac{5 + 6}{9}\) = \(\frac{11}{9}\) as numerator is greater than denominator

we write in mixed fraction as (1 X 9 + 2 by 9), So

\(\frac{5}{9}\) + \(\frac{2}{3}\) =

\(\frac{5}{9}\) + \(\frac{6}{9}\) =

\(\frac{11}{9}\) or 1\(\frac{2}{9}\).

**Practice**

Solve. Show your work on the back of the page.

Question 5.

8,170 ÷ 75 → ___108 R70______

Answer:

8,170 ÷ 75 = 108 R70,

Explanation:

Given to solve 8,170 ÷ 75 =

108

75)8,170(

750

670

600

70

Therefore, 8,170 ÷ 75 = 108 R70.

Question 6.

298 ÷ 17 → ___17R9______

Answer:

298 ÷ 17 = 17 R9,

Explanation:

Given to solve 298 ÷ 17 =

17

17)298(

17

128

119

9

Therefore, 298 ÷ 17 = 17 R9.

### Everyday Mathematics Grade 5 Home Link 5.3 Answers

**Adding Fractions and Mixed Numbers**

Estimate and then solve. Show your work.

Use your estimates to check your answers.

Remember: Before adding fractions and mixed numbers

with different denominators, you must rename one or

both fractions so both fractions have a common denominator.

Example: 2\(\frac{3}{5}\) + 4 \(\frac{2}{3}\) = ?

- Find a common denominator for the fraction parts.

The quick common denominator for \(\frac{3}{5}\) and \(\frac{2}{3}\) is the product of the

denominators, 5 ∗ 3, or 15. - Use the multiplication rule for equivalent fractions to rename each fraction so both fractions have the common denominator.
- Add.

- Rename the sum. 6\(\frac{19}{15}\) = 6 + \(\frac{15}{15}\) + \(\frac{4}{15}\) = 6 + 1 \(\frac{4}{15}\) = 7 + \(\frac{4}{15}\) = 7\(\frac{4}{15}\)

Question 1.

Estimate: ___5\(\frac{5}{6}\) ______

3\(\frac{4}{6}\) + 2\(\frac{1}{6}\) = __________

Answer:

3\(\frac{4}{6}\) + 2\(\frac{1}{6}\) = 5\(\frac{5}{6}\),

Explanation:

Given to solve 3\(\frac{4}{6}\) + 2\(\frac{1}{6}\) =

both have common denominators as 6, So

3\(\frac{4}{6}\) = \(\frac{18 + 4}{6}\) =

\(\frac{22}{6}\) and 2\(\frac{1}{6}\) =

\(\frac{12 + 1}{6}\) = \(\frac{13}{6}\),

now we add \(\frac{22}{6}\) + \(\frac{13}{6}\) =

as both have common denominators 6 we add numerators as

\(\frac{22 + 13}{6}\) = \(\frac{35}{6}\) as

numerator is greater than denominator we write in

mixed fraction as (5 X 6 + 5 by 6) = 5\(\frac{5}{6}\),

therefore, 3\(\frac{4}{6}\) + 2\(\frac{1}{6}\) = 5\(\frac{5}{6}\).

Question 2.

Estimate: _________

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

Answer:

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

\(\frac{19}{3}\) + \(\frac{13}{6}\) =

\(\frac{38}{6}\) + \(\frac{13}{6}\) =

\(\frac{51}{6}\) = 8\(\frac{3}{6}\),

Explanation:

Given to solve 6\(\frac{1}{3}\) + 2\(\frac{1}{6}\) =

first we write mixed fraction into fraction as

6\(\frac{1}{3}\) = \(\frac{18 + 1}{3}\) =

\(\frac{19}{3}\) and 2\(\frac{1}{6}\) =

\(\frac{12 + 1}{6}\) = \(\frac{13}{6}\),

Now we need to make both common denominators as 6 so

we need to multiply numerator and denominator by 2 for

\(\frac{19}{3}\) we get \(\frac{19}{3}\) X 2 =

\(\frac{38}{6}\) , now we add \(\frac{38}{6}\) + \(\frac{13}{6}\) as both have common denominators 6

we add numerators as \(\frac{38 + 13}{6}\) = \(\frac{51}{6}\) as numerator is greater than denominator we write in

mixed fraction as (8 X 6 + 3 by 6) = 8\(\frac{3}{6}\),

therefore, 6\(\frac{1}{3}\) + 2\(\frac{1}{6}\) =

\(\frac{51}{6}\) = 8\(\frac{3}{6}\).

Question 3.

Estimate: ___________

\(\frac{3}{4}\) + \(\frac{7}{12}\) = ____________

Answer:

\(\frac{3}{4}\) + \(\frac{7}{12}\) =

\(\frac{16}{12}\) = 1\(\frac{4}{12}\),

Explanation:

Given to solve \(\frac{3}{4}\) + \(\frac{7}{12}\),

Now we need to make both common denominators as 12 so

we need to multiply numerator and denominator by 3 for

\(\frac{3}{4}\) we get \(\frac{3}{4}\) X 3 =

\(\frac{9}{12}\) , now we add \(\frac{9}{12}\) + \(\frac{7}{12}\) as both have common denominators 12

we add numerators as \(\frac{9 + 7}{12}\) = \(\frac{16}{12}\) as numerator is greater than denominator we write in

mixed fraction as (1 X 12 + 4 by 12) = 1\(\frac{4}{12}\),

therefore, \(\frac{3}{4}\) + \(\frac{7}{12}\) =

\(\frac{16}{12}\) = 1\(\frac{4}{12}\).

Question 4.

Estimate: ____________

15\(\frac{1}{2}\) + 12\(\frac{2}{5}\) = _________

Answer:

15\(\frac{1}{2}\) + 12\(\frac{2}{5}\) =

\(\frac{31}{2}\) + \(\frac{62}{5}\) =

\(\frac{155}{10}\) + \(\frac{124}{10}\) =

\(\frac{279}{10}\) = 27\(\frac{9}{10}\),

Explanation:

Given to solve 15\(\frac{1}{2}\) + 12\(\frac{2}{5}\) =

first we write mixed fraction into fraction as

15\(\frac{1}{2}\) = \(\frac{30 + 1}{2}\) =

\(\frac{31}{2}\) and 12\(\frac{2}{5}\) =

\(\frac{60 + 2}{5}\) = \(\frac{62}{5}\),

Now we need to make both common denominators as 10 so

we need to multiply numerator and denominator by 5 for

\(\frac{31}{2}\) we get \(\frac{31}{2}\) X 5 =

\(\frac{155}{10}\) and \(\frac{62}{5}\) by 2 we get

\(\frac{124}{10}\) now we add \(\frac{155}{10}\) + \(\frac{124}{10}\) as both have common denominators 10

we add numerators as \(\frac{155 + 124}{10}\) = \(\frac{279}{10}\) as numerator is greater than denominator we write in

mixed fraction as (27 X 10 + 9 by 10) = 27\(\frac{9}{10}\),

therefore, 15\(\frac{1}{2}\) + 12\(\frac{2}{5}\) =

\(\frac{31}{2}\) + \(\frac{62}{5}\) =

\(\frac{155}{10}\) + \(\frac{124}{10}\) =

\(\frac{279}{10}\) = 27\(\frac{9}{10}\).

**Practice**

Write each decimal using numerals.

Question 5.

three and six hundred twenty-four thousandths ___3.624____

Answer:

three and six hundred twenty-four thousandths = 3.624,

Explanation:

Given to write three and six hundred twenty-four thousandths

using numerals, So three and six hundred twenty-four thousandths =

3 + 6 X \(\frac{1}{100}\) + 24 X \(\frac{1}{1,000}\) =

3 + 0.6 + 0.024 = 3.624, therefore, three and

six hundred twenty-four thousandths = 3.624.

Question 6.

fourteen and twelve thousandths ____14.012________

Answer:

fourteen and twelve thousandths = 14.012,

Explanation:

Given to write fourteen and twelve thousandths

using numerals, So fourteen and twelve thousandths =

14 + 12 X \(\frac{1}{1,000}\) =

14 + 0.012 = 14.012, therefore, fourteen and

twelve thousandths = 14.012.

Write each decimal using words.

Question 7

1.46 ____________

Answer:

1.46 = one and forty-six hundredths,

Explanation:

Given to write 1.46 decimal in words as 1 is at

units place,4 is at tenths place and 6 at hundredths place,

therefore, 1.46 in words isone and forty-six hundredths.

Question 8.

4.309 ____________

Answer:

4.309 = four and three hundred and nine thousandths,

Explanation:

Given to write 4.309 decimal in words as 4 is at

units place and 309 is at hundred and thousandths place,

therefore, 4.309 = four and three hundred and nine thousandths.

### Everyday Math Grade 5 Home Link 5.4 Answer Key

**Marathon Training**

Katie is training to run a marathon.

She keeps track of how many miles she runs each day.

Use the information in the table to answer the questions.

Question 1.

How many more miles did Katie run on Day 1 than on Day 2?

Number model: ____________

Estimate: ____________

Show your work: ____________

____________ miles

Answer:

Number model : 8\(\frac{1}{8}\) – 4\(\frac{3}{8}\),

Estimate : 8\(\frac{1}{8}\) – 4\(\frac{3}{8}\) =

\(\frac{65}{8}\) – \(\frac{35}{8}\) =

\(\frac{30}{8}\)miles or 3\(\frac{6}{8}\) miles

more miles did Katie ran on Day 1 than on Day 2,

Explanation:

Katie ran on Day 1 is 8\(\frac{1}{8}\) and

on Day 2 is 4\(\frac{3}{8}\), So miles did Katie run

on Day 1 than on Day 2 is 8\(\frac{1}{8}\) – 4\(\frac{3}{8}\), first we write mixed fractions in fractions as

8\(\frac{1}{8}\) = \(\frac{64 + 1}{8}\) = \(\frac{65}{8}\) and 4\(\frac{3}{8}\) = \(\frac{32 + 3}{8}\) =

\(\frac{35}{8}\), Now we subtract numerators as we

have common denominators as 8 so \(\frac{65}{8}\) – \(\frac{35}{8}\) = \(\frac{65 – 35}{8}\)miles =

\(\frac{30}{8}\)miles as numerator is greater than denomintor

we write in mixed fraction as (3 X 8 + 6 by 8) =

3\(\frac{6}{8}\) miles, therefore more miles did

Katie ran on Day 1 than on Day 2 is \(\frac{30}{8}\)miles or 3\(\frac{6}{8}\) miles.

Question 2.

How many miles did Katie run on Day 3 and Day 4 combined?

Number model: __12\(\frac{3}{4}\)miles +5\(\frac{1}{3}\) miles________

Estimate: ____________

Show your work: ____________

____________ miles

Answer:

Number model:

12\(\frac{3}{4}\)miles + 5\(\frac{1}{3}\) miles,

Estimate :

12\(\frac{3}{4}\)miles + 5\(\frac{1}{3}\) miles =

\(\frac{51}{4}\)miles + \(\frac{16}{3}\) miles =

\(\frac{217}{12}\)miles or 18\(\frac{1}{12}\) miles

did Katie run on Day 3 and Day 4 combinedly,

Explanation:

Katie ran on Day 3 is 12\(\frac{3}{4}\) and

on Day 4 is 5\(\frac{1}{3}\), So miles did Katie ran

on Day 3 and Day 4 combinedly is 12\(\frac{3}{4}\) +

5\(\frac{1}{3}\), first we write mixed fractions in fractions as

12\(\frac{3}{4}\) = \(\frac{48 + 3}{4}\) = \(\frac{51}{4}\) and 5\(\frac{1}{3}\) = \(\frac{15 + 1}{3}\) =

\(\frac{16}{3}\), Now we add them as

\(\frac{51}{4}\) + \(\frac{16}{3}\) =

\(\frac{51 X 3 + 16 X 4}{12}\)miles = \(\frac{153 + 64}{12}\) = \(\frac{217}{12}\)miles as numerator is greater than denomintor we write in mixed fraction as (18 X 12 + 1 by 12) =

18\(\frac{1}{12}\) miles, therefore more miles did

Katie ran on Day 3 and on Day 4 combinedly is \(\frac{217}{12}\)miles or 18\(\frac{1}{12}\) miles.

Question 3.

Katie set a goal to run 4 \(\frac{1}{2}\) miles on Day 5.

How much farther than her goal did she run?

Number model: ____________

Estimate: ____________

Show your work: ____________

____________ miles

Answer:

Number model : 9\(\frac{1}{8}\) – 4\(\frac{1}{2}\),

Estimate : 9\(\frac{1}{8}\) – 4\(\frac{1}{2}\) =

\(\frac{73}{8}\) – \(\frac{9}{2}\) =

\(\frac{37}{8}\)miles or 4\(\frac{5}{8}\) miles

farther more miles did Katie ran on Day 5,

Explanation:

Katie ran on Day 5 is 9\(\frac{1}{8}\) and

Katie set a goal to run 4 \(\frac{1}{2}\) miles on Day 5

So farther more miles did Katie ran on Day 5 is

9\(\frac{1}{8}\) – 4\(\frac{1}{2}\), first we write mixed fractions in fractions as 9\(\frac{1}{8}\) = \(\frac{72 + 1}{8}\) = \(\frac{73}{8}\) and 4\(\frac{1}{2}\) = \(\frac{8 + 1}{2}\) = \(\frac{9}{2}\),

Now we subtract as \(\frac{73}{8}\) – \(\frac{9}{2}\) = \(\frac{73 – 36}{8}\)miles = \(\frac{37}{8}\)miles as numerator is greater than denomintor we write

in mixed fraction as (4 X 8 + 5 by 8) = 4\(\frac{5}{8}\) miles, therefore more miles did Katie ran on Day 5 than

her setted goal is \(\frac{37}{8}\)miles or 4\(\frac{5}{8}\) miles.

**Practice**

Choose from the list above. Write the number that has:

Question 4.

a 7 in the hundredths place.

Answer:

128.174

Explanation:

Choosing from the list the number that has

a 7 in the hundredths place is in 128.174.

Question 5.

a 5 in the thousandths place.

Answer:

1,737.405,

Explanation:

Choosing from the list the number that has

a 5 in the thousandths place is in 1,737.405.

Question 6.

a 2 that is worth 0.2.

Answer:

8.25,

Explanation:

Choosing from the list the number that has

a 2 that is worth 0.2 is 8.25.

### Everyday Mathematics Grade 5 Home Link 5.5 Answers

**Fraction-Of Problems**

Solve each fraction-of problem. Include a unit in your answer.

Then write a multiplication number model for each problem.

Question 1.

Suri made 6 gallons of lemonade to sell at her lemonade stand.

In one day she sold \(\frac{2}{3}\) of the lemonade.

How much lemonade did she sell?

Number model: _________

Answer:

Suri sells 4 gallons of lemonade,

Number model : \(\frac{2}{3}\) X 6 =4,

Explanation:

Given Suri made 6 gallons of lemonade to sell

at her lemonade stand.

In one day she sold \(\frac{2}{3}\) of the lemonade.

So lemonade did Suri sell is \(\frac{2}{3}\) X 6 =

\(\frac{2 X 6}{3}\) = \(\frac{12}{3}\) = 4 gallons,

therefore, Suri sells 4 gallons of lemonade and

Number model : \(\frac{2}{3}\) X 6 = 4.

Question 2.

Antonio planned to read 15 books over the summer

for the library’s summer reading challenge.

At the end of July he had read \(\frac{4}{5}\) of the books.

How many books had he read?

Number model: _________

Answer:

Antonio read 12 books,

Number model : \(\frac{4}{5}\) X 15 = 12,

Explanation:

Given Antonio planned to read 15 books over the summer

for the library’s summer reading challenge.

At the end of July he had read \(\frac{4}{5}\) of the books.

So number of many books had he read is

\(\frac{4}{5}\) X 15 = \(\frac{4 X 15}{5}\) =

\(\frac{60}{5}\) = 12, therefore Antonio read 12 books,

Number model : \(\frac{4}{5}\) X 15 = 12.

Question 3.

Elliot is riding in a 100-mile bike race to raise money for a charity.

So far he has completed \(\frac{7}{10}\) of the race.

How far has Elliot biked?

Number model: _________

Answer:

Elliot has biked 70 miles,

Number model : \(\frac{7}{10}\) X 100 = 70,

Explanation:

Given Elliot is riding in a 100-mile bike race to raise money for a charity.

So far he has completed \(\frac{7}{10}\) of the race.

So far has Elliot biked is \(\frac{7}{10}\) X 100 =

\(\frac{7 X 100}{10}\) = \(\frac{700}{10}\) = 70,

therefore, Elliot has biked 70 miles,

Number model : \(\frac{7}{10}\) X 100 = 70.

Question 4.

Erica’s garden has an area of 24 square feet.

She will use \(\frac{3}{4}\) of the space for

vegetables and \(\frac{1}{4}\) of the space for flowers.

How much space will she use for vegetables?

Number model: _________

Answer:

Erica’s used space for vegetables is 18 square feet,

Number model : \(\frac{3}{4}\) X 24 = 18,

Explanation:

Given Erica’s garden has an area of 24 square feet.

She will use \(\frac{3}{4}\) of the space for

vegetables and \(\frac{1}{4}\) of the space for flowers.

So space will she use for vegetables is \(\frac{3}{4}\) X 24 =

\(\frac{3 X 24}{4}\) = \(\frac{72}{4}\) =18 square feet,

therefore, Erica’s used space for vegetables is 18 square feet,

Number model : \(\frac{3}{4}\) X 24 = 18.

**Practice**

Write <, >, or = to make true number sentences.

Question 5.

0.3 ____<_____ 0.32

Answer:

0.3 < 0.32,

Explanation:

Given 0.3 and 0.32,

True number sentence: 0.3 < 0.32.

Question 6.

0.428 ____<_____ 0.43

Answer:

0.428 < 0.43,

Explanation:

Given 0.428 and 0.43,

True number sentence: 0.428 < 0.43.

Question 7.

1.68 ____=_____ 1.680

Answer:

1.68 = 1.680,

Explanation:

Given 1.68 and 1.680,

True number sentence: 1.68 = 1.680.

Question 8.

2.988 ___>____ 1.989

Answer:

2.988 > 1.989,

Explanation:

Given 2.988 and 1.989,

True number sentence: 2.988 > 1.989.

Question 9.

0.06 ____>_____ 0.006

Answer:

0.06 > 0.006,

Explanation:

Given 0.06 and 0.006,

True number sentence: 0.06 < 0.006.

Question 10.

5.64 ____>_____ 5.46

Answer:

5.64 > 5.46,

Explanation:

Given 5.64 and 5.46,

True number sentence: 5.64 > 5.46.

### Everyday Math Grade 5 Home Link 5.6 Answer Key

**Multiplying Whole Numbers and Fractions**

Question 1.

a. What is 199–200 \(\frac{1}{6}\) of 18? _________

b. What is \(\frac{4}{6}\) of 18? _________

c. Fill in the blank to make a true number sentence.

18 ∗ \(\frac{4}{6}\) = _________

Answer:

a. 3,

b. 12,

c.12,

Explanation:

Given to find thw values of

a. (199 – 200) \(\frac{1}{6}\) of 18 =

(199 – 200)\(\frac{1}{6}\) X 18 =

1 X \(\frac{1 X 18}{6}\) =

1 X \(\frac{18}{6}\) =1 X 3 = 3.

b. \(\frac{4}{6}\) of 18 =

\(\frac{4}{6}\) X 18 =

\(\frac{4 X 18}{6}\) =

\(\frac{72}{6}\) =12.

c. 18 ∗ \(\frac{4}{6}\) =

\(\frac{18 X 4}{6}\) =

\(\frac{72}{6}\) = 12.

Question 2.

a. What is 15 ∗ 3? ____45_____

b. What is 45 ÷ 8? ___5 R5______

c. What is 15 ∗ 3 ÷ 8? ___5 R5______

d. Fill in the blank to make a true number sentence.

15 ∗ \(\frac{3}{8}\) = ___5 R5______

Answer:

a. 15 X 3 = 45,

b. 45 ÷ 8 = 5 R5,

c. 15 X 3 ÷ 8 = 5 R5,

d. 15 ∗ \(\frac{3}{8}\) = 5 R5,

Explanation:

a. Given to find 15 X 3 = 45,

so multiplying 15 by 3 we get 45.

b. 45 ÷ 8 =

5 R5

8)45(

40

5 _

Therfore, 45 ÷ 8 = 5 R5.

c. 15 X 3 ÷ 8 =

45 ÷ 8 =

5 R5

8)45(

40

5 _

Therfore, 15 X 3 ÷ 8 = 5 R5.

d. 15 ∗ \(\frac{3}{8}\) =

\(\frac{15 X 3}{8}\) =

\(\frac{45}{8}\) =

5 R5

8)45(

40

5 _

Therfore, 15 ∗ \(\frac{3}{8}\) = 5 R5.

Question 3.

The art teacher has 7 bottles of glue that are each \(\frac{2}{5}\) full. He combines them so he will have fewer bottles.

How many bottles of glue does he have after he combines them?

Number model: _7 X \(\frac{2}{5}\)________

__ \(\frac{14}{5}\) or 2\(\frac{4}{5}\)_______ bottles

Answer:

Number model: 7 X \(\frac{2}{5}\),

\(\frac{14}{5}\) or 2\(\frac{4}{5}\) bottles

of glue he have after he combines them,

Explanation:

Given the art teacher has 7 bottles of glue that are each \(\frac{2}{5}\) full. He combines them so he will have fewer bottles.

2So number of bottles of glue does he have after

he combines themis 7 X \(\frac{2}{5}\) =

\(\frac{7 X 2}{5}\) = \(\frac{14}{5}\) as

numerator is greater than denominator we write in mixed fraction

as (2 X 5 + 4 by 5) =2\(\frac{4}{5}\),

Therefore, Number model: 7 X \(\frac{2}{5}\),

\(\frac{14}{5}\) or 2\(\frac{4}{5}\) bottles

of glue he have after he combines them.

Question 4.

The librarian needs to return 24 books to the shelf.

In one hour she finished \(\frac{3}{4}\) of the job.

How many books has she returned to the shelf so far?

Number model: ____24 X \(\frac{3}{4}\),_____

______18____ books

Answer:

24 X \(\frac{3}{4}\),

18 books she has returned to the shell so far,

Explanation:

Given the librarian needs to return 24 books to the shelf.

In one hour she finished \(\frac{3}{4}\) of the job.

Number of books has she returned to the shelf so far are

24 X \(\frac{3}{4}\) = \(\frac{24 X 3}{4}\) =

\(\frac{72}{4}\) = 18, therefore 18 books she

has returned to the shell so far.

**Practice**

For Problems 5–7, round each decimal to the nearest tenth.

Question 5.

0.93 ___0.9____

Answer:

0.93 the nearest tenth is 0.9,

Explanation:

Rounded the decimal 0.93 to the nearest tenth is 0.9.

Question 6.

0.417 ___0.4____

Answer:

0.417 the nearest tenth is 0.4,

Explanation:

Rounded the decimal 0.417 to the nearest tenth is 0.4.

Question 7.

7.06 ___7.1_____

Answer:

7.06 the nearest tenth is 7.1,

Explanation:

Rounded the decimal 7.06 to the nearest tenth is 7.1.

For Problems 8–10, round each decimal to the nearest hundredth.

Question 8.

1.482 __1.48_____

Answer:

1.482 the nearest hundredth is 1.48,

Explanation:

Rounded the decimal 1.482 the nearest hundredth is 1.48.

Question 9.

5.715 ____5.72_____

Answer:

5.715 the nearest hundredth is 5.72,

Explanation:

Rounded the decimal 5.715 the nearest hundredth is 5.72.

Question 10.

2.996 ___3.00_____

Answer:

2.996 the nearest hundredth is 3.00,

Explanation:

Rounded the decimal 2.996 the nearest hundredth is 3.00.

### Everyday Mathematics Grade 5 Home Link 5.7 Answers

**Finding Fractions of Fractions**

Follow the directions to solve the problems.

You will need two pieces of paper.

Question 1.

What is \(\frac{1}{3}\) of \(\frac{2}{4}\)?

a. Fold the paper into fourths. Unfold it and shade two of the fourths.

b. Fold the paper into thirds the other way, with the new folds crossing your folds from Part a. Unfold the paper and double-shade one -third of the shaded part.

c. Record what your paper looks like.

d. How much of the paper is double-shaded ? ____ \(\frac{2}{12}\)____

e. Fill in the blank: \(\frac{1}{3}\) of \(\frac{2}{4}\) is __ \(\frac{2}{12}\)_____.

Answer:

a.

Folded the paper into fourths, shaded two of the fourths,

b.

Folded the paper into thirds, doubled-shaded

one -third of the shaded part,

c. Recorded how it looks like on the paper,

d. \(\frac{2}{12}\),

e. \(\frac{2}{12}\),

Explanation:

Given to solve \(\frac{1}{3}\) of \(\frac{2}{4}\) =

\(\frac{2}{4}\) X \(\frac{1}{3}\) = \(\frac{2 X 1}{4 X 3}\) = \(\frac{2}{12}\),

a. Folded the paper into fourths.

Unfolded it and shaded two of the fourths as shown above,

b. Folded the paper into thirds the other way,

with the new folds crossing your folds from Part a.

Unfolded the paper and double-shaded one -third

of the shaded part as shown above.

c. Recorded how it looks like on the paper,

d. The amount of paper that is double-shaded

\(\frac{1}{3}\) of \(\frac{2}{4}\) =

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

e. \(\frac{1}{3}\) of \(\frac{2}{4}\) is

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

Question 2.

What is \(\frac{3}{4}\) of \(\frac{2}{3}\)?

a. Fold the paper into thirds. Unfold it and shade two of the thirds.

b. Fold the paper into fourths the other way, with the new folds crossing your folds from Part a. Unfold the paper and double-shade three-fourths of the shaded part.

c. Record what your paper looks like.

d. How much of the paper is double-shaded? ________

e. Fill in the blank: \(\frac{3}{4}\) of \(\frac{2}{3}\) is ________.

Answer:

a.

Folded the paper into thirds, shaded two of the thirds,

b.

Folded the paper into fourths, double-shaded

three-fourths of the shaded part,

c. Recorded how it looks like on the paper,

d. \(\frac{6}{12}\),

e. \(\frac{6}{12}\),

Explanation:

Given to solve \(\frac{3}{4}\) of \(\frac{2}{3}\) =

\(\frac{3}{4}\) X \(\frac{2}{3}\) = \(\frac{3 X 2}{4 X 3}\) = \(\frac{6}{12}\),

a. Folded the paper into thirds.

Unfolded it and shaded two of the thirds as shown above,

b. Folded the paper into fourths the other way,

with the new folds crossing your folds from Part a.

Unfolded the paper and double-shaded three-fourths of

the shaded part as shown above.

c. Recorded how it looks like on the paper,

d. The amount of paper that is double-shaded

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

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

\(\frac{3 X 2}{4 X 3}\) = \(\frac{6}{12}\).

e. \(\frac{3}{4}\) of \(\frac{2}{3}\) is

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

\(\frac{3 X 2}{4 X 3}\) = \(\frac{6}{12}\).

**Practice**

Make an estimate. Then solve.

Use your estimate to check whether your answer makes sense.

Question 3.

Answer:

Explanation:

Estimate : 1.42 + 3. 37 = 4.79,

Used my estimate to check whether my answer is true

as 1.42

+3.37

4.79, which is true.

Question 4.

Answer:

Explanation:

Estimate : 6.76 + 2.91 = 9.67,

Used my estimate to check whether my answer is true

as 6.76

+2.91

9.67, which is true.

Question 5.

Answer:

Explanation:

Estimate : 5.9 + 4.14 = 10.04,

Used my estimate to check whether my answer is true

as 5.9

+4.14

10.04, which is true.

### Everyday Math Grade 5 Home Link 5.8 Answer Key

**Using Area Models to Multiply Fractions**

Label the blank tick marks on the number lines.

- Use the number lines to write the length and width of the shaded rectangle.
- Find the area of the shaded rectangle.

(The area of the big square is 1 square unit.)

Think: Into how many equal parts is the big square divided?

How many parts are shaded? - Write a multiplication number sentence for the area

of the shaded rectangle.

Question 1.

Length of shaded rectangle: __3/4______unit

Width of shaded rectangle: ___1/2_____unit

Area of shaded rectangle: ___3/8_____square unit

Number sentence: ____3/4____ × ___1/2_____ = ___3/8_____

Answer:

Length of shaded rectangle: 3/4 unit

Width of shaded rectangle: 1/2 unit

Area of shaded rectangle: 3/8 square unit

Number sentence: 3/4 × 1/2 = 3/8,

Explanation:

* Used the number lines to write the length and width of

the shaded rectangle as

Length of shaded rectangle: 3/4 unit

Width of shaded rectangle: 1/2 unit

* Founded the area of the shaded rectangle as

(The area of the big square is 1 square unit.)

Thinking: Into how many equal parts is the big square divided and

How many parts are shaded as

\(\frac{3}{4}\) X \(\frac{1}{2}\) =

\(\frac{3 X 1}{4 X 2}\) = \(\frac{3}{8}\),

* Wrote a multiplication number sentence for the area of the shaded rectangle as \(\frac{3}{4}\) X \(\frac{1}{2}\) =

\(\frac{3}{8}\) respectively.

Question 2.

Length of shaded rectangle: ___1/3_____unit

Width of shaded rectangle: ___2/3_____unit

Area of shaded rectangle: ___2/9_____square unit

Number sentence: ___1/3_____ × ___2/3_____ = ___2/9_____

Answer:

Length of shaded rectangle: 1/3 unit

Width of shaded rectangle: 2/3 unit

Area of shaded rectangle: 2/9 square unit

Number sentence: 1/3 × 2/3 = 2/9,

Explanation:

* Used the number lines to write the length and width of

the shaded rectangle as

Length of shaded rectangle: 1/3 unit

Width of shaded rectangle: 2/3 unit

* Founded the area of the shaded rectangle as

(The area of the big square is 1 square unit.)

Thinking: Into how many equal parts is the big square divided and

How many parts are shaded as

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

\(\frac{1 X 2}{3 X 3}\) = \(\frac{2}{9}\),

* Wrote a multiplication number sentence for the area of the shaded rectangle as \(\frac{1}{3}\) X \(\frac{2}{3}\) =

\(\frac{2}{9}\) respectively.

**Practice**

Make an estimate. Then solve. Use your estimate

to check whether your answer makes sense.

Question 3.

Answer:

Explanation:

Estimate : 6.75 – 2.44 = 4.31,

Used my estimate to check whether my answer is true

as 6.75

– 2.44

4.31, which is true.

Question 4.

Answer:

Explanation:

Estimate : 5.32 – 2.37 = 2.95,

Used my estimate to check whether my answer is true

as 5.32

– 2.37

2.95, which is true.

Question 5.

Answer:

Explanation:

Estimate : 8.6 – 6.27 = 2.33,

Used my estimate to check whether my answer is true

as 8.6

– 6.27

2.33, which is true.

### Everyday Mathematics Grade 5 Home Link 5.9 Answers

**Using an Algorithm to Multiply Fractions**

A Fraction Multiplication Algorithm To multiply two fractions, multiply the numerators and multiply the denominators.

For example: \(\frac{2}{3} * \frac{3}{8}=\frac{(2 * 3)}{(3 * 8)}=\frac{6}{24}\)

For Problems 1–6, use the algorithm to multiply the fractions.

Question 1.

\(\frac{1}{3}\) * \(\frac{1}{2}\) = ___1/6______

Answer:

\(\frac{1}{3}\) * \(\frac{1}{2}\) = \(\frac{1}{3}\),

Explanation:

Multiplying the fractions \(\frac{1}{3}\) * \(\frac{1}{2}\) by multiplying the numerators and multiplying the denominators as

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

Question 2.

\(\frac{2}{4}\) * \(\frac{2}{3}\) = ____4/12_______

Answer:

\(\frac{2}{4}\) * \(\frac{2}{3}\) = \(\frac{4}{12}\),

Explanation:

Multiplying the fractions \(\frac{2}{4}\) * \(\frac{2}{3}\) by multiplying the numerators and multiplying the denominators as

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

Question 3.

\(\frac{4}{5}\) * \(\frac{2}{5}\) = ____8/25______

Answer:

\(\frac{2}{4}\) * \(\frac{2}{3}\) = \(\frac{4}{12}\),

Explanation:

Multiplying the fractions \(\frac{2}{4}\) * \(\frac{2}{3}\) by multiplying the numerators and multiplying the denominators as

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

Question 4.

\(\frac{2}{10}\) * \(\frac{2}{3}\) = _____4/30_____

Answer:

\(\frac{2}{10}\) * \(\frac{2}{3}\) = \(\frac{4}{30}\),

Explanation:

Multiplying the fractions \(\frac{2}{10}\) * \(\frac{2}{3}\) by multiplying the numerators and multiplying the denominators as

\(\frac{2 X 2}{10 X 3}\) = \(\frac{4}{30}\).

Question 5.

\(\frac{2}{8}\) * \(\frac{5}{6}\) = _____10/48______

Answer:

\(\frac{2}{8}\) * \(\frac{5}{6}\) = \(\frac{10}{48}\),

Explanation:

Multiplying the fractions \(\frac{2}{8}\) * \(\frac{5}{6}\) by multiplying the numerators and multiplying the denominators as

\(\frac{2 X 5}{8 X 6}\) = \(\frac{10}{48}\).

Question 6.

\(\frac{5}{12}\) * \(\frac{2}{7}\) = ____10/84_______

Answer:

\(\frac{5}{12}\) * \(\frac{2}{7}\) = \(\frac{10}{84}\),

Explanation:

Multiplying the fractions \(\frac{5}{12}\) * \(\frac{2}{7}\) by multiplying the numerators and multiplying the denominators as

\(\frac{5 X 2}{12 X 7}\) = \(\frac{10}{84}\).

Question 7.

If you multiply \(\frac{2}{3}\) ∗ \(\frac{6}{10}\), will the product be more than \(\frac{2}{3}\) or less than \(\frac{2}{3}\)? How do you know?

Answer:

Less than \(\frac{2}{3}\) by checking,

Explanation:

First we multiply \(\frac{2}{3}\) X \(\frac{6}{10}\) =

\(\frac{2 X 6}{3 X 10}\) = \(\frac{12}{30}\), Now

\(\frac{12}{30}\) = 0.4 and \(\frac{2}{3}\) = 0.66,

as 0.4 < 0.66, So \(\frac{12}{30}\) < \(\frac{2}{3}\).

Question 8.

If you multiply \(\frac{2}{3}\) ∗ \(\frac{6}{10}\), will the product be more than \(\frac{6}{10}\) or less than \(\frac{6}{10}\)? How do you know?

Answer:

Less than \(\frac{6}{10}\) by checking,

Explanation:

First we multiply \(\frac{2}{3}\) X \(\frac{6}{10}\) =

\(\frac{2 X 6}{3 X 10}\) = \(\frac{12}{30}\), Now

\(\frac{12}{30}\) = 0.4 and \(\frac{6}{10}\) = 0.6,

as 0.4 < 0.6, So \(\frac{12}{30}\) < \(\frac{6}{10}\).

In Problems 9–12, write true or false. Do not multiply.

Question 9.

\(\frac{3}{4}\) ∗ \(\frac{7}{10}\) is less than \(\frac{3}{4}\).

Answer:

True,

Explanation:

First we multiply \(\frac{3}{4}\) X \(\frac{7}{10}\) =

\(\frac{3 X 7}{4 X 10}\) = \(\frac{21}{40}\), Now

\(\frac{21}{40}\) = 0.525 and \(\frac{3}{4}\) = 0.75,

So true \(\frac{3}{4}\) ∗ \(\frac{7}{10}\) is less than \(\frac{3}{4}\).

Question 10.

\(\frac{7}{9}\) ∗ \(\frac{11}{12}\) is greater than \(\frac{11}{12}\).

Answer:

False,

Explanation:

First we multiply \(\frac{7}{9}\) X \(\frac{11}{12}\) =

\(\frac{7 X 11}{9 X 12}\) = \(\frac{77}{108}\), Now

\(\frac{77}{108}\) = 0.712 and \(\frac{11}{12}\) = 0.916,

So false as \(\frac{7}{9}\) ∗ \(\frac{11}{12}\) is not greater than \(\frac{11}{12}\).

Question 11.

\(\frac{4}{5}\) ∗ \(\frac{2}{8}\) is greater than\(\frac{2}{8}\) but less than \(\frac{4}{5}\).

Answer:

False,

Explanation:

First we multiply \(\frac{4}{5}\) X \(\frac{2}{8}\) =

\(\frac{4 X 2}{5 X 8}\) = \(\frac{8}{40}\), Now

\(\frac{8}{40}\) = 0.2, \(\frac{2}{8}\) = 0.25 and

\(\frac{4}{5}\) = 0.8,

So false as \(\frac{4}{5}\) ∗ \(\frac{2}{8}\) is not greater than \(\frac{2}{8}\) but less than \(\frac{4}{5}\).

Question 12.

\(\frac{6}{7}\) ∗ \(\frac{1}{4}\) is less than \(\frac{6}{7}\) and less than \(\frac{1}{4}\).

Answer:

True,

Explanation:

First we multiply \(\frac{6}{7}\) X \(\frac{1}{4}\) =

\(\frac{6 X 1}{7 X 4}\) = \(\frac{6}{28}\), Now

\(\frac{6}{28}\) = 0.214, \(\frac{6}{7}\) = 0. 857 and

\(\frac{1}{4}\) = 0.250,

So true as \(\frac{6}{7}\) ∗ \(\frac{1}{4}\) is less than \(\frac{6}{7}\) and also less than \(\frac{1}{4}\).

**Practice**

Question 13.

\(\frac{2}{3}\) + \(\frac{1}{6}\) = ___5/6_____

Answer:

\(\frac{2}{3}\) + \(\frac{1}{6}\) = \(\frac{5}{6}\),

Explanation:

Given \(\frac{2}{3}\) + \(\frac{1}{6}\) before

adding as both denominators need to be same so we multiply

\(\frac{2}{3}\) by 2 before adding as \(\frac{2 x 2}{3 x 6}\) = \(\frac{4}{6}\), now denominators are same 6 so we add

numerators as \(\frac{4}{6}\) + \(\frac{1}{6}\) =

\(\frac{4 + 1}{6}\) = \(\frac{5}{6}\),

Therefore, \(\frac{2}{3}\) + \(\frac{1}{6}\) = \(\frac{5}{6}\).

Question 14.

\(\frac{3}{4}\) + \(\frac{3}{8}\) = ___9/8 or 1_1/8_____

Answer:

\(\frac{3}{4}\) + \(\frac{3}{8}\) = \(\frac{9}{8}\) or 1\(\frac{1}{8}\),

Explanation:

Given \(\frac{3}{4}\) + \(\frac{3}{8}\) before

adding as both denominators need to be same so we multiply

\(\frac{3}{4}\) by 2 before adding as \(\frac{3 x 2}{4 x 2}\) = \(\frac{6}{8}\), now denominators are same 8 so we add

numerators as \(\frac{6}{8}\) + \(\frac{3}{8}\) =

\(\frac{6 + 3}{8}\) = \(\frac{9}{8}\),

as numerator is greater we can write in mixed fraction as

(1 X 8 + 1 by 8) = 1\(\frac{1}{8}\),

Therefore, \(\frac{3}{4}\) + \(\frac{3}{8}\) = \(\frac{9}{8}\) or 1\(\frac{1}{8}\).

Question 15.

\(\frac{2}{5}\) + \(\frac{1}{4}\) = ___13/20_____

Answer:

\(\frac{2}{5}\) + \(\frac{1}{4}\) = \(\frac{13}{20}\),

Explanation:

Given \(\frac{2}{5}\) + \(\frac{1}{4}\) before

adding as both denominators need to be same so we

multiply numerator and denominator by 4 to\(\frac{2}{5}\) before adding as \(\frac{2 x 4}{5 x 4}\) = \(\frac{8}{20}\) and \(\frac{1}{4}\) by 5 before adding as \(\frac{1 x 5}{4 x 5}\) = \(\frac{5}{20}\) now denominators are same 20 so we add numerators as \(\frac{8}{20}\) + \(\frac{5}{20}\) =

\(\frac{8 + 5}{20}\) = \(\frac{13}{20}\),

Therefore, \(\frac{2}{5}\) + \(\frac{1}{4}\) = \(\frac{13}{20}\).

### Everyday Math Grade 5 Home Link 5.10 Answer Key

**Mystery Models**

Write a multiplication number sentence that represents the

amount of shaded space in the pictures below.

Add to the picture or create a new drawing to represent

your number sentence.

Question 1.

Answer:

\(\frac{1}{3}\) x \(\frac{2}{4}\) = \(\frac{2}{12}\) or

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

Explanation:

Wrote a multiplication number sentence that represents the

amount of shaded space in the picture as

\(\frac{1}{3}\) x \(\frac{2}{4}\) = \(\frac{1 X 2}{3 X 4}\) = \(\frac{2}{12}\),

Added to the picture to create a new drawing to represent

my number sentence as shown above.

Question 2.

Answer:

\(\frac{3}{4}\) x \(\frac{2}{5}\) = \(\frac{6}{20}\),

\(\frac{2}{5}\) x \(\frac{3}{4}\) = \(\frac{6}{20}\),

Explanation:

Wrote a multiplication number sentence that represents the

amount of shaded space in the picture as

\(\frac{3}{4}\) X \(\frac{2}{5}\) = \(\frac{3 X 2}{4 X 5}\) = \(\frac{6}{20}\),

Added to the picture to create a new drawing to represent

my number sentence as shown above.

**Practice**

Solve.

Question 3.

1\(\frac{1}{2}\) + 2\(\frac{2}{8}\) = __________

Answer:

1\(\frac{1}{2}\) + 2\(\frac{2}{8}\) = \(\frac{30}{8}\) or 3\(\frac{6}{8}\),

Explanation:

Given 1\(\frac{1}{2}\) + 2\(\frac{2}{8}\),

First we will write mixed fractions into fractions as 1\(\frac{1}{2}\) = (1 X 2 + 1 by 2) = \(\frac{3}{2}\) and 2\(\frac{2}{8}\) =

(2 x 8 + 2 by 8) = \(\frac{18}{8}\), before

adding as both denominators need to be same so we

multiply numerator and denominator by 4 to \(\frac{3}{2}\)

before adding as \(\frac{3 x 4}{2 x 4}\) = \(\frac{12}{8}\) now denominators are same 8 so we add numerators as \(\frac{12}{8}\) + \(\frac{18}{8}\) =

\(\frac{12 + 18}{8}\) = \(\frac{30}{8}\),

as numerator is greater than denominator we write in

mixed fraction as (3 X 8 + 6 by 8) = 3\(\frac{6}{8}\),

Therefore, 1\(\frac{1}{2}\) + 2\(\frac{2}{8}\) = \(\frac{30}{8}\) or 3\(\frac{6}{8}\).

Question 4.

6 – 3\(\frac{1}{3}\) = ___2 2/3______

Answer:

6 – 3\(\frac{1}{3}\) = \(\frac{8}{3}\) or 2\(\frac{2}{3}\),

Explanation:

Given 6 – 3\(\frac{1}{3}\),

First we will write mixed fraction into fractions as 3\(\frac{1}{3}\) =

(3 X 3 + 1 by 3) = \(\frac{10}{3}\) before

subtracting as both denominators need to be same so we

multiply numerator and denominator by 3 to \(\frac{6}{1}\)

before adding as \(\frac{6 x 3}{1 x 3}\) = \(\frac{18}{3}\) now denominators are same 3 so we subtract numerators as \(\frac{18}{3}\) – \(\frac{10}{3}\) =

\(\frac{18 – 10}{3}\) = \(\frac{8}{3}\),

as numerator is greater than denominator we write in

mixed fraction as (2 X 3 + 2 by 3) = 2\(\frac{2}{3}\),

Therefore, 6 – 3\(\frac{1}{3}\) = \(\frac{8}{3}\) or 2\(\frac{2}{3}\),

Question 5.

1\(\frac{4}{9}\) + 5\(\frac{2}{3}\) = _________

Answer:

1\(\frac{4}{9}\) + 5\(\frac{2}{3}\) =

\(\frac{64}{9}\) or 7\(\frac{1}{9}\),

Explanation:

Given 1\(\frac{4}{9}\) + 5\(\frac{2}{3}\),

First we will write mixed fractions into fractions as 1\(\frac{4}{9}\) = (1 X 9 + 4 by 9) = \(\frac{13}{9}\) and 5\(\frac{2}{3}\) =

(5 x 3 + 2 by 3) = \(\frac{17}{3}\), before

adding as both denominators need to be same so we

multiply numerator and denominator by 3 to \(\frac{17}{3}\) before adding as \(\frac{17 x 3}{3 x 3}\) = \(\frac{51}{9}\) now denominators are same 9 so we add numerators as \(\frac{13}{9}\) + \(\frac{51}{9}\) =

\(\frac{13 + 51}{9}\) = \(\frac{64}{9}\),

as numerator is greater than denominator we write in

mixed fraction as (7 X 9 + 1 by 9) = 7\(\frac{1}{9}\),

Therefore, 1\(\frac{4}{9}\) + 5\(\frac{2}{3}\) =

\(\frac{64}{9}\) or 7\(\frac{1}{9}\).

Question 6.

8\(\frac{1}{3}\) – 3\(\frac{3}{4}\) = ___4 7/12_______

Answer:

8\(\frac{1}{3}\) – 3\(\frac{3}{4}\) =

\(\frac{55}{12}\) or 4\(\frac{7}{12}\),

Explanation:

Given 8\(\frac{1}{3}\) – 3\(\frac{3}{4}\),

First we will write mixed fractions into fractions as 8\(\frac{1}{3}\) = (8 X 3 + 1 by 3) = \(\frac{25}{3}\) and 3\(\frac{3}{4}\) =

(3 x 4 + 3 by 4) = \(\frac{15}{4}\), before

subtracting as both denominators need to be same so we

multiply numerator and denominator by 4 to \(\frac{25}{3}\) before subtracting as \(\frac{25 x 4}{3 x 4}\) = \(\frac{100}{12}\) and multiply numerator and denominator by 3 to \(\frac{15}{4}\) as \(\frac{15 X 3}{4 X 3}\) = \(\frac{45}{12}\) now denominators are same 12 so we subtract numerators as \(\frac{100}{12}\) – \(\frac{45}{12}\) =

\(\frac{100 – 45}{12}\) = \(\frac{55}{12}\),

as numerator is greater than denominator we write in

mixed fraction as (4 X 12 + 7 by 12) = 4\(\frac{7}{12}\),

Therefore, 8\(\frac{1}{3}\) – 3\(\frac{3}{4}\) =

\(\frac{55}{12}\) or 4\(\frac{7}{12}\).

### Everyday Mathematics Grade 5 Home Link 5.11 Answers

**Finding Equivalent Fractions**

Question 1.

a. List three fractions that are equivalent to 1.

___2/2____, ___3/3____, ____5/5___

b. Use the fractions you wrote in Part a to find three

fractions equivalent to \(\frac{6}{7}\).

Example: _______, _______, _______

Answer:

a. \(\frac{2}{2}\), \(\frac{3}{3}\), \(\frac{5}{5}\),

b. \(\frac{24}{28}\), \(\frac{54}{63}\) and

\(\frac{150}{175}\),

Explanation:

a. Three fractions that are equivalent to 1 are

\(\frac{2}{2}\), \(\frac{3}{3}\), \(\frac{5}{5}\),

b. Using the fractions I wrote in Part a to find three

fractions equivalent to \(\frac{6}{7}\) are

\(\frac{24}{28}\), \(\frac{54}{63}\), \(\frac{150}{175}\) because as \(\frac{2}{2}\) X \(\frac{12}{14}\) = \(\frac{24}{28}\) = \(\frac{6}{7}\),

\(\frac{3}{3}\) X \(\frac{18}{21}\) = \(\frac{54}{63}\) = \(\frac{6}{7}\),

\(\frac{5}{5}\) X \(\frac{30}{35}\) = \(\frac{150}{175}\) =\(\frac{6}{7}\) respectively.

Question 2.

You are solving fraction addition problems.

Use the information to find equivalent fractions.

a. Original fraction: \(\frac{4}{5}\)

Denominator needed: 20

Multiply by: ____4/4______

Equivalent fraction: ____16/20_______

Answer:

Denominator needed: 20

Multiply by: \(\frac{4}{4}\)

Equivalent fraction: \(\frac{16}{20}\),

Explanation:

Given \(\frac{4}{5}\) the equivalent fraction is

as numerator is 4 so we multiply numerator and

denominator by 4 as \(\frac{4}{5}\) X \(\frac{4}{4}\) =

\(\frac{4 X 4}{5 X 4}\) = \(\frac{16}{20}\),

therefore denominator needed is 20,

Multiply by: \(\frac{4}{4}\) and

Equivalent fraction: \(\frac{16}{20}\).

b. Original fraction: \(\frac{1}{3}\)

Denominator needed: 18

Multiply by: ____6/6______

Equivalent fraction: ____6/18______

Answer:

Denominator needed: 18

Multiply by: \(\frac{6}{6}\)

Equivalent fraction: \(\frac{6}{18}\),

Explanation:

Given \(\frac{1}{3}\) the equivalent fraction is

as numerator is 6 so we multiply numerator and

denominator by 6 as \(\frac{1}{3}\) X \(\frac{6}{6}\) =

\(\frac{1 X 6}{3 X 6}\) = \(\frac{6}{18}\),

therefore denominator needed is 18,

Multiply by: \(\frac{6}{6}\) and

Equivalent fraction: \(\frac{6}{18}\).

Question 3.

Addison wanted to find a fraction equivalent to \(\frac{3}{8}\) with 16 in the denominator. He thought: “8 ∗ 2 = 16, so I need to multiply \(\frac{3}{8}\) by 2.” He got an answer of \(\frac{3}{16}\).

a. Is \(\frac{3}{16}\) equivalent to \(\frac{3}{8}\)? How do you know?

Answer:

No,

\(\frac{3}{16}\) ≠ \(\frac{3}{8}\),

Explanation:

Given Addison wanted to find a fraction equivalent to \(\frac{3}{8}\) with 16 in the denominator. He thought: “8 ∗ 2 = 16, so I need to multiply \(\frac{3}{8}\) by 2.” He got an answer of \(\frac{3}{16}\) but Addison is incorrect as \(\frac{3}{16}\)

is not equivalent to \(\frac{3}{8}\).

b. What mistake did Addison make?

Answer:

Addison multiplyed only denominator by 2 not numerator,

Explanation:

Given Addison wanted to find a fraction equivalent to \(\frac{3}{8}\) with 16 in the denominator. He thought: “8 ∗ 2 = 16, so I need to multiply \(\frac{3}{8}\) by 2.” He got an answer of \(\frac{3}{16}\) but Addison is incorrect as \(\frac{3}{16}\)

is not equivalent to \(\frac{3}{8}\) as he multipled

only denominator by 2 not numerator.

**Practice**

Solve.

Question 4.

What is \(\frac{2}{3}\) of 9?

Answer:

\(\frac{2}{3}\) of 9 is 6,

Explanation:

Given to solve \(\frac{2}{3}\) of 9,

So \(\frac{2}{3}\) X 9 = \(\frac{2 X 9}{3}\) =

\(\frac{18}{3}\) = 6.

Question 5.

What is \(\frac{3}{5}\) of 20?

Answer:

\(\frac{3}{5}\) of 20 is 12,

Explanation:

Given to solve \(\frac{3}{5}\) of 20,

So \(\frac{3}{5}\) X 20 = \(\frac{3 X 20}{5}\) =

\(\frac{60}{5}\) = 12.

Question 6.

Explain how you found your answer for Problem 5.

Answer:

Solving and multiplying \(\frac{3}{5}\) X 20,

Explanation:

By solving \(\frac{3}{5}\) X 20 \(\frac{3 X 20}{5}\) =

\(\frac{60}{5}\) = 12 I found the answer for Problem 5.

### Everyday Math Grade 5 Home Link 5.12 Answer Key

**Writing Fraction Multiplication Stories**

Solve each multiplication problem. Then write a number

story that matches the number sentence and representation.

Example:

Number Story: Mr. Danielson had a tray of pumpkin bread that was \(\frac{5}{6}\) full. After sharing his bread with students, \(\frac{1}{4}\) of what he had brought was left.

What fraction of the whole tray was left?

Question 1.

4 ∗ \(\frac{2}{3}\) = _____8/3_ or 2 2/3____

Number Story: __________

Answer:

4 ∗ \(\frac{2}{3}\) = \(\frac{8}{3}\) or 2\(\frac{2}{3}\),

Number Story :

Our class has 4 groups each group have 10 children who can play

cricket, in that \(\frac{2}{3}\) of children participated

in the competition, So how many groups of children

participated in all?,

Explanation:

Given 4 ∗ \(\frac{2}{3}\) = \(\frac{4 X 2}{3}\) =

\(\frac{8}{3}\) or 2\(\frac{2}{3}\),

Number Story :

Our class has 4 groups each group have 10 children who can play

cricket, in that \(\frac{2}{3}\) of children participated

in the competition, So how many groups of children

participated in all? Wrote number story above.

Question 2.

\(\frac{1}{2}\) ∗ 16 = ___8______

Number Story: __________

Answer:

\(\frac{1}{2}\) X 16 = 8,

Number Story :

There are 16 books in library out which \(\frac{1}{2}\) of books

are moral stories, Therefore how many books are moral stories

in library?,

Explanation:

Given \(\frac{1}{2}\) X 16 = 8,

Number Story :

There are 16 books in library out which \(\frac{1}{2}\) of books

are moral stories, Therefore how many books are moral stories

in library?, Wrote number story above.

**Practice**

Make an estimate. Then add or subtract. Show your work on

the back of this page.

Question 3

4.79 + 2.03 = ?

Estimate: ____6.82______

4.79 + 2.03 = ___6.82_______

Answer:

Estimate: 6.82,

4.79 + 2.03 = 6.82,

Explanation:

My estimate is 6.82,

4.79

+2.03

6.82.

Question 4.

8.25 – 3.91 = ?

Estimate: ____4.34______

8.25 – 3.91 = __4.34________

Answer:

Estimate : 4.34,

8.25 – 3.91 = 4.34,

Explanation:

My estimate is 4.34,

8.25

-3.91

4.34.

### Everyday Mathematics Grade 5 Home Link 5.13 Answers

**Solving Fraction Division Problems**

Write a number model using a letter for the unknown.

Solve, showing your solution strategy with representations or drawings. Summarize your work with a division number model.

Check your answer using multiplication and

write a number sentence to show how you checked.

Question 1.

Ben has \(\frac{1}{2}\) of a loaf of bread.

If he and his 3 friends share the \(\frac{1}{2}\) loaf equally,

how much of the whole loaf will each person get?

Number model: _____1/2 X 1/4 = 1/8_______

Each person will get __1/2_____ loaf of bread.

Answer:

Number model:

\(\frac{1}{2}\) ÷ 4 = \(\frac{1}{2}\) X \(\frac{1}{4}\) = \(\frac{1}{8}\),

Each person will get \(\frac{1}{2}\) loaf of bread,

Explanation:

Given Ben has \(\frac{1}{2}\) of a loaf of bread.

If he and his 3 friends share the \(\frac{1}{2}\) loaf equally,

Part of the whole loaf will each person get is

Number model:

\(\frac{1}{2}\) ÷ 4 = \(\frac{1}{2}\) X \(\frac{1}{4}\) = \(\frac{1}{8}\),

Each person will get \(\frac{1}{8}\) X 4 = [/latex] = \(\frac{4}{8}\) = \(\frac{1}{2}\) loaf of bread.

Question 2.

Amanda has a piece of ribbon that is \(\frac{1}{4}\) yard long.

She wants to share the ribbon with 2 friends so that they can each wear a ribbon for Breast Cancer Awareness Month.

If each of the 3 friends gets the same amount, how much

ribbon will each person get?

Number model: ____1/4 X 1/3 = 1/12______

Each person will get ___1/4_______ yard of ribbon.

Answer:

Number model:

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

Each person will get \(\frac{1}{4}\) yard of ribbon,

Explanation:

Given Amanda has a piece of ribbon that is \(\frac{1}{4}\) yard long. She wants to share the ribbon with 2 friends so that they can each wear a ribbon for Breast Cancer Awareness Month.

If each of the 3 friends gets the same amount,

Number model:

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

Each person will get ribbon is \(\frac{1}{12}\) X 3 =

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

**Practice**

Make an estimate. Then use U.S. traditional multiplication to solve.

Show your work on the back of this page.

Question 3.

Estimate: ___22,113_____

Answer:

Explanation:

Given 567 X 39 =

Estimate = 567 X 39 =22,113 which is reasonable as shown above.

Question 4.

Estimate: ___71,568_____

Answer:

Explanation:

Given 3,408 X 21 =

Estimate = 3,408 X 21 =71,568 which is reasonable as shown above.

### Everyday Math Grade 5 Home Link 5.14 Answer Key

**More Fraction Division Problems**

For Problems 1 and 2, write a number model using a

letter for the unknown. Solve, showing your solution strategy.

Summarize your work with a division number model.

Check your answer using multiplication, and

write a number sentence to show how you checked.

Question 1.

Charity is packing a 2-pound container of trail mix into

bags for a camping trip.

Each bag holds \(\frac{1}{8}\) pound of trail mix.

If Charity uses all 2 pounds of trail mix,

how many \(\frac{1}{8}\) pound bags will she have?

Number model: __2 ÷ 1/8 =16_______

Charity will have _____16 ,___ \(\frac{1}{8}\) pound bags.

Answer:

Number model: __2 ÷ \(\frac{1}{8}\) =16_______

Charity will have _____16 ,___ \(\frac{1}{8}\) pound bags,

Explanation:

Given Charity is packing a 2-pound container of trail mix into

bags for a camping trip.

Each bag holds \(\frac{1}{8}\) pound of trail mix.

If Charity uses all 2 pounds of trail mix then

Number model = 2 ÷\(\frac{1}{8}\) = 2 X 8 = 16,

Charity will have 16, \(\frac{1}{8}\) pound bags she will have.

Question 2.

Davis has a thin box that is 5 inches wide.

He wants to use the box to store markers that

are \(\frac{1}{2}\) inch wide. If he lines up

the markers side by side and uses the entire width of the box,

how many markers can Davis fit in the box?

Number model: __5 ÷ 1/2 =10________

Davis will be able to fit _____5_____ markers in the box.

Answer:

Number model: 5 ÷ \(\frac{1}{2}\) = 10,

Davis will be able to fit 5 markers in the box,

Explanation:

Given Davis has a thin box that is 5 inches wide.

He wants to use the box to store markers that

are \(\frac{1}{2}\) inch wide. If he lines up

the markers side by side and uses the entire width of the box,

number of markers can Davis fit in the box are

5 ÷ \(\frac{1}{2}\) = 5 X 2 = 10,

So 10 X \(\frac{1}{2}\) = 5 markers in the box.

**Practice**

Make an estimate. Then solve. Show your work on the back of this page

Question 3.

623 ÷ 8 → ____77R7_______

Estimate: ___77R7_____

Answer:

623 ÷ 8 = 77 remainder 7,

Estimate: 77R7,

Explanation:

Given 623 ÷ 8 =

77 R 7

8)623(

56

63

56

7

So, 623 ÷ 8 = 77 remainder 7 and

estimate is also reasonable.

Question 4.

4,495 ÷ 50 → ___89R45________

Estimate: ___89R45________

Answer:

4,495 ÷ 50 = 89 remainder 45,

Estimate: 89R45,

Explanation:

Given 4,495 ÷ 50 =

89 R 45

50)4,495(

4,450

45

So, 4,495 ÷ 50 = 89 remainder 45 and

estimate is also reasonable.