## Everyday Mathematics 6th Grade Answer Key Unit 2 Fraction Operations and Ratios

### Everyday Math Grade 6 Home Link 2.1 Answer Key

Finding the Greatest Common Factor

Question 1.

Use any method to find the greatest common factor for the number pairs.

a. GCF (42, 56) = ___

b. GCF (32, 80) = ___

c. GCF (72, 16) = ___

d. GCF (10, 40, 25) = ____

Answer:

a. GCF of 42 and 56 = 14.

b. GCF of 32 and 80 = 16.

c. GCF of 72 and 16 = 8.

d. GCF of 10, 40, and 25 = 5.

Explanation:

In the above-given question,

given that,

Use any method to find the greatest common factor for the number pairs.

GCF = Greatest Common Factor.

a. GCF of 42 and 56 = 14.

factors of 42 = 1, 2, 3, 6, 7, 14, 21, and 42.

factors of 56 = 1, 2, 4, 7, 8, 14, 28, and 56.

so among those the greatest common factor is 14.

b. GCF of 32 and 80 = 16.

factors of 32 = 1, 2, 4, 8, 16, and 32.

factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

so among those the greatest common factor is 16.

c. GCF of 72 and 16 = 8.

factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

factors of 16 = 1, 2, 4, 8, and 16.

so among those the greatest common factor is 8.

d. GCF of 10, 40, and 25 = 5.

factors of 10 = 1, 2, 5, and 10.

factors of 40 = 1, 2, 4, 5, 8, 10, 20, and 40.

factors of 25 = 1, 5, and 25.

so among those the greatest common factor is 5.

Question 2.

Explain how you found GCF (42, 56) in Problem 1a.

Answer:

GCF of 42 and 56 = 14.

Explanation:

In the above-given question,

given that,

GCF = Greatest Common Factor.

GCF of 42 and 56 = 14.

factors of 42 = 1, 2, 3, 6, 7, 14, 21, and 42.

factors of 56 = 1, 2, 4, 7, 8, 14, 28, and 56.

so among those, the greatest common factor is 14.

Question 3.

Use the GCF to find an equivalent fraction for \(\frac{48}{64}\). Show your work.

Answer:

48/64 = 3/4.

Explanation:

In the above-given question,

given that,

use the GCF to find an equivalent fraction for 48/64.

48 = 6 x 8.

64 = 8 x 8.

6/8 = 3/4.

6 = 2 x 3.

8 = 2 x 4.

so 48/64 = 6/8.

Question 4.

Jenny will use 28 blue beads and 21 red beads to make identical bracelets.

a. What is the greatest number of bracelets she can make?

Answer:

The greatest number of bracelets she can make = 7.

Explanation:

In the above-given question,

given that,

Jenny will use 28 blue beads and 21 red beads to make identical bracelets.

factors of 28 = 1, 2, 4, 7, 14, and 28.

factors of 21 = 1, 3, 7, and 21.

so among those, the greatest common factor = 7.

b. How many blue beads and how many red beads will be on each bracelet?

Answer:

The number of blue beads and red beads will be on each bracelet = 7.

Explanation:

In the above-given question,

given that,

the number of blue beads = 4.

the number of red beads = 3.

4 + 3 = 7.

so the number of blue beads and red beads will be on each bracelet = 7.

Question 5.

Explain how a set of numbers can have a GCF greater than 1.

Answer:

**Try This**

Question 6.

GCF (12, 24, 30, 42) =

Answer:

GCF of 12, 24, 30, and 42= 6.

Explanation:

In the above-given question,

given that,

GCF of 12, 24, 30, and 42.

factors of 12 = 1, 2, 3, 4, 6, and 12.

factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

factors of 30 = 1, 2, 3, 5, 6, 10, 15, and 30.

factors of 42 = 1, 2, 3, 6, 7, 14, 21, and 42.

so among those, the greatest common factor = 6.

**Practice**

Insert the missing digits to make each number sentence true.

Question 7.

___, ____ 63 – 3,9 ___ 9 = 2,83 ___

Answer:

Question 8.

71, __ 4 ___ – 4,8 6 = 6 ___ ,270

Answer:

### Everyday Mathematics Grade 6 Home Link 2.2 Answers

**Least Common Multiple**

Question 1.

Find the least common multiple for each pair of numbers.

a. LCM (10, 15) = ___

b. LCM (12, 15) = ___

c. LCM (6, 10) = ___

d. LCM (7, 5) = _____

Answer:

a. LCM of 10 and 15 = 30.

b. LCM of 12 and 15 = 60.

c. LCM of 6 and 10 = 30.

d. LCM of 7 and 5 = 35.

Explanation:

In the above-given question,

given that,

LCM of 10 and 15.

2 x 5 = 10.

3 x 5 = 15.

5 x 1 = 5.

2 x 3 x 5 = 30.

so LCM of 10 and 15 = 30.

LCM of 12 and 15.

12 = 3 x 4.

15 = 3 x 5.

3 x 4 x 5 = 60.

LCM of 6 and 10.

6 = 2 x 3.

10 = 2 x 5.

3 x 1 = 3.

5 = 5 x 1.

2 x 3 x 5 = 30.

LCM of 5 and 7.

5 x 7 = 35.

Question 2.

Find the greatest common factor and least common multiple for each pair of numbers.

a. GCF (75, 100) = ___

LCM (75, 100) =

Answer:

a. GCF of 75 and 100 = 25.

b. LCM of 75 and 100 = 300.

Explanation:

In the above-given question,

given that,

LCM of 75 and 100.

75 = 5 x 15.

100 = 5 x 20.

15 = 5 x 3.

20 = 5 x 4.

5 x 5 x 3 x 4 = 300.

GCF of 75 and 100.

75 = 3 x 5 x 5.

100 = 2 x 2 x 5 x 5.

5 x 5 = 25.

b. GCF (36, 48) = ___

LCM (36, 48) =

Answer:

a. GCF of 36 and 48 = 12.

b. LCM of 36 and 48 = 144.

Explanation:

In the above-given question,

given that,

LCM of 36 and 48.

36 = 2 x 2 x 3 x 3.

48 = 2 x 2 x 2 x 2 x 3.

2 x 3 x 2 x 2 x 2 = 144.

GCF of 36 and 48.

36 = 2 x 2 x 3 x 3.

48 = 2 x 2 x 2 x 2 x 3.

2 x 2 x 3 = 12.

Use the LCM to find equivalent fractions with the least common denominator.

Question 3.

\(\frac{3}{4}\) and \(\frac{5}{6}\)

LCM (4, 6) = ____

Fractions: ____

Answer:

LCM of 4 and 6 = 12.

Explanation:

In the above-given question,

given that,

LCM of 4 and 6.

4 = 2 x 2.

6 = 2 x 3.

2 x 2 x 3 = 12.

Question 4.

\(\frac{1}{6}\) and \(\frac{3}{8}\)

LCM (6, 8) = ___

Fractions: ____

Answer:

LCM of 6 and 8 = 24.

Explanation:

In the above-given question,

given that,

LCM of 6 and 8.

8 = 2 x 4.

6 = 2 x 3.

2 x 4 x 3 = 24.

Question 5.

\(\frac{4}{25}\) and \(\frac{4}{15}\)

LCM (25, 15) = ___

Fractions: ____

Answer:

LCM of 25 and 15 = 75.

Explanation:

In the above-given question,

given that,

LCM of 25 and 15.

25 = 5 x 5.

15 = 3 x 5.

5 x 5 x 3 = 75.

Question 6.

a. On a website, there is an ad for jeans every 5 minutes, an ad for sneakers every 10 minutes, and an ad for scarves every 45 minutes.

If they all appeared together at 9:00 P.M., when is the next time they will all appear together? _____

Answer:

The next time they will all appear together = 10:00 P.M.

Explanation:

In the above-given question,

given that,

On a website, there is an ad for jeans every 5 minutes, an ad for sneakers every 10 minutes, and an ad for scarves every 45 minutes.

5 + 10 = 15.

45 + 15 = 60 minutes.

60 minutes = 1 hour.

9:00 + 1 hour = 10: 00.

the next time they will all appear together = 10:00 p.m.

b. Explain how you used GCF or LCM to solve the problem.

Answer:

LCM of 5, 10, and 45 = 450.

GCF of 5, 10, and 45 = 5.

Explanation:

In the above-given question,

given that,

LCM of 5, 10, and 45.

5 = 5 x 1.

10 = 2 x 5.

45 = 3 x 15.

15 = 3 x 5.

2 x 3 x 3 x 5 x 5 = 450.

GCF of 5, 10, and 45.

5 = 1, 5.

10 = 5, 1, 10, and 2.

45 = 1, 45, 15, 3, 5, 9.

among all those, the greatest common factor is 5.

Question 7.

Explain why the LCM is at least as large as the GCF.

Answer:

LCM = Least common multiple.

GCF = greatest common factor.

Explanation:

In the above-given question,

given that,Aa

In LCM we will write the answer as the least common multiple.

In GCF we will write the answer as the greatest common factor.

**Practice**

Estimate.

Question 8.

5,692 âˆ— 3 = ____

Answer:

5692 x 3 = 17076.

Explanation:

In the above-given question,

given that,

5692 x 3.

Question 9.

69 âˆ— 54 = ___

Answer:

69 x 54 = 3726.

Explanation:

In the above-given question,

given that,

69 x 54.

Question 10.

78 âˆ— 123 = ___

Answer:

78 x 123 = 9594.

Explanation:

In the above-given question,

given that,

78 x 123.

### Everyday Math Grade 6 Home Link 2.3 Answer Key

**Fraction-Multiplication Review**

Represent the problem on a number line, and then solve the problem.

Question 1.

\(\frac{2}{3}\)*\(\frac{9}{12}\) = ___

Answer:

2/3 x 9/12 = 0.42.

Explanation:

In the above-given question,

given that,

2/3 x 9/12.

2/3 = 0.6.

9/12 = 0.7.

0.6 x 0.7 = 0.42.

5/12 = 0.42.

2/3 x 9/12 = 5/12.

Question 2.

Maliah has \(\frac{2}{3}\) cup of raisins. She used \(\frac{1}{2}\) of her raisins to make muffins. What fraction of a cup of raisins did she use?

Number sentence: ____

Answer:

2/3 – 1/2 = 0.6.

Explanation:

In the above-given question,

given that,

Maliah has 2/3 cups of raisins.

she used 1/2 of her raisins to make muffins.

2/3 = 0.6.

0.3 + 0.3 = 0.6.

so Maliah use 0.6 cups of her raisins.

Question 3.

On the back of this page, write and solve a number story for \(\frac{1}{4}\) * \(\frac{1}{2}\).

Answer:

1/4 x 1/2 = 1/10.

Explanation:

In the above-given question,

given that,

1/4 x 1/2.

1/4 = 0.25.

1/2 = 0.5.

0.2 x 0.5 = 0.1.

**Try This**

Question 4.

Ryse sprinted \(\frac{3}{4}\) of a lap around the running track at school. A whole lap is \(\frac{1}{4}\) mile. How far did he sprint?

Number sentence: _______

Answer:

3/4 x 1/4 = 1/2.

Explanation:

In the above-given question,

given that,

Ryse sprinted 3/4 of a lap around the running track at school.

A whole lap is 1/4 mile.

3/4 x 1/4.

3/4 = 0.75.

1/4 = 0.25..

0.75 – 0.25 = 0.50.

1/2 = 0.5.

**Practice**

Estimate.

Question 5.

845 Ã· 24 = ___

Answer:

845 Ã· 24 = 35.

Explanation:

In the above-given question,

given that,

845 Ã· 24 = 35.

Question 6.

6,450 Ã· 639 = ___

Answer:

6450 Ã· 639 = 10.

Explanation:

In the above-given question,

given that,

6450 Ã· 639 = 10.

Question 7.

129 Ã· 19 = ___

Answer:

129 Ã· 19 = 10.

Explanation:

In the above-given question,

given that,

129 Ã· 19 = 10.

Everyday Mathematics Grade 6 Home Link 2.4 Answers

**Companion Gardening**

Draw and label area models and write number sentences to represent and solve Problems 1â€“2.

Question 1.

In companion planting, marigold flowers are used to repel insects that harm melon plants. Community gardeners plant \(\frac{2}{3}\) of a rectangular garden bed with melon plants. They plant \(\frac{3}{4}\) of the melon area with marigolds. What fraction of the garden bed will have both plants growing together? _____

Number sentence: _______

Answer:

Question 2.

Two plants that grow well together are tomatoes and basil. This year, \(\frac{1}{5}\) of a garden bed was planted with tomatoes and basil. Next year, the area will be 3 times as large. What will the area be next year? ____

Number sentence: ____

Answer:

First estimate, then use a partial-products diagram to solve Problem 3.

Question 3.

Last year a community garden produced 5\(\frac{1}{3}\) pounds of carrots. This year, better weather resulted in a harvest 2\(\frac{2}{3}\) times as large. How many pounds of carrots were harvested this year?

Estimate: ____

Number sentence: ___

**Practice** Find equivalent fractions.

Question 4.

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

Answer:

3/4 = 9/12.

Explanation:

In the above-given question,

given that,

equivalent fractions of 3/4.

3/4 = 3 x 3/4 x 3.

3 x 3 = 9.

4 x 3 = 12.

3/4 = 9/12.

Question 5.

\(\frac{18}{20}\) =

Answer:

18/20 = 9/10.

Explanation:

In the above-given question,

given that,

equivalent fraction of 18/20.

18/20 = 9 x 2/10 x 2.

9 x 2 = 18.

10 x 2 = 20.

18/20 = 9/10.

Question 6.

\(\frac{6}{7}\) =

Answer:

6/7 = 24/28.

Explanation:

In the above-given question,

given that,

equivalent fraction of 6/7.

6/7 = 6 x 4/7 x 4.

6 x 4 = 24.

7 x 4 = 28.

6/7 = 24/28.

Question 7.

\(\frac{24}{36}\)

Answer:

24/36 = 2/3.

Explanation:

In the above-given question,

given that,

equivalent fraction of 24/36.

24/36 = 60/90.

6/9 = 4/6.

4/6 = 2/3.

24/26 = 2/3.

### Everyday Math Grade 6 Home Link 2.5 Answer Key

**Fraction Multiplication**

Maraâ€™s strategy: \(\frac{6}{8}\) âˆ— \(\frac{2}{3}\) = (6 âˆ— \(\frac{1}{8}\)) âˆ— (2 âˆ— \(\frac{1}{3}\))

= (6 âˆ— 2) âˆ— (\(\frac{1}{8}\) âˆ— \(\frac{1}{3}\))

= 12 âˆ— \(\frac{1}{24}\)

= \(\frac{12}{24}\)

Question 1.

Use Maraâ€™s strategy to rename the fractions as whole numbers and unit fractions. Then group your factors to make the problem easier. Show the steps you use.

a. \(\frac{5}{2}\) âˆ— \(\frac{2}{4}\)=

w

Answer:

\(\frac{10}{8}\).

Explanation:

In the above-given question,

given that,

Use Mara’s strategy to rename the fractions as whole numbers and unit fractions.

(5 âˆ— \(\frac{1}{2}\)) âˆ— (2 âˆ— \(\frac{1}{4}\))

(5 âˆ— 2) âˆ— (\(\frac{1}{2}\) âˆ— \(\frac{1}{4}\))

= 10 âˆ— \(\frac{1}{8}\)

= \(\frac{10}{8}\)

b. \(\frac{10}{8}\) âˆ— \(\frac{8}{10}\) =

Answer:

\(\frac{80}{80}\).

Explanation:

In the above-given question,

given that,

Use Mara’s strategy to rename the fractions as whole numbers and unit fractions.

(10 âˆ— \(\frac{1}{8}\)) âˆ— (8 âˆ— \(\frac{1}{10}\))

(10 âˆ— 8) âˆ— (\(\frac{1}{8}\) âˆ— \(\frac{1}{10}\))

= 80 âˆ— \(\frac{1}{80}\)

= \(\frac{80}{80}\)

c. __ = 12 âˆ— \(\frac{5}{6}\)

Answer:

\(\frac{60}{6}\).

Explanation:

In the above-given question,

given that,

Use Mara’s strategy to rename the fractions as whole numbers and unit fractions.

(12 âˆ— \(\frac{5}{6}\)).

(12 âˆ— 5) âˆ— (\(\frac{1}{6}\).

= 60 âˆ— \(\frac{1}{6}\)

= \(\frac{60}{6}\)

d. ___ = \(\frac{5}{2}\) âˆ— 4

Answer:

\(\frac{20}{2}\).

Explanation:

In the above-given question,

given that,

Use Mara’s strategy to rename the fractions as whole numbers and unit fractions.

(4 âˆ— \(\frac{5}{2}\)).

(4 âˆ— 5) âˆ— (\(\frac{1}{2}\).

= 20 âˆ— \(\frac{1}{2}\)

= \(\frac{20}{2}\)

e. \(\frac{21}{3}\) âˆ— \(\frac{6}{7}\) = ___

Answer:

\(\frac{126}{21}\).

Explanation:

In the above-given question,

given that,

Use Mara’s strategy to rename the fractions as whole numbers and unit fractions.

(21 âˆ— \(\frac{1}{3}\)) âˆ— (6 âˆ— \(\frac{1}{7}\))

(21 âˆ— 6) âˆ— (\(\frac{1}{3}\) âˆ— \(\frac{1}{7}\))

= 126 âˆ— \(\frac{1}{21}\)

= \(\frac{126}{21}\)

f. 9 âˆ— \(\frac{2}{9}\) = ___

Answer:

\(\frac{18}{9}\).

Explanation:

In the above-given question,

given that,

Use Mara’s strategy to rename the fractions as whole numbers and unit fractions.

(9 âˆ— \(\frac{2}{9}\)).

(9 âˆ— 2) âˆ— (\(\frac{1}{9}\).

= 18 âˆ— \(\frac{1}{9}\)

= \(\frac{18}{9}\)

Question 2.

Choose two problems from above that are alike in some way. Describe how they are alike.

Answer:

Use any model or strategy to solve Problems 3â€“4. Write a number sentence.

Question 3.

Samantha had 6 pages of homework. She finished \(\frac{2}{3}\) of her assignment. How many pages did she finish?

Number sentence:

_____________

Answer:

The number of pages did she finish = 5 pages.

Explanation:

In the above-given question,

given that,

Samantha had 6 pages of homework.

She finished 2/3 of her assignment.

2/3 = 0.6.

6 – 0.6 = 5.4.

so the number of pages did she finish = 5 pages.

Question 4.

A room measures 8\(\frac{1}{2}\) feet by 10\(\frac{2}{3}\)feet. What is the area of the room?

Number sentence:

________________

Answer:

\(\frac{160}{6}\).

Explanation:

In the above-given question,

given that,

(8 âˆ— \(\frac{1}{2}\)) âˆ— (10 âˆ— \(\frac{2}{3}\))

(8 âˆ— 10) âˆ— (\(\frac{1}{2}\) âˆ— \(\frac{2}{3}\))

= 80 âˆ— \(\frac{2}{6}\)

= \(\frac{160}{6}\)

Practice

Question 5.

389 âˆ— 17 = _________

Answer:

389 x 17 = 6613.

Explanation:

In the above-given question,

given that,

389 x 17.

Question 6.

____ = 176 âˆ— 48

Answer:

176 x 48 = 8448.

Explanation:

In the above-given question,

given that,

176 x 48.

Question 7.

453 âˆ— 24 = ____

Answer:

453 x 24 = 10872.

Explanation:

In the above-given question,

given that,

453 x 24.

### Everyday Mathematics Grade 6 Home Link 2.6 Answers

**Division Using Home Link 2-6 Common Denominators**

Question 1.

Draw a picture or diagram and solve the problem. Rudi has 4 cups of almonds. His trail mix recipe calls for \(\frac{2}{3}\) cup of almonds. How many batches of trail mix can he make?

Answer:

Question 2.

Use common denominators to solve the problems.

Write a number sentence to show how you rewrote the problem with common denominators.

Check your answers.

a. \(\frac{3}{4}\) Ã· \(\frac{3}{8}\) = _______ Number sentence: _________

Answer:

3/4 Ã· 3/8 = 2.

Explanation:

In the above-given question,

given that,

Use common denominators to solve the problems.

3/4 = 0.75.

3/8 = 0.3.

0.75/0.375 = 2.

b. 3\(\frac{1}{3}\) Ã· \(\frac{5}{6}\) = ___ Number sentence: ____

Answer:

3(1/3) Ã· 5/6 = 4.

Explanation:

In the above-given question,

given that,

Use common denominators to solve the problems.

3 x 3 = 9.

9 + 1 = 10.

10/3 = 3.3.

5/6 = 0.8.

3.3/0.8 = 4.1.

c. \(\frac{36}{8}\) Ã· \(\frac{1}{2}\) = ___ Number sentence: _______

Answer:

36/8 Ã· 1/2 = 9.

Explanation:

In the above-given question,

given that,

Use common denominators to solve the problems.

36/8 = 4.5.

1/2 = 0.5.

4.5/0.5 = 9.

Question 3.

Michelle is cutting string to make necklaces. She has 15 feet of string. She needs 1\(\frac{1}{2}\) feet of string for each necklace.

How many necklaces can she make? Number model: ______ Solution: _________

Answer:

The number of necklaces she can make = 10.

Explanation:

In the above-given question,

given that,

Michelle is cutting string to make necklaces.

She has 15 feet of string.

she needs 3/2 feet of string for each necklace.

3/2 = 1.5.

1.5 x 10 = 15.

so she can make 10 necklaces.

Question 4.

A rectangular window has an area of 4\(\frac{1}{2}\) square meters. Its width is \(\frac{3}{4}\) meter. What is its length?

Number model: ____ Solution: ___

Answer:

The length of the rectangular window = 6 m.

Explanation:

In the above-given question,

given that,

A rectangular window has an area of 4 x 1/2 sq m.

4 x 2 = 8.

8 + 1 = 9.

9/2 = 4.5.

width = 3/4.

3/4 = 0.75.

area = l x w.

4.5 = l x 0.75.

l = 4.5/0.75.

length = 6.

so the length of the rectangular window = 6 meters.

Practice

Solve.

Question 5.

GCF (20, 30) = ___

Answer:

GCF of 20 and 30 = 10.

Explanation:

In the above-given question,

given that,

GCF of 2 and 30.

GCF = greatest common factor.

factors of 20 = 1, 2, 4, 5, 10, and 20.

factors of 30 = 1, 2, 3, 5, 6, 10, 15, and 30.

among all those 10 is the common factor.

Question 6.

GCF (6, 16) = ___

Answer:

GCF of 6 and 16 = 2.

Explanation:

In the above-given question,

given that,

GCF of 6 and 16.

GCF = greatest common factor.

factors of 6 = 1, 2, and 3.

factors of 16 = 1, 2, 4, and 8.

among all those 2 is the common factor.

Question 7.

GCF (36, 54) = __

Answer:

GCF of 36 and 54 = 2.

Explanation:

In the above-given question,

given that,

GCF of 36 and 54.

GCF = greatest common factor.

factors of 36 = 1, 2, and 3.

factors of 54 = 1, 2, 4, and 8.

among all those 2 is the common factor.

### Everyday Math Grade 6 Home Link 2.7 Answer Key

**More Exploring Fraction Division**

For problems 1â€“3, circle the best estimate and the correct number model. Then solve the problem.

Question 1.

Stan is in wood working class with 6 friends. They have to split a board that is 4\(\frac{2}{3}\) feet long equally among the seven of them. How long will each personâ€™s piece be?

Answer: ____

The long will each person’s piece be = 4.6 feet.

Explanation:

In the above-given question,

given that,

Stan is in woodworking class with 6 friends.

They have to split a board that is 4\(\frac{2}{3}\) feet long equally among the seven of them.

4(2/3) = 3 x 4 = 12.

12 + 2 = 14.

14/3 = 4.6.

Question 2.

The area of a rectangle is 10\(\frac{1}{2}\) square feet. The length is 5\(\frac{1}{4}\) feet. How wide is the rectangle?

Answer: ____

The width of the rectangle = 2 ft.

Explanation:

In the above-given question,

given that,

the area of a rectangle is 10(1/2) sq ft.

length = 5 (1/4) ft.

10 x 2 = 20.

20 + 1 = 21.

21/2 = 10.5.

5 x 4 = 20.

20 + 1 = 21.

21/4 = 5.25.

area = l x w.

10.5 = 5.25 x w.

w = 10.5/5.25.

w = 2 ft.

so the width of the rectangle = 2 ft.

Question 3.

Sounya walks dogs on Saturdays. It takes \(\frac{3}{4}\) of an hour to walk each dog. She has 5\(\frac{1}{4}\) hours. How many dogs can she walk?

Answer: ___

The number of dogs she can walk = more than 5 dogs.

Explanation:

In the above-given question,

given that,

Sounya walks dogs on Saturdays.

It takes 3/4 of an hour to walk each dog.

she has 5(1/4) hours.

3/4 = 0.75.

5(1/4) = 5 x 4 = 20.

20 + 1 = 21.

21/4 = 5.25.

Practice

Find the LCM.

Question 4.

LCM (3, 7) = ___

Answer:

LCM of 3 and 7 = 21.

Explanation:

In the above-given question,

given that,

LCM of 3 and 7.

LCM = least common multiple.

3 = 3 x 1.

7 = 7 x 1.

3 x 7 = 21.

Question 5.

LCM (8, 4) = __

Answer:

LCM of 8 and 4 = 8.

Explanation:

In the above-given question,

given that,

LCM of 8 and 4.

LCM = least common multiple.

4 = 2 x 2.

2 = 2 x 1.

8 = 2 x 4.

4 = 2 x 2.

2 = 2 x 1.

2 x 2 x 2 = 8.

Question 6.

LCM (10, 4) = ___

Answer:

LCM of 10 and 4 = 20.

Explanation:

In the above-given question,

given that,

LCM of 10 and 4.

LCM = least common multiple.

10 = 2 x 5.

4 = 2 x 2

5 = 5 x 1.

2 x 2 x 5 = 20.

### Everyday Mathematics Grade 6 Home Link 2.8 Answers

**Fraction Division**

Rewrite and solve the division problems using the Division of Fractions Property.

Example: \(\frac{3}{8}\) Ã· \(\frac{2}{5}\) = \(\frac{3}{8}\) âˆ— \(\frac{5}{2}\) = \(\frac{15}{16}\)

Question 1.

3 Ã· \(\frac{2}{3}\) = ___

Answer:

3 Ã· 2/3 = 9/2.

Explanation:

In the above-given question,

given that,

3 Ã· 2/3.

3 Ã· 3/2.

9/2.

Question 2.

\(\frac{1}{5}\) Ã· \(\frac{8}{9}\) = ___

Answer:

\(\frac{9}{40}\).

Explanation:

In the above-given question,

given that,

\(\frac{1}{5}\) Ã· \(\frac{8}{9}\)

\(\frac{1}{5}\) âˆ— \(\frac{8}{9}\).

\(\frac{1}{5}\) âˆ— \(\frac{9}{8}\).

\(\frac{9}{40}\)

Question 3.

4 Ã· \(\frac{5}{7}\) = ___

Answer:

\(\frac{28}{5}\)

Explanation:

In the above-given question,

given that,

4 Ã· \(\frac{5}{7}\)

4 âˆ— \(\frac{5}{7}\).

4 âˆ— \(\frac{7}{5}\).

\(\frac{28}{5}\)

Question 4.

1\(\frac{2}{3}\) Ã· \(\frac{3}{5}\) = ______

Answer:

\(\frac{25}{9}\)

Explanation:

In the above-given question,

given that,

1\(\frac{2}{3}\) Ã· \(\frac{3}{5}\)

\(\frac{5}{3}\) âˆ— \(\frac{3}{5}\).

\(\frac{5}{3}\) âˆ— \(\frac{5}{3}\).

\(\frac{25}{9}\)

Question 5.

\(\frac{2}{5}\) Ã· \(\frac{3}{4}\) = ____

Answer:

\(\frac{8}{15}\).

Explanation:

In the above-given question,

given that,

\(\frac{2}{5}\) Ã· \(\frac{3}{4}\)

\(\frac{2}{5}\) âˆ— \(\frac{3}{4}\).

\(\frac{2}{5}\) âˆ— \(\frac{4}{3}\).

\(\frac{8}{15}\)

Question 6.

\(\frac{3}{5}\) Ã· 4 = ____

Answer:

\(\frac{20}{3}\)Explanation:

In the above-given question,

given that,

4 Ã· \(\frac{3}{5}\)

4 âˆ— \(\frac{3}{5}\).

4 âˆ— \(\frac{5}{3}\).

\(\frac{20}{3}\)

Question 7.

How many \(\frac{1}{4}\)-cup servings of cottage cheese are in a 3-cup container?

Division number model: ______ Multiplication number model: _______

Solution: _________

Answer:

\(\frac{12}{1}\)

Explanation:

In the above-given question,

given that,

3 Ã· \(\frac{1}{4}\)

3 âˆ— \(\frac{1}{4}\).

3 âˆ— \(\frac{4}{1}\).

\(\frac{12}{1}\)

Question 8.

Philip went on a 3\(\frac{1}{2}\)-mile hike. He hiked for 2 hours.

About how far did he go in 1 hour?

Division number model: ____ Multiplication number model: ______

Solution: _________

Answer:

Question 9.

Adam is using ribbon to decorate name tags for the class picnic.

He has 8\(\frac{2}{3}\) feet of blue ribbon. He needs \(\frac{1}{3}\) foot of ribbon for each name tag. How many name tags can he decorate?

Division number model: ______ Multiplication number model: ________

Solution: _______

Answer:

The number ofÂ name tags he can decorate = 28.

Explanation:

In the above-given question,

given that,

Adam is using ribbon to decorate name tags for the class picnic.

he as 8(2/3) feet of blue ribbon.

8 x 3 = 24.

24 + 2 = 26.

26/3 = 8.6.

1/3 = 0.3.

0.3 x 28 = 8.6.

so the number of name tags he can decorate = 28.

**Practice**

Add or subtract.

Question 10.

$4.50 + $3 = ___

Answer:

$4.50 + $3 = $7.5.

Explanation:

In the above-given question,

given that,

Add or Subtract.

$4.50 + $3.

$7.5.

Question 11.

$5.00 – $3.20 = ___

Answer:

$5 – $3.2 = $1.8.

Explanation:

In the above-given question,

given that,

Add or Subtract.

$5 – $3.2.

$1.8.

Question 12.

___ = $6.30 + $0.45 + $1.35

Answer:

$6.30 + $0.45 + $1.35 = $8.1

Explanation:

In the above-given question,

given that,

$6.30 + $0.45 + $1.35.

$6.30 + $0.45 = $6.75.

$6.75 + $1.35 = $8.1.

## Everyday Math Grade 6 Home Link 2.9 Answer Key

**Using Ratios to Represent Situations**

Question 1.

Lenoreâ€™s dog gave birth to a litter of 9 puppies.

Two of the puppies are male. Write ratios for the following:

Number of female puppies to the total number of puppies ___________

Number of male puppies to female puppies ________

Answer:

The number of female puppies to the total number of puppies = 7: 9.

The number of male puppies to the total number of puppies = 2: 9.

Explanation:

In the above-given question,

given that,

Lenoreâ€™s dog gave birth to a litter of 9 puppies.

Two of the puppies are male.

The number of female puppies to the total number of puppies = 7: 9.

The number of male puppies to the total number of puppies = 2: 9.

For Problems 2â€“4, draw a picture to help you solve the problem. Record a ratio.

Question 2.

There are 15 tiles. 2 out of 5 tiles are white. How many tiles are white? ____ Write the ratio of white tiles to total tiles.

Answer:

The ratio of white tiles to total tiles = 5:15.

Explanation:

In the above-given question,

given that,

There are 15 tiles.

2 out of 5 tiles are white.

5:15.

so the ratio of white tiles to the total tiles = 5;15.

Question 3.

There are 24 tiles. 3 out of 4 tiles are white. How many tiles are white? ___ Write the ratio of white tiles to shaded tiles.

Answer:

The ratio of white tile to shaded tiles = 3:20.

Explanation:

In the above-given question,

given that,

There are 24 tiles.

3 out of 4 tiles are white.

3: 20.

so the ratio of white tiles to shaded tiles = 3:20.

Question 4.

There are 3 times as many white tiles as there are shaded tiles. Write this ratio. How many tiles are white if there are 12 tiles in total?

Answer:

The number of tiles are white = 9.

Explanation:

In the above-given question,

given that,

There are 3 times as many white tiles as there are shaded tiles.

3 x 3 = 9.

so the number of tiles are white = 9.

Question 5.

The Mighty Marble Company fills bags of marbles with a ratio of 3 Special Swirls out of every 9 marbles. How many Special Swirls are in a bag that has 21 marbles? ____

Answer:

The number of Special Swirls are in a bag that has 21 marbles = 7.

Explanation:

In the above-given question,

given that,

The Mighty marble Company fills bags of marbles with a ratio of 3 special swirls out of every 9 marbles.

3 x 3 = 9.

6 x 3 = 18.

7 x 3 = 21.

so the number of special swirls are in a bag that has 21 marbles = 7.

**Try This**

Question 6.

One class of 28 students has a ratio of 3 girls to 4 boys. What is the ratio for the number of boys to total number of students in the class?

______________

There are 60 girls in the whole sixth grade and the ratio is the same. How many students are there in sixth grade?

Answer:

The total number of boys to the total number of students = 7:28.

Explanation:

In the above-given question,

given that,

One class of 28 students has a ratio of 3 girls to 4 boys.

7 x 4 = 28.

7: 28.

so the total number of boys to the total number of students = 7:28.

**Practice** Solve.

Question 7.

\(\frac{5}{6}\) âˆ— \(\frac{3}{4}\) = ___

Answer:

5/6 x 3/4 = 0.6225.

Explanation:

In the above-given question,

given that,

5/6 x 3/4.

5/6 = 0.8.

3/4 = 0.75.

0.83 x 0.75 = 0.6225.

Question 8.

\(\frac{2}{3}\) âˆ— 1\(\frac{1}{2}\) = ___

Answer:

2/3 x 3/2 = 0.9.

Explanation:

In the above-given question,

given that,

2/3 x 1(1/2).

2 x 1 = 2.

2 + 1 = 3.

3/2 = 1.5.

2/3 = 0.6.

2/3 x 3/2 = 0.9.

Question 9.

\(\frac{8}{9}\) âˆ— \(\frac{2}{7}\) =

Answer:

8/9 x 2/7 = 0.16.

Explanation:

In the above-given question,

given that,

8/9 x 2/7.

8/9 = 0.8.

2/7 = 0.2.

8/9 x 2/7 = 0.16.

### Everyday Mathematics Grade 6 Home Link 2.10 Answers

**More with Tape Diagrams**

Draw tape diagrams to solve the problems. Label your diagrams and your answers.

Frances is helping her father tile their bathroom floor. They have tiles in two colors: green and white. They want a ratio of 2 green tiles to 5 white tiles.

a. They use 30 white tiles. How many green tiles do they use?

______________

Answer:

b. How many white tiles would they need if they use 16 green tiles?

Answer:

c. They use 35 tiles in all. How many are green?

Answer:

d. They use 49 tiles. How many of each color did they use?

Answer:

e. Explain how you used the tape diagram to solve Part d.

Answer:

**Try This**

Question 2.

Frances and her father decide to also tile their kitchen floor. For every 3 white tiles they plan to use 7 green tiles. The kitchen floor has room for 63 tiles total. Explain why they cannot cover the kitchen floor using the ratio 3 : 7.

Answer:

Yes, they cannot cover the kitchen floor using 3:7.

Explanation:

In the above-given question,

given that,

Frances and her father decide to also tile their kitchen floor.

For every 3 white tiles, they plan to use 7 green tiles.

but they used to keep for every 9 white tiles they plan to use 7 green tiles.

7 x 9 = 63.

**Practice** Divide.

Question 3.

\(\frac{4}{5}\) Ã· \(\frac{1}{5}\) = ____

Answer:

4/5 Ã· 1/5 = 4.

Explanation:

In the above-given question,

given that,

4/5 = 0.8.

1/5 = 0.2.

0.8/0.2 = 4.

4/5 Ã· 1/5 = 4.

Question 4.

\(\frac{1}{5}\) Ã· \(\frac{4}{5}\) = ____

Answer:

1/5 Ã· 4/5 = 1/4.

Explanation:

In the above-given question,

given that,

4/5 = 0.8.

1/5 = 0.2.

0.2/0.8 = 0.25.

1/5 Ã· 4/5 = 1/4.

Question 5.

7 Ã· \(\frac{1}{2}\) = _____

Answer:

7 Ã· 1/2 = 14.

Explanation:

In the above-given question,

given that,

1/2 = 0.5.

7 Ã· 0.5 = 14.

Everyday Mathematics Grade 6 Home Link 2.11 Answers

Finding Equivalent Ratios

Use the pictures to help you figure out the equivalent ratios

Question 1.

Answer:

1 foot = 12 inches.

3 feet = 36 inches.

7 feet = 84 inches.

144 inches = 12 feet.

Explanation:

In the above-given question,

given that,

the ratio of the foot to inches.

1 foot = 12 inches.

3 feet = 36 inches.

3 x 12 = 36.

7 feet = 84 inches.

7 x 12 = 84.

12 feet = 144 inches.

12 x 12 = 144.

Question 2.

Answer:

10 mm = 1 cm.

50 mm = 5 cm.

3000 mm = 300 cm.

250 mm = 25 cm.

Explanation:

In the above-given question,

given that,

the ratio of the mm to cm.

10 mm = 1 cm.

50 mm = 5 cm.

5 x 10 = 50 mm.

3000 mm = 300 cm.

300 x 10 = 3000.

250 mm = 25 cm.

25 x 10 = 250.

Question 3.

Answer:

8 legs = 1 spider.

Explanation:

In the above-given question,

given that,

the ratio of the legs to the spider.

8 legs are there in the figure.

8 legs = 1 spider.

Question 4.

a. Circle the similar rectangles.

Answer:

The rectangles are not similar.

Explanation:

In the above-given question,

given that,

circle the similar rectangles.

the area of the rectangle = l x b.

where l = length and b = breadth.

the area ofÂ A = 4 x 2.

4 x 2 = 8.

rectangle B = 3 x 2

3 x 2 = 6.

rectangle C = 6 x 4.

6 x 4 = 24.

rectangle D = 5 x 1.

5 x 1 = 5.

b. Explain why the rectangles you circled are similar.

Answer:

The rectangles are not similar.

Explanation:

In the above-given question,

given that,

rectangle A = 4 x 2.

4 x 2 = 8.

rectangle B = 3 x 2

3 x 2 = 6.

rectangle C = 6 x 4.

6 x 4 = 24.

rectangle D = 5 x 1.

5 x 1 = 5.

so the rectangles are not similar.

c. Under each rectangle, use fraction notation to write the width-to-height ratio.

Answer:

Rectangle A = 4 : 2.

Rectangle B = 3 : 2.

Rectangle C = 6 : 4.

Rectangle D = 5 : 1.

Explanation:

In the above-given question,

given that,

rectangle A = 4 x 2.

4 x 2 = 8.

rectangle B = 3 x 2

3 x 2 = 6.

rectangle C = 6 x 4.

6 x 4 = 24.

rectangle D = 5 x 1.

5 x 1 = 5.

**Practice** Multiply mentally to find the cost.

Question 5.

4 pens at $2.98 each ___

Answer:

4 x $2.98 = 11.92.

Explanation:

In the above-given question,

given that,

4 pens at $2.98 each.

4 x $2.98.

11.92.

Question 6.

3 books at $24.95 each ____

Answer:

3 x $24.95 = $74.85.

Explanation:

In the above-given question,

given that,

3 books at $24.95 each.

3 x $24.95.

$74.85.

### Everyday Math Grade 6 Home Link 2.12 Answer Key

**Using Ratios to Make Fruit Cups**

Oliver has two fruit-cup recipes that have different ratios of raspberries and watermelon.

Question 1.

a. Which fruit-cup recipe would have a stronger raspberry taste? ______

Answer:

Recipe A has a stronger raspberry taste.

Explanation:

In the above-given question,

given that,

Oliver has two fruit-cup recipes that have different ratios of raspberries and watermelon.

Recipe A has 2 cups raspberries and 3 cups watermelon.

Recipe B has 5 cups raspberries 11 cups total.

so Recipe A has a stronger raspberry taste.

b. Draw a picture or diagram to support your answer.

Answer:

c. Explain how your picture or diagram supports your answer.

Answer:

Question 2.

Create a fruit-cup recipe that would taste the same as Recipe B, but uses more than 11 cups of fruit.

List your ingredients: ______

Answer:

The ingredients are bananas and grapes.

Explanation:

In the above-given question,

given that,

create a fruit-cup recipe that would taste the same as Recipe B, but uses more than 11 cups of fruit.

the 8 cups of bananas and 4 cups of grapes.

Question 3.

Create a fruit-cup recipe that would make a fruit cup with a weaker raspberry taste than Recipes A and B.

List your ingredients: _______

Answer:

The ingredients are bananas and grapes.

Explanation:

In the above-given question,

given that,

create a fruit-cup recipe that would make a fruit cup with a weaker raspberry taste than recipes A and B.

the 8 cups of bananas and 3 cups of grapes.

**Try This**

Question 4.

If you only want 1 cup of fruit salad made from Recipe A, what measurements of watermelon and raspberries do you need?

Answer:

**Practice** Divide.

Question 5.

560 Ã· 7 = ____

Answer:

560 Ã· 7 = 80.

Explanation:

In the above-given question,

given that,

560 / 8.

Question 6.

842 Ã· 2 = ____

Answer:

842 Ã· 2 = 421.

Explanation:

In the above-given question,

given that,

842 / 2.

Question 7.

930 Ã· 3 = ____

Answer:

930 Ã· 3 = 310.

Explanation:

In the above-given question,

given that,

930 / 3.

Everyday Math Grade 6 Home Link 2.13 Answer Key

**Ratio/Rate Tables and Unit Rates**

Question 1.

List three examples of a rate:

____________

Draw a ratio/rate table to solve each problem. The first table has been drawn for you, but it is not complete.

Answer:

Question 2.

One 12-ounce can of frozen juice is mixed with three 12-ounce cans of water. How many cans of water do you need for 4 cans of juice?

_____________

Answer:

The number of cans of water need for 4 cans of juice = 12 cans.

Explanation:

In the above-given question,

given that,

One 12-ounce can of frozen juice is mixed with three 12-ounce cans of water.

1 x 3 = 3.

4 x 3 = 12.

so the 4 cans of juice are mixed with 12 cans of water.

Question 3.

A hikerâ€™s map has a scale of 3 inches to 10 miles. The trail is 4 inches long on the map. How long is the actual hike? ______

Answer:

Question 4.

Amy types 125 words in 2 minutes. About how long will it take her to type a 1,500-word report? ____

Answer:

Amy types a 1,500-word report in 24 minutes.

Explanation:

In the above-given question,

given that,

Amy types 125 words in 2 minutes.

125 + 125 = 250.

250 x 6 = 1500.

Amy types a 1,500-word report in 24 minutes.

**Try This**

Question 5.

A recipe for lime salad dressing calls for \(\frac{1}{4}\) cup lime juice and \(\frac{3}{4}\) cup olive oil. How much lime juice would you use with 1 cup olive oil? _______

Answer:

**Practice** Record >, <, or =.

Question 6.

-3 ___ -5

Answer:

-3 > -5.

Explanation:

In the above-given question,

given that,

-3 and -5.

-3 is greater than -5.

-3 > -5.

Question 7.

6 ____ -7

Answer:

6 > -7.

Explanation:

In the above-given question,

given that,

6 and -7.

6 is greater than -7.

6 > -7.

Question 8.

-8 ____ -9

Answer:

-8 > -9.

Explanation:

In the above-given question,

given that,

-8 and -9.

-8 is greater than -9.

-8 > -9.

Everyday Math Grade 6 Home Link 2.14 Answer Key

Graphing Rates

Snails move slowly. Jada, Reality, and Barb had a snail race. Then they compared the rates at which the snails crawled.

Question 1.

Fill in the ratio/rate table with equivalent rates.

Answer:

Question 2.

Treat each rate as an ordered pair. Graph each snailâ€™s rate using a different color.

Answer:

Question 3.

Which snail is the fastest? Use the graph to explain how you know

Answer:

**Practice** Insert >, <, or = to make each sentence true.

Question 4.

7 ___ 4.65

Answer:

7 > 4.65.

Explanation:

In the above-given question,

given that,

7 and 4.65.

7 is greater than 4.65.

4.65 = 5.

7 > 4.65.

Question 5.

0.1 __ 0.01

Answer:

0.1 > 0.01.

Explanation:

In the above-given question,

given that,

0.1 and 0.01.

0.1 is greater than 0.01.

0.1 > 0.01.

Question 6.

0.205 ___ 0.22

Answer:

0.205 < 0.22.

Explanation:

In the above-given question,

given that,

0.205 and 0.22.

0.205 is less than 0.22.

0.205 < 0.22.