Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 3 Lesson 3.1 Dividing Fractions to finish your assignments.

## Math in Focus Grade 6 Course 1 A Chapter 3 Lesson 3.1 Answer Key Dividing Fractions

### Math in Focus Grade 6 Chapter 3 Lesson 3.1 Guided Practice Answer Key

**Solve.**

Question 1.

Rina cut 3 paper squares into a number of equal pieces. Each piece was \(\frac{1}{6}\) of a square. Into how many pieces did Rina cut the 3 paper squares?

The model shows that:

Number of one-sixths in 1 paper square =

Number of one-sixths in 3 paper squares = ×

Answer:

Rina cut the 3 paper squares into 18 pieces.

Explanation:

Given that Rina cut 3 paper squares into a number of equal pieces and each piece was \(\frac{1}{6}\) of a square. So the number of many pieces did Rina cut the 3 paper squares is 3 ÷ \(\frac{1}{6}\)

= 3 × 6

= 18 pieces.

**Divide.**

Question 2.

3 ÷ \(\frac{1}{5}\) =

Answer:

3 ÷ \(\frac{1}{5}\) = 15.

Explanation:

The division of 3 ÷ \(\frac{1}{5}\) is 3 × 5 = 15.

Question 3.

7 ÷ \(\frac{1}{4}\) =

Answer:

7 ÷ \(\frac{1}{4}\) = 28.

Explanation:

The division of 7 ÷ \(\frac{1}{4}\) is 7 × 4 = 28.

Question 4.

4 ÷ \(\frac{1}{2}\) =

Answer:

4 ÷ \(\frac{1}{2}\) = 8.

Explanation:

The division of 4 ÷ \(\frac{1}{2}\) is 4 × 2 = 8.

Question 5.

5 ÷ \(\frac{1}{3}\) =

Answer:

5 ÷ \(\frac{1}{3}\) = 15.

Explanation:

The division of 5 ÷ \(\frac{1}{3}\) is 5 × 3 = 15.

Question 6.

6 ÷ \(\frac{1}{5}\) =

Answer:

6 ÷ \(\frac{1}{5}\) = 15.

Explanation:

The division of 6 ÷ \(\frac{1}{5}\) is 6 × 5 = 15.

Question 7.

8 ÷ \(\frac{1}{8}\) =

Answer:

8 ÷ \(\frac{1}{8}\) = 64.

Explanation:

The division of 8 ÷ \(\frac{1}{8}\) is 8 × 8 = 64.

**Hands-On**

**Activity Materials:**

- 5 paper strips

Dividing Whole Numbers By A Fraction

Use 5 paper strips of the same size and length. Each strip represents 1 whole.

Step 1.

Take 2 paper strips. Divide each of them into thirds using vertical lines and place them as shown. Then find 2 ÷ \(\frac{2}{3}\)

Refer to your model.

Complete:

There are two-thirds in the 2 paper strips.

So, 2 ÷ \(\frac{2}{3}\) = .

Step 2.

Divide each of the other 3 paper strips into fourths using vertical lines and place them as shown. Then find 3 ÷ \(\frac{3}{4}\).

Refer to your model.

Complete:

There are three-fourths in the 3 paper strips.

So, 3 ÷ \(\frac{3}{4}\) = .

**Complete:**

Question 8.

Find 7 ÷ \(\frac{3}{4}\)

Question 9.

Mrs. Johnson bought 6 pizzas. She cut them into many equal pieces for the students in her class. Each piece was \(\frac{3}{10}\) of a whole pizza. How many students were there in the class if each child received only one piece of pizza?

Answer:

There were 20 students in the class.

Explanation:

Given that Mrs. Johnson bought 6 pizzas and she cut them into many equal pieces for the students in her class. Each piece was \(\frac{3}{10}\) of a whole pizza. So the number of students were there in the class is 6 ÷ \(\frac{3}{10}\) which is 6 × \(\frac{10}{3}\)

= 2 × 10

= 20 students.

**Divide. Express the quotient in simplest form.**

Question 10.

4 ÷ \(\frac{4}{7}\)

Answer:

4 ÷ \(\frac{4}{7}\) = 7.

Explanation:

The division of 4 ÷ \(\frac{4}{7}\) is 4 × \(\frac{7}{4}\) = 7.

Question 11.

6 ÷ \(\frac{2}{7}\)

Answer:

6 ÷ \(\frac{2}{7}\) = 21.

Explanation:

The division of 6 ÷ \(\frac{2}{7}\) is 6 × \(\frac{7}{2}\) which is 3 × 7 = 21.

Question 12.

9 ÷ \(\frac{3}{8}\)

Answer:

9 ÷ \(\frac{3}{8}\) = 24.

Explanation:

The division of 9 ÷ \(\frac{3}{8}\) is 9 × \(\frac{8}{3}\) which is 3 × 8 = 24.

Question 13.

5 ÷ \(\frac{10}{13}\)

Answer:

6\(\frac{1}{2}\).

Explanation:

The division of 5 ÷ \(\frac{10}{13}\) is 5 × \(\frac{13}{10}\) which is \(\frac{13}{2}\) = 6\(\frac{1}{2}\).

Question 14.

10 ÷ \(\frac{5}{14}\)

Answer:

10 ÷ \(\frac{5}{14}\) = 28.

Explanation:

The division of 10 ÷ \(\frac{5}{14}\) is 10 × \(\frac{14}{5}\) which is 2 × 14 = 28.

Question 15.

12 ÷ \(\frac{9}{10}\)

Answer:

12 ÷ \(\frac{9}{10}\) = 13 \(\frac{1}{3}\).

Explanation:

The division of 12 ÷ \(\frac{9}{10}\) is 12 × \(\frac{10}{9}\) which is \(\frac{40}{3}\) = 13 \(\frac{1}{3}\).

**Hands-On Activity**

**Materials:**

- 2 paper strips

Use 2 paper strips of the same size and length. Each strip represents 1 whole.

Step 1.

Take 1 paper strip and divide it into halves using vertical lines.

Then find \(\frac{1}{2}\) ÷ \(\frac{1}{4}\)

Refer to your model.

Complete:

There are fourths in a half.

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

Step 2.

Find \(\frac{1}{2}\) ÷ \(\frac{1}{4}\) by multiplication.

\(\frac{1}{2}\) ÷ \(\frac{1}{4}\) = Rewrite using the reciprocal of the divisor.

= Multiply.

Step 3.

Divide the other paper strip into one-thirds using vertical lines.

Then find \(\frac{2}{3}\) ÷ \(\frac{1}{6}\).

Refer to your model.

Complete.

Step 4.

Find \(\frac{2}{3}\) ÷ \(\frac{1}{6}\) by multiplication.

\(\frac{2}{3}\) ÷ \(\frac{1}{6}\) = Rewrite using the reciprocal of the divisor

= Multiply.

**Hands-On Activity**

**Dividing Fractions with Remainder**

A pitcher contains \(\frac{4}{5}\) quart of orange juice.

Step 1.

Copy the model and divide

Complete: \(\frac{4}{5}\) qt = qt

Step 2.

Use the model to answer this question.

Into how many glasses, each containing \(\frac{3}{10}\) quart, can the orange juice be poured .

How many quarts of orange juice will be left in the pitcher? qt

Step 3.

Now find the number of glasses by division. Express your answer as a mixed number.

The answer 2\(\frac{2}{3}\) means there are 2 glasses of orange juice, each containing \(\frac{3}{10}\) quart, and a remaining glass of orange juice that contains of \(\frac{2}{3}\) of \(\frac{3}{10}\) quart.

How many quarts of orange juice will be left in the pitcher.

**Complete.**

Question 16.

Adam had \(\frac{5}{7}\) liter of water. He used the water to fill a few glasses completely. The capacity of each glass was \(\frac{2}{7}\) liter. How many glasses of water did Adam fill?

Answer:

Question 17.

Lina had \(\frac{2}{3}\) of a pizza. She cut it into pieces that were each \(\frac{1}{9}\) of the whole pizza. Into how many pieces did she cut it?

Answer:

**Divide. Express the quotient in simplest form.**

Question 18.

\(\frac{2}{3}\) ÷ \(\frac{1}{6}\)

Answer:

\(\frac{2}{3}\) ÷ \(\frac{1}{6}\)

Explanation:

The simplest form of \(\frac{2}{3}\) ÷ \(\frac{1}{6}\) is \(\frac{2}{3}\) × \(\frac{6}{1}\) = 4.

Question 19.

\(\frac{3}{5}\) ÷ \(\frac{1}{10}\)

Answer:

\(\frac{3}{5}\) ÷ \(\frac{1}{10}\) = 6.

Explanation:

The simplest form of \(\frac{3}{5}\) ÷ \(\frac{1}{10}\) is \(\frac{3}{5}\) × \(\frac{10}{1}\) which is 3 × 2 = 6.

Question 20.

\(\frac{3}{4}\) ÷ \(\frac{1}{2}\)

Answer:

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

Explanation:

The simplest form of

\(\frac{3}{4}\) ÷ \(\frac{1}{2}\) = \(\frac{3}{4}\) × \(\frac{2}{1}\) which is \(\frac{3}{2}\) = 1 \(\frac{1}{2}\).

Question 21.

\(\frac{1}{6}\) ÷ \(\frac{2}{3}\)

Answer:

\(\frac{1}{6}\) ÷ \(\frac{2}{3}\) = \(\frac{1}{4}\).

Explanation:

The simplest form of

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

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

Question 22.

\(\frac{5}{8}\) ÷ \(\frac{15}{16}\)

Answer:

\(\frac{5}{8}\) ÷ \(\frac{15}{16}\) = \(\frac{2}{3}\).

Explanation:

The simplest form of

\(\frac{5}{8}\) ÷ \(\frac{15}{16}\) = \(\frac{5}{8}\) × \(\frac{16}{15}\)

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

Question 23.

\(\frac{7}{16}\) ÷ \(\frac{5}{12}\)

Answer:

\(\frac{7}{16}\) ÷ \(\frac{5}{12}\) = 1\(\frac{1}{20}\).

Explanation:

The simplest form of

\(\frac{7}{16}\) ÷ \(\frac{5}{12}\) = \(\frac{7}{16}\) × \(\frac{12}{5}\)

= \(\frac{21}{20}\)

= 1\(\frac{1}{20}\).

**Complete.**

Question 24.

Divide \(\frac{5}{9}\) by 4\(\frac{1}{3}\).

Answer:

Caution

Before finding the reciprocal of a whole number or a mixed number, you need to first write ¡t as an improper fraction.

Question 25.

Divide 2\(\frac{3}{5}\) by 1\(\frac{8}{9}\).

2\(\frac{3}{5}\) and 1\(\frac{8}{9}\) are both mixed numbers. Express the mixed numbers as improper fractions.

Answer:

**Hands-On Activity**

**Division Involving Whole Numbers and Fractions**

Work in pairs.

Step 1.

Find each quotient.

a) 4 ÷ \(\frac{2}{5}\) and \(\frac{2}{5}\) ÷ 4

Answer:

4 ÷ \(\frac{2}{5}\) = 10.

\(\frac{2}{5}\) ÷ 4 = \(\frac{1}{10}\).

Explanation:

The quotient of 4 ÷ \(\frac{2}{5}\) is

4 ÷ \(\frac{2}{5}\) = 4 × \(\frac{5}{2}\)

= 2 × 5

= 10.

And the quotient of \(\frac{2}{5}\) ÷ 4 is

\(\frac{2}{5}\) ÷ 4 = \(\frac{2}{5}\) × \(\frac{1}{4}\)

= \(\frac{1}{10}\).

b) \(\frac{1}{4}\) ÷ \(\frac{2}{3}\) and \(\frac{2}{3}\) ÷ \(\frac{1}{4}\)

Answer:

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

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

Explanation:

The quotient of \(\frac{1}{4}\) ÷ \(\frac{2}{3}\) is

\(\frac{1}{4}\) ÷ \(\frac{2}{3}\) = \(\frac{1}{4}\) × \(\frac{3}{2}\)

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

The quotient of \(\frac{2}{3}\) ÷ \(\frac{1}{4}\) is

\(\frac{2}{3}\) ÷ \(\frac{1}{4}\) = \(\frac{2}{3}\) × \(\frac{4}{1}\)

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

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

c) \(\frac{4}{5}\) ÷ \(\frac{3}{10}\) and \(\frac{3}{10}\) ÷ \(\frac{4}{5}\)

Answer:

\(\frac{4}{5}\) ÷ \(\frac{3}{10}\) = 2\(\frac{2}{3}\).

\(\frac{3}{10}\) ÷ \(\frac{4}{5}\) = \(\frac{3}{8}\).

Explanation:

The quotient of \(\frac{4}{5}\) ÷ \(\frac{3}{10}\) is

\(\frac{4}{5}\) ÷ \(\frac{3}{10}\) = \(\frac{4}{5}\) × \(\frac{10}{3}\)

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

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

And the quotient of \(\frac{3}{10}\) ÷ \(\frac{4}{5}\) is

\(\frac{3}{10}\) ÷ \(\frac{4}{5}\) = \(\frac{3}{10}\) × \(\frac{5}{4}\)

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

d) \(\frac{5}{8}\) ÷ \(\frac{3}{4}\) and \(\frac{3}{4}\) ÷ \(\frac{5}{8}\)

Answer:

\(\frac{5}{8}\) ÷ \(\frac{3}{4}\) = \(\frac{5}{6}\).

\(\frac{3}{4}\) ÷ \(\frac{5}{8}\) = 1\(\frac{1}{5}\).

Explanation:

The quotient of \(\frac{5}{8}\) ÷ \(\frac{3}{4}\) is

\(\frac{5}{8}\) ÷ \(\frac{3}{4}\) = \(\frac{5}{8}\) × \(\frac{4}{3}\)

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

The quotient of \(\frac{3}{4}\) ÷ \(\frac{5}{8}\) is

\(\frac{3}{4}\) ÷ \(\frac{5}{8}\) = \(\frac{3}{4}\) × \(\frac{8}{5}\)

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

= 1\(\frac{1}{5}\).

Step 2.

What do you observe about the products of each pair of quotients?

Step 3.

Given that \(\frac{6}{7}\) ÷ 9 = \(\frac{2}{21}\) and \(\frac{10}{11}\) ÷ \(\frac{5}{6}\) = \(\frac{12}{11}\), find the following quotients mentally.

a) 9 ÷ \(\frac{6}{7}\)

Answer:

9 ÷ \(\frac{6}{7}\) = 10\(\frac{1}{2}\).

Explanation:

The quotient of 9 ÷ \(\frac{6}{7}\) is

9 ÷ \(\frac{6}{7}\) = 9 × \(\frac{7}{6}\)

= \(\frac{21}{2}\)

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

b) \(\frac{5}{6}\) ÷ \(\frac{10}{11}\)

Answer:

\(\frac{5}{6}\) ÷ \(\frac{10}{11}\) = \(\frac{11}{12}\).

Explanation:

The quotient of \(\frac{5}{6}\) ÷ \(\frac{10}{11}\) is

\(\frac{5}{6}\) ÷ \(\frac{10}{11}\) = \(\frac{5}{6}\) × \(\frac{11}{10}\)

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

Math Journal Explain in words the meaning of each division statement.

a) 4 ÷ \(\frac{2}{5}\) and \(\frac{2}{5}\) ÷ 4

Answer:

4 ÷ \(\frac{2}{5}\) = 10.

\(\frac{2}{5}\) ÷ 4 = \(\frac{1}{10}\).

Explanation:

The quotient of 4 ÷ \(\frac{2}{5}\) is

4 ÷ \(\frac{2}{5}\) = 4 × \(\frac{5}{2}\)

= 2 × 5

= 10.

And the quotient of \(\frac{2}{5}\) ÷ 4 is

\(\frac{2}{5}\) ÷ 4 = \(\frac{2}{5}\) × \(\frac{1}{4}\)

= \(\frac{1}{10}\).

b) \(\frac{1}{4}\) ÷ \(\frac{2}{3}\) and \(\frac{2}{3}\) ÷ \(\frac{1}{4}\)

Answer:

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

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

Explanation:

The quotient of \(\frac{1}{4}\) ÷ \(\frac{2}{3}\) is

\(\frac{1}{4}\) ÷ \(\frac{2}{3}\) = \(\frac{1}{4}\) × \(\frac{3}{2}\)

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

And the quotient of \(\frac{2}{3}\) ÷ \(\frac{1}{4}\) is

\(\frac{2}{3}\) ÷ \(\frac{1}{4}\) = \(\frac{2}{3}\) × \(\frac{4}{1}\)

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

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

### Math in Focus Course 1A Practice 3.1 Answer Key

**Divide. Express the quotient ¡n simplest form. Use models to help you.**

Question 1.

1 ÷ \(\frac{1}{4}\)

Answer:

1 ÷ \(\frac{1}{4}\) = 4.

Explanation:

The simplest form of 1 ÷ \(\frac{1}{4}\) is

1 ÷ \(\frac{1}{4}\) = 1 × \(\frac{4}{1}\)

= 4.

Question 2.

3 ÷ \(\frac{3}{5}\)

Answer:

3 ÷ \(\frac{3}{5}\) = 5.

Explanation:

The simplest form of 3 ÷ \(\frac{3}{5}\) is

3 ÷ \(\frac{3}{5}\) = 3 × \(\frac{5}{3}\)

= 5.

Question 3.

\(\frac{3}{4}\) ÷ \(\frac{1}{8}\)

Answer:

\(\frac{3}{4}\) ÷ \(\frac{1}{8}\) = 6.

Explanation:

The simplest form of \(\frac{3}{4}\) ÷ \(\frac{1}{8}\) is

\(\frac{3}{4}\) ÷ \(\frac{1}{8}\) = \(\frac{3}{4}\) × \(\frac{8}{1}\)

= 6.

Question 4.

\(\frac{2}{3}\) ÷ \(\frac{2}{9}\)

Answer:

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

Explanation:

The simplest form of \(\frac{2}{3}\) ÷ \(\frac{2}{9}\) is

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

= 3.

**Draw a model to find each quotient.**

Question 5.

1 ÷ \(\frac{1}{5}\)

Answer:

1 ÷ \(\frac{1}{5}\) = 5.

Explanation:

The quotient of 1 ÷ \(\frac{1}{5}\) is

1 ÷ \(\frac{1}{5}\) = 1 × \(\frac{5}{1}\)

= 5.

Question 6.

4 ÷ \(\frac{8}{9}\)

Answer:

4 ÷ \(\frac{8}{9}\) = 4\(\frac{1}{2}\).

Explanation:

The quotient of 4 ÷ \(\frac{8}{9}\) is

4 ÷ \(\frac{8}{9}\) = 4 × \(\frac{9}{8}\)

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

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

Question 7.

\(\frac{2}{5}\) ÷ \(\frac{3}{10}\)

Answer:

\(\frac{2}{5}\) ÷ \(\frac{3}{10}\) = 1\(\frac{1}{3}\).

Explanation:

The quotient of \(\frac{2}{5}\) ÷ \(\frac{3}{10}\) is

\(\frac{2}{5}\) ÷ \(\frac{3}{10}\) = \(\frac{2}{5}\) × \(\frac{10}{3}\)

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

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

Question 8.

\(\frac{3}{4}\) ÷ \(\frac{3}{16}\)

Answer:

\(\frac{3}{4}\) ÷ \(\frac{3}{16}\) = 4.

Explanation:

The quotient of \(\frac{3}{4}\) ÷ \(\frac{3}{16}\) is

\(\frac{3}{4}\) ÷ \(\frac{3}{16}\) = \(\frac{3}{4}\) × \(\frac{16}{3}\)

= 4.

**Find each quotient. Express your answer in its simplest form.**

Question 9.

4 ÷ \(\frac{1}{7}\)

Answer:

4 ÷ \(\frac{1}{7}\) = 28.

Explanation:

The quotient of 4 ÷ \(\frac{1}{7}\) is

4 ÷ \(\frac{1}{7}\) = 4 × \(\frac{7}{1}\)

= 28.

Question 10.

12 ÷ \(\frac{1}{3}\)

Answer:

12 ÷ \(\frac{1}{3}\) = 36.

Explanation:

The quotient of 12 ÷ \(\frac{1}{3}\) is

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

= 36.

Question 11.

9 ÷ \(\frac{3}{4}\)

Answer:

9 ÷ \(\frac{3}{4}\) = 12.

Explanation:

The quotient of 9 ÷ \(\frac{3}{4}\) is

9 ÷ \(\frac{3}{4}\) = 9 × \(\frac{4}{3}\)

= 3 × 4

= 12.

Question 12.

10 ÷ \(\frac{4}{5}\)

Answer:

10 ÷ \(\frac{4}{5}\) = 12\(\frac{1}{2}\).

Explanation:

The quotient of 10 ÷ \(\frac{4}{5}\) is

10 ÷ \(\frac{4}{5}\) = 10 × \(\frac{5}{4}\)

= \(\frac{25}{2}\)

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

Question 13.

\(\frac{1}{2}\) ÷ \(\frac{1}{8}\)

Answer:

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

Explanation:

The quotient of \(\frac{1}{2}\) ÷ \(\frac{1}{8}\) is

\(\frac{1}{2}\) ÷ \(\frac{1}{8}\) = \(\frac{1}{2}\) × \(\frac{8}{1}\)

= 4.

Question 14.

\(\frac{1}{4}\) ÷ \(\frac{1}{2}\)

Answer:

\(\frac{1}{4}\) ÷ \(\frac{1}{2}\) = \(\frac{1}{2}\).

Explanation:

The quotient of \(\frac{1}{4}\) ÷ \(\frac{1}{2}\) is

\(\frac{1}{4}\) ÷ \(\frac{1}{2}\) = \(\frac{1}{4}\) × \(\frac{2}{1}\)

= \(\frac{1}{2}\).

Question 15.

\(\frac{3}{5}\) ÷ \(\frac{11}{15}\)

Answer:

\(\frac{3}{5}\) ÷ \(\frac{11}{15}\) = 1\(\frac{4}{11}\).

Explanation:

The quotient of \(\frac{3}{5}\) ÷ \(\frac{11}{15}\) is

\(\frac{3}{5}\) ÷ \(\frac{11}{15}\) = \(\frac{3}{5}\) × \(\frac{15}{11}\)

= \(\frac{15}{11}\)

= 1\(\frac{4}{11}\).

Question 16.

\(\frac{2}{3}\) ÷ \(\frac{10}{13}\)

Answer:

\(\frac{2}{3}\) ÷ \(\frac{10}{13}\) = \(\frac{13}{15}\).

Explanation:

The quotient of \(\frac{2}{3}\) ÷ \(\frac{10}{13}\) is

\(\frac{2}{3}\) ÷ \(\frac{10}{13}\) = \(\frac{2}{3}\) × \(\frac{13}{10}\)

= \(\frac{13}{15}\).

Question 17.

\(\frac{5}{6}\) ÷ \(\frac{7}{12}\)

Answer:

\(\frac{5}{6}\) ÷ \(\frac{7}{12}\) = 1\(\frac{3}{7}\).

Explanation:

The quotient of \(\frac{5}{6}\) ÷ \(\frac{7}{12}\) is

\(\frac{5}{6}\) ÷ \(\frac{7}{12}\) = \(\frac{5}{6}\) × \(\frac{12}{7}\)

= \(\frac{10}{7}\)

= 1\(\frac{3}{7}\).

Question 18.

\(\frac{3}{4}\) ÷ \(\frac{9}{16}\)

Answer:

\(\frac{3}{4}\) ÷ \(\frac{9}{16}\) = 1\(\frac{1}{3}\).

Explanation:

The quotient of \(\frac{3}{4}\) ÷ \(\frac{9}{16}\) is

\(\frac{3}{4}\) ÷ \(\frac{9}{16}\) = \(\frac{3}{4}\) × \(\frac{16}{9}\)

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

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

**Find each quotient. Express your answer in its simplest form.**

Question 19.

\(\frac{1}{3}\) ÷ \(\frac{7}{4}\)

Answer:

\(\frac{1}{3}\) ÷ \(\frac{7}{4}\) = \(\frac{4}{21}\).

Explanation:

The quotient of \(\frac{1}{3}\) ÷ \(\frac{7}{4}\) is

\(\frac{1}{3}\) ÷ \(\frac{7}{4}\) = \(\frac{1}{3}\) × \(\frac{4}{7}\)

= \(\frac{4}{21}\).

Question 20.

\(\frac{1}{2}\) ÷ \(\frac{8}{4}\)

Answer:

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

Explanation:

The quotient of \(\frac{1}{2}\) ÷ \(\frac{8}{4}\) is

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

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

Question 21.

\(\frac{1}{9}\) ÷ \(\frac{14}{3}\)

Answer:

\(\frac{1}{9}\) ÷ \(\frac{14}{3}\) = \(\frac{1}{42}\).

Explanation:

The quotient of \(\frac{1}{9}\) ÷ \(\frac{14}{3}\) is

\(\frac{1}{9}\) ÷ \(\frac{14}{3}\) = \(\frac{1}{9}\) × \(\frac{3}{14}\)

= \(\frac{1}{42}\).

Question 22.

\(\frac{5}{8}\) ÷ \(\frac{21}{4}\)

Answer:

\(\frac{5}{8}\) ÷ \(\frac{21}{4}\) = \(\frac{5}{42}\).

Explanation:

The quotient of \(\frac{5}{8}\) ÷ \(\frac{21}{4}\) is

\(\frac{5}{8}\) ÷ \(\frac{21}{4}\) = \(\frac{5}{8}\) × \(\frac{4}{21}\)

= \(\frac{5}{42}\).

Question 23.

3\(\frac{1}{2}\) ÷ 2\(\frac{1}{8}\)

Answer:

3\(\frac{1}{2}\) ÷ 2\(\frac{1}{8}\) = 1 \(\frac{11}{17}\).

Explanation:

The quotient of 3\(\frac{1}{2}\) ÷ 2\(\frac{1}{8}\) is

3\(\frac{1}{2}\) ÷ 2\(\frac{1}{8}\) = \(\frac{7}{2}\) ÷ \(\frac{17}{8}\)

= \(\frac{7}{2}\) × \(\frac{8}{17}\)

= \(\frac{28}{17}\)

= 1 \(\frac{11}{17}\).

Question 24.

5\(\frac{1}{4}\) ÷ 3\(\frac{1}{2}\)

Answer:

5\(\frac{1}{4}\) ÷ 3\(\frac{1}{2}\) = \(\frac{3}{2}\).

Explanation:

The quotient of 5\(\frac{1}{4}\) ÷ 3\(\frac{1}{2}\) is

5\(\frac{1}{4}\) ÷ 3\(\frac{1}{2}\) = \(\frac{21}{4}\) ÷ \(\frac{7}{2}\)

= \(\frac{21}{4}\) × \(\frac{2}{7}\)

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

Question 25.

7\(\frac{3}{5}\) ÷ 8\(\frac{11}{15}\)

Answer:

7\(\frac{3}{5}\) ÷ 8\(\frac{11}{15}\) = \(\frac{114}{131}\).

Explanation:

The quotient of 7\(\frac{3}{5}\) ÷ 8\(\frac{11}{15}\) is

7\(\frac{3}{5}\) ÷ 8\(\frac{11}{15}\) =\(\frac{38}{5}\) ÷ \(\frac{131}{15}\)

= \(\frac{38}{5}\) × \(\frac{15}{131}\)

= \(\frac{114}{131}\).

Question 26.

12\(\frac{2}{3}\) ÷ 5\(\frac{11}{13}\)

Answer:

12\(\frac{2}{3}\) ÷ 5\(\frac{11}{13}\) = 2\(\frac{1}{6}\).

Explanation:

The quotient of 12\(\frac{2}{3}\) ÷ 5\(\frac{11}{13}\) is

12\(\frac{2}{3}\) ÷ 5\(\frac{11}{13}\) = \(\frac{26}{3}\) ÷ \(\frac{76}{13}\)

= \(\frac{38}{3}\) × \(\frac{13}{76}\)

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

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

**Solve. Show your work.**

Question 27.

6 pizzas were shared equally among a group of children. Each child got \(\frac{1}{9}\) of a pizza. How many children were in the group?

Answer:

The number of children were in the group is 54 children.

Explanation:

Given that 6 pizzas were shared equally among a group of children and each child got \(\frac{1}{9}\) of a pizza. So the number of children were in the group is 6 ÷ \(\frac{1}{9}\)

= 6 × 9

= 54 children.

Question 28.

A rectangle has an area of 15 square meters. It ¡s divided into parts, each with an area of \(\frac{3}{8}\) square meter. Into how many parts has the rectangle been divided?

Answer:

The number of parts has the rectangle been divided is 40 square meters.

Explanation:

Given that a rectangle has an area of 15 square meters and it ¡s divided into parts, each with an area of \(\frac{3}{8}\) square meter. So the number of parts has the rectangle been divided is 15 ÷ \(\frac{3}{8}\)

= 15 × \(\frac{8}{3}\)

= 5 × 8

= 40 square meters.

Question 29.

How many \(\frac{3}{8}\)-cup servings are in a pitcher containing 6\(\frac{3}{4}\) cups of orange juice?

Answer:

The number of serving pitchers be 18 cups.

Explanation:

Given that 1 cup contains \(\frac{3}{8}\) servings are in a pitcher containing and the total is 6\(\frac{3}{4}\) which is \(\frac{27}{4}\). So the number of serving pitchers be \(\frac{27}{4}\) ÷ \(\frac{3}{8}\)

= \(\frac{27}{4}\) × \(\frac{8}{3}\)

= 9 × 2

= 18 cups.

Question 30.

Maria buys 8\(\frac{1}{3}\) pounds of beef to make tacos for a party. She uses \(\frac{5}{9}\) pound of beef for each taco. How many tacos can Maria make?

Answer:

The number of tacos can Maria make is 15 tacos.

Explanation:

Given that Maria buys 8\(\frac{1}{3}\) pounds of beef to make tacos for a party which is \(\frac{25}{3}\) and she uses \(\frac{5}{9}\) pound of beef for each taco. So the number of tacos can Maria make is \(\frac{25}{3}\) ÷ \(\frac{5}{9}\)

= \(\frac{25}{3}\) × \(\frac{9}{5}\)

= 5 × 3

= 15.

The capacity of a large milk carton is 1\(\frac{1}{2}\) liters. A dozen large cartons are poured into a container and then poured into small cartons that each hold \(\frac{3}{10}\) liter. How many small cartons of milk can be filled?

Answer:

The number of small cartons of milk that can be filled is 60 cartons.

Explanation:

Given that the capacity of a large milk carton is 1\(\frac{1}{2}\) liters which is \(\frac{3}{2}\), so in pounds, it will be 12 × \(\frac{3}{2}\)

= 6 × 3

= 18.

And a dozen large cartons are poured into a container and then poured into small cartons that each hold \(\frac{3}{10}\) liter. Here, the total number of small cartons of milk can be filled = Total number of pounds of a dozen large cartons ÷ small carton capacity which is

= 18 ÷ \(\frac{3}{10}\)

= 18 × \(\frac{10}{3}\)

= 6 × 10

= 60.

The number of small cartons of milk that can be filled is 60 cartons.