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

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 = ×

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 ÷ $$\frac{1}{5}$$ =
3 ÷ $$\frac{1}{5}$$ = 15.

Explanation:
The division of 3 ÷ $$\frac{1}{5}$$  is 3 × 5 = 15.

Question 3.
7 ÷ $$\frac{1}{4}$$ =
7 ÷ $$\frac{1}{4}$$ = 28.

Explanation:
The division of 7 ÷ $$\frac{1}{4}$$ is 7 × 4 = 28.

Question 4.
4 ÷ $$\frac{1}{2}$$ =
4 ÷ $$\frac{1}{2}$$ = 8.

Explanation:
The division of 4 ÷ $$\frac{1}{2}$$ is 4 × 2 = 8.

Question 5.
5 ÷ $$\frac{1}{3}$$ =
5 ÷ $$\frac{1}{3}$$ = 15.

Explanation:
The division of 5 ÷ $$\frac{1}{3}$$ is 5 × 3 = 15.

Question 6.
6 ÷ $$\frac{1}{5}$$ =
6 ÷ $$\frac{1}{5}$$ = 15.

Explanation:
The division of 6 ÷ $$\frac{1}{5}$$ is 6 × 5 = 15.

Question 7.
8 ÷ $$\frac{1}{8}$$ =
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 ÷ $$\frac{2}{3}$$

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 ÷ $$\frac{3}{4}$$.

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?

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 ÷ $$\frac{4}{7}$$
4 ÷ $$\frac{4}{7}$$ = 7.

Explanation:
The division of 4 ÷ $$\frac{4}{7}$$ is 4 × $$\frac{7}{4}$$ = 7.

Question 11.
6 ÷ $$\frac{2}{7}$$
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 ÷ $$\frac{3}{8}$$
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 ÷ $$\frac{10}{13}$$
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 ÷ $$\frac{5}{14}$$
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 ÷ $$\frac{9}{10}$$
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 $$\frac{1}{2}$$ ÷ $$\frac{1}{4}$$
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 $$\frac{2}{3}$$ ÷ $$\frac{1}{6}$$.
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?

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?

Divide. Express the quotient in simplest form.

Question 18.
$$\frac{2}{3}$$ ÷ $$\frac{1}{6}$$
$$\frac{2}{3}$$ ÷ $$\frac{1}{6}$$

Explanation:
The simplest form of $$\frac{2}{3}$$ ÷ $$\frac{1}{6}$$ is $$\frac{2}{3}$$ × $$\frac{6}{1}$$ = 4.

Question 19.
$$\frac{3}{5}$$ ÷ $$\frac{1}{10}$$
$$\frac{3}{5}$$ ÷ $$\frac{1}{10}$$ = 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.
$$\frac{3}{4}$$ ÷ $$\frac{1}{2}$$
$$\frac{3}{4}$$ ÷ $$\frac{1}{2}$$ = 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.
$$\frac{1}{6}$$ ÷ $$\frac{2}{3}$$
$$\frac{1}{6}$$ ÷ $$\frac{2}{3}$$ = $$\frac{1}{4}$$.

Explanation:
The simplest form of
$$\frac{1}{6}$$ ÷ $$\frac{2}{3}$$ = $$\frac{1}{6}$$ × $$\frac{3}{2}$$
= $$\frac{1}{4}$$.

Question 22.
$$\frac{5}{8}$$ ÷ $$\frac{15}{16}$$
$$\frac{5}{8}$$ ÷ $$\frac{15}{16}$$ = $$\frac{2}{3}$$.

Explanation:
The simplest form of
$$\frac{5}{8}$$ ÷ $$\frac{15}{16}$$ = $$\frac{5}{8}$$ × $$\frac{16}{15}$$
= $$\frac{2}{3}$$.

Question 23.
$$\frac{7}{16}$$ ÷ $$\frac{5}{12}$$
$$\frac{7}{16}$$ ÷ $$\frac{5}{12}$$ = 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$$\frac{1}{3}$$.

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.

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
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 $$\frac{2}{3}$$ ÷ $$\frac{1}{4}$$
$$\frac{1}{4}$$ ÷ $$\frac{2}{3}$$ = $$\frac{3}{8}$$.
$$\frac{2}{3}$$ ÷ $$\frac{1}{4}$$ = 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 $$\frac{3}{10}$$ ÷ $$\frac{4}{5}$$
$$\frac{4}{5}$$ ÷ $$\frac{3}{10}$$ = 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 $$\frac{3}{4}$$ ÷ $$\frac{5}{8}$$
$$\frac{5}{8}$$ ÷ $$\frac{3}{4}$$ = $$\frac{5}{6}$$.
$$\frac{3}{4}$$ ÷ $$\frac{5}{8}$$ = 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 ÷ $$\frac{6}{7}$$
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) $$\frac{5}{6}$$ ÷ $$\frac{10}{11}$$
$$\frac{5}{6}$$ ÷ $$\frac{10}{11}$$ = $$\frac{11}{12}$$.

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

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 ÷ $$\frac{3}{5}$$

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.
$$\frac{3}{4}$$ ÷ $$\frac{1}{8}$$

$$\frac{3}{4}$$ ÷ $$\frac{1}{8}$$ = 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.
$$\frac{2}{3}$$ ÷ $$\frac{2}{9}$$

$$\frac{2}{3}$$ ÷ $$\frac{2}{9}$$ = 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 ÷ $$\frac{1}{5}$$
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 ÷ $$\frac{8}{9}$$
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.
$$\frac{2}{5}$$ ÷ $$\frac{3}{10}$$
$$\frac{2}{5}$$ ÷ $$\frac{3}{10}$$ = 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.
$$\frac{3}{4}$$ ÷ $$\frac{3}{16}$$
$$\frac{3}{4}$$ ÷ $$\frac{3}{16}$$ = 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.

Question 9.
4 ÷ $$\frac{1}{7}$$
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 ÷ $$\frac{1}{3}$$
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 ÷ $$\frac{3}{4}$$
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 ÷ $$\frac{4}{5}$$
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.
$$\frac{1}{2}$$ ÷ $$\frac{1}{8}$$
$$\frac{1}{2}$$ ÷ $$\frac{1}{8}$$ = 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.
$$\frac{1}{4}$$ ÷ $$\frac{1}{2}$$
$$\frac{1}{4}$$ ÷ $$\frac{1}{2}$$ = $$\frac{1}{2}$$.

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.
$$\frac{3}{5}$$ ÷ $$\frac{11}{15}$$
$$\frac{3}{5}$$ ÷ $$\frac{11}{15}$$ = 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.
$$\frac{2}{3}$$ ÷ $$\frac{10}{13}$$
$$\frac{2}{3}$$ ÷ $$\frac{10}{13}$$ = $$\frac{13}{15}$$.

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.
$$\frac{5}{6}$$ ÷ $$\frac{7}{12}$$
$$\frac{5}{6}$$ ÷ $$\frac{7}{12}$$ = 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.
$$\frac{3}{4}$$ ÷ $$\frac{9}{16}$$
$$\frac{3}{4}$$ ÷ $$\frac{9}{16}$$ = 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$$\frac{1}{3}$$.

Question 19.
$$\frac{1}{3}$$ ÷ $$\frac{7}{4}$$
$$\frac{1}{3}$$ ÷ $$\frac{7}{4}$$ = $$\frac{4}{21}$$.

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.
$$\frac{1}{2}$$ ÷ $$\frac{8}{4}$$
$$\frac{1}{2}$$ ÷ $$\frac{8}{4}$$ = $$\frac{1}{4}$$.

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

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

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$$\frac{1}{8}$$
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$$\frac{1}{2}$$
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$$\frac{11}{15}$$
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$$\frac{11}{13}$$
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$$\frac{1}{6}$$.

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?
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?
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?
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?
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?
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 × $$\frac{3}{2}$$
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 × $$\frac{10}{3}$$