**Modeling fraction division :**

For some real-world problems, we may need to divide a fraction by a fraction.Sometimes, we may need to divide a fraction by a whole number.

Let us see how fraction division can be modeled through some examples.

**Example 1 : **

David has 3/4 cup of salsa for making burritos. Each burrito requires 1/8 cup of salsa. How many burritos can David make ?

**Solution : **

To find the number of burritos that can be made, you need to determine how many 1/8 -cup servings are in 3/4 cup.

In the diagram given below, 3/4 of a whole is divided into quarters and into eighths.

In the whole cup, there are eight 1/8 cups.

But, David has 3/4 cup of salsa.

So, we have to count the number of 1/8 cups in 3/4 cup in the above diagram.

And there are six 1/8 cups in 3/4 cup of salsa.

Hence, David can make 6 burritos from 3/4 cup of salsa.

**Example 2 : **

Five people share 1/2 pound of cheese equally. How much cheese does each person receive?

**Solution : **

To find how much cheese each person receives, you can divide 1/2 pound into 5 equal parts. Use the diagram to determine what fraction of a whole pound each person receives.

In the diagram given below, 1/2 of a whole is divided into halves and into tenths.

In one pound of cheese, there are ten 1/10s.

But, there is 1/2 pound of cheese.

So, we have to count the number of 1/10s in 1/2 pound of cheese.

And there are five 1/10s in 1/2 pound of cheese.

Hence, Each person will receive 1/10 pound of cheese.

**Step 1 :**

When we divide a fraction by another fraction, first we have to change the division sign as multiplication.

**Step 2 :**

Take reciprocal of the second fraction.

**Step 3 :**

Multiply the two fractions. (Numerator times numerator and denominator times denominator).

**Example 1 : **

Divide 2/5 by 6/7

**Solution : **

Using the method explained above, we have

2/5 ÷ 6/7 = 2/5 x 7/6

2/5 ÷ 6/7 = (2x7) / (5x6)

2/5 ÷ 6/7 = 7/15

**Example 2 :**

Divide 7/5 by 3/2

**Solution : **

Using the method explained above, we have

7/5 ÷ 3/2 = 7/5 x 2/3

7/5 ÷ 3/2 = (7x2) / (5x3)

7/5 ÷ 3/2 = 14/15

**Example 3 :**

Divide 5/12 by 20/13

**Solution : **

Using the method explained above, we have

5/12 ÷ 20/13 = 5/12 ÷ 20/13

5/12 ÷ 20/13 = 5/12 x 13/20

5/12 ÷ 20/13 = (5x13) / (12x20)

5/12 ÷ 20/13 = 13/48

**Example 4 :**

Divide 2/19 by 6 1/2

**Solution : **

First, let us convert the mixed number 6 1/2 in to improper fraction.

6 1/2 = 13/2

Now,m we have 2/19 ÷ 6 1/2 = 2/19 ÷ 13/2

Using the method explained above, we have

2/19 ÷ 13/2 = 2/19 x 13//2

2/19 ÷ 13/2 = (2x13) / (19x2)

2/19 ÷ 13/2 = 13 / 19

**Example 5 :**

One pizza can be made in 1/2 hour. How many pizzas can be made in 5/2 hours ?

**Solution : **

Time taken to make one pizza = 1/2 hour

No. of pizzas made in 5/2 hours = 5/2 ÷ 1/2

No. of pizzas made in 5/2 hours = 5/2 x 2/1

No. of pizzas made in 5/2 hours = (5x2) / (2x1)

No. of pizzas made in 5/2 hours = 5

**Method 1 : **

**Step 1 :**

When we divide a fraction by a whole number, first we have to write the whole number as fraction with denominator 1.

**Step 2 :**

Change the division sign as multiplication.

**Step 3 :**

Take reciprocal of the second fraction (Whole number with denominator 1).

**Step 4 :**

Multiply the two fractions. (Numerator times numerator and denominator times denominator).

**Method 2**

To divide a fraction by a whole number,

multiply the denominator of the fraction by the whole number and simplify, if possible.

**Example 1 : **

Simplify : 2/5 ÷ 6

**Solution : **

Using method 1, we have

2/5 ÷ 6 = 2/5 ÷ 6/1

2/5 ÷ 6 = 2/5 x 1/6

2/5 ÷ 6 = (2x1) / (5x6)

2/5 ÷ 6 = 1/15

**Example 2 :**

Simplify : 5/12 ÷ 20

**Solution : **

Using method 2, we have

5/12 ÷ 20 = 5 / (12x20)

5/12 ÷ 20 = 1/48

**Example 3 :**

David eats 1/4 of a pizza and divides the remaining in to two equal parts for his two kids. What is the part of the pizza will each kid receive ?

**Solution : **

Part of the pizza eaten by David = 1/4

Remaining pizza = 3/4

Given : Remaining pizza is divided in to equal parts for his two kids.

So, part of the pizza received by each kid is

= 3/4 ÷ 2

= 3/(4x2)

= 3/8

Hence, each kid will receive 3/8 part of the pizza.

After having gone through the stuff given above, we hope that the students would have understood "Modeling fraction division".

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