# MODELING FRACTION DIVISION

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.

## Modeling fraction division - 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.

## Using reciprocal to divide fractions - Steps

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).

## Using reciprocal to divide fractions - Examples

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

## Dividing fractions by whole numbers - Methods

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.

## Dividing fractions by whole numbers - Examples

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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