# MODELING MIXED NUMBER DIVISION

## About "Modeling mixed number division"

Modeling mixed number division :

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

Let us see how division of mixed numbers can be modeled through some examples.

## Modeling mixed number division - Examples

Example 1 :

If 1/4 cup of rice is used to make each sushi roll, how many sushi rolls can be made using 2 1/2 cups of rice ?

Solution :

To find the number of sushi rolls that can be made, we need to determine how many fourths are in 2 1/2 .

Since 1/4 cup of rice is used to make each sushi roll, in the diagram given below, 2 1/2 is divided into fourths.

In 1 cup, we have four 1/4 cups of rice.

But, we have 2 1/2 cups of rice.

So, we have to count the number of 1/4 cups in 2 1/2 cups in the above diagram.

And there are ten 1/4 cups in 1 cup of rice.

Hence, we can make 10 sushi rolls from 2 1/2 cups of rice.

Example 2 :

We have 1 1/4 pounds of cheese. And we are going to pack this 1 1/4 pounds of cheese in two cans where each can has the capacity of 5/8 pound. In how many cans can we fill 1 1/4 pounds of cheese ?

Solution :

To find the number of cans required, let us use the diagram given below.

The diagram below represents 2 pounds and it is divided into quarters and into eighths.

We have to fill 1 1/4 pounds of cheese in two cans where each can has the capacity of 5/8 pound.

So, we have to count the number of 5/8 pounds in 1 1/4 pounds.

And there are two 5/8 pounds in 1 1/4 pounds of cheese.

Hence, we can fill 1 1/4 pounds of cheese in two cans.

## Using reciprocal to divide mixed numbers - Steps

Step 1 :

When we divide a mixed number by fraction or another mixed number or whole number, first we have to convert the mixed numbers into fractions.

Step 2 :

Change the division sign as multiplication.

Step 3 :

Take reciprocal of the second number.

Step 3 :

Multiply the two numbers.

## Using reciprocal to divide mixed numbers - Examples

Example 1 :

Divide  3 2/5  by  6/7

Solution :

Using the method explained above, we have

3 2/5 ÷ 6/7  =  17/5 ÷ 7/6

3 2/5 ÷ 6/7  =  (17/5) x (6/7)

3 2/5 ÷ 6/7  =  (17x6) / (5x7)

3 2/5 ÷ 6/7  =  102/35

3 2/5 ÷ 6/7  =  2 32/35

Example 2 :

Divide  2 3/5  by  3

Solution :

Using the method explained above, we have

2 3/5 ÷ 3  =  13/5 ÷ 3

2 3/5 ÷ 3  =  (13/5) x (1/3)

2 3/5 ÷ 3  =  (13x1) x (5x3)

2 3/5 ÷ 3  =  13 / 15

Example 3 :

Divide  1 1/2  by  2 3/5

Solution :

Using the method explained above, we have

1 1/2 ÷ 2 3/5  =  3/2 ÷ 13/5

1 1/2 ÷ 2 3/5  =  3/2 x 5/13

1 1/2 ÷ 2 3/5  =  (3x5) /  (2x13)

1 1/2 ÷ 2 3/5  =  15/26

Example 4 :

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

Solution :

Time taken to make one pizza  =  1/2 hour

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

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

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

No. of pizzas made in 2 1/2 hours  =  (5x2) / (2x1)

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

Example 5 :

David eats 1 1/8 pizzas and divides into two equal parts for his two kids. What is the part of the pizza will each kid receive ?

Solution :

1 1/8 pizzas is divided in to two equal parts for his two kids.

So, amount of part pizza received by each kid is

=  1 1/8 ÷ 2

=  9/8 ÷ 2

=  9/8 x 1/2

=  (9x1) / (8x2)

=  9/16

Hence, the amount of pizza received by each kid is 9/16.

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

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