**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.

**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.

**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.

**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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