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 3 :
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 4 :
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 5 :
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 6 :
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 7 :
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.
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