The following steps would be useful to understand how to divide a fraction by another fraction.
Step 1 :
In division of two fractions, change the division 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 :
Simplify :
2/5 ÷ 6/7
Solution :
In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction.
2/5 ÷ 6/7 = 2/5 ⋅ 7/6
Simplify.
2/5 ÷ 6/7 = (2 ⋅ 7)/(5 ⋅ 6)
2/5 ÷ 6/7 = (1 ⋅ 7)/(5 ⋅ 3)
2/5 ÷ 6/7 = 7/15
Example 2 :
Simplify :
7/5 ÷ 3/2
Solution :
In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction.
7/5 ÷ 3/2 = 7/5 ⋅ 2/3
Simplify.
7/5 ÷ 3/2 = (7 ⋅ 2)/(5 ⋅ 3)
7/5 ÷ 3/2 = (7 ⋅ 2)/(5 ⋅ 3)
7/5 ÷ 3/2 = 14/15
Example 3 :
Simplify :
5/12 ÷ 20/13
Solution :
In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction.
5/12 ÷ 20/13 = 5/12 ⋅ 13/20
Simplify.
5/12 ÷ 20/13 = (5 ⋅ 13)/(12 ⋅ 20)
5/12 ÷ 20/13 = (1 ⋅ 13)/(12 ⋅ 4)
5/12 ÷ 20/13 = 13/48
Example 4 :
Simplify :
2/19 ÷ 6 1/2
Solution :
2/19 ÷ 6 1/2 = 2/19 ÷ 13/2
In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction.
2/19 ÷ 6 1/2 = 2/19 ⋅ 2/13
Simplify.
2/19 ÷ 6 1/2 = (2 ⋅ 2)/(19 ⋅ 13)
2/19 ÷ 6 1/2 = 4/247
Example 5 :
David can make one pizza in 1/2 hour. How many pizzas can he make in 5/2 hours ?
Solution :
Time taken to make one pizza is 1/2 hour.
No. of pizzas made in 5/2 hours is
= 5/2 ÷ 1/2
In the division of above two fractions, change the division as multiplication and take reciprocal of the second fraction.
= 5/2 ⋅ 2/1
= (5 ⋅ 2)/(2 ⋅ 1)
= 10/2
= 5
So, David can make 5 pizzas in 5/2 hours.
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