COMPLEX FRACTIONS
Complex Fractions :
A complex fraction is a fraction where the numerator, denominator or both contain fraction.
Examples :
(a/b) / c
a / (b/c)
(a/b) / (c/d)
Complex Fractions - Practice Problems with Solutions
Problem 1 :
Find the value of :
(2/5) / (7/15)
Solution :
In the above complex fraction, change the division as multiplication and take reciprocal of fraction in denominator.
(2/5) / (7/15) = 2/5 ⋅ 15/7
Simplify.
(2/5) / (7/15) = (2 ⋅ 3) / (1 ⋅ 7)
(2/5) / (7/15) = 6/7
Problem 2 :
Find the value of :
(7/10) / (-1/5)
Solution :
In the above complex fraction, change the division as multiplication and take reciprocal of fraction in denominator.
(7/10) / (-1/5) = 7/10 ⋅ (-5/1)
Simplify.
(7/10) / (-1/5) = [7 ⋅ (-5)] / (10 ⋅ 1)
(7/10) / (-1/5) = [7 ⋅ (-1)] / (2 ⋅ 1)
(7/10) / (-1/5) = -7/2
Problem 3 :
Find the value of :
(3/7) / 5
Solution :
In the above complex fraction, change the division as multiplication and take reciprocal of integer in denominator.
(3/7) / 5 = 3/7 ⋅ 1/5
Simplify.
(3/7) / 5 = (3 ⋅ 1) / (7 ⋅ 5)
(3/7) / 5 = 3 / 35
Problem 4 :
Find the value of :
4 / (16/21)
Solution :
In the above complex fraction, change the division as multiplication and take reciprocal of the fraction in denominator.
4 / (16/21) = 4 ⋅ 21/16
Simplify.
(3/7) / 5 = (3 ⋅ 1) / (7 ⋅ 5)
(3/7) / 5 = 3 / 35
Problem 5 :
Maya wants to divide a 3/4 pound box of trail mix into small bags. Each bag will hold 1/12 pound of trail mix. How many bags of trail mix can Maya fill ?
Solution :
Given : Each bag will hold 1/12 pound of trail mix.
Amount of trail mix each bag holds = 1/12 pound.
Then, the number bags required for 3/4 pounds of trail mix is
= (3/4) / (1/12)
In the above complex fraction, change the division as multiplication and take reciprocal of the fraction in denominator.
= 3/4 ⋅ 12/1
Simplify.
= (3 ⋅ 12) / (4 ⋅ 1)
= (3 ⋅ 3) / (1 ⋅ 1)
= 9 / 1
= 9
So, Maya can fill 3/4 pound of trail mix in 9 bags.
After having gone through the stuff given above, we hope that the students would have understood complex fractions.
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