Complex fractions are those fractions which have a fraction in numerator or denominator or in both. For example, 1/ (¾), ½ / 3, (¾ )/ (½ ) are some of the complex fractions
Let us now learn to simplify complex fractions. While simplifying complex fraction, let us consider the following example for better understanding,
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| Complex Fractions |
Simplify the complex fraction 4a²b/(8/ab)
Here the numerator is 4a²b and
the denominator is 8/ab
It can be written as 4a²b ÷ (8/ab)
to simplify, we need to flip the fraction in the denominator and multiply it with the terms in the numerator as follows,
4a²b × ab/8 (division of fractions)
Now, we can simplify the terms
4/8 × a²b × ab
which gives us ½ a³b²
Complex fraction solver
In solving complex fractions, we can use one more method, which is the LCD method. Let us learn how to solve complex fractions with some example problems
1.Simplify (4/5)/(2/15)
Solution: Numerator = 4/5
Denominator = 2/15
LCD of 5 and 15 (denominators of the two fractions) is 15
Multiply LCD with each of the fractions of the numerator and the denominator
4/5 x 15 = 4 x 3 = 12
2/15 x 15 = 2 x 1 = 2
The simplified fraction, 12/2 = 6
2.Simplify (1/a + 1/b) ÷ (1/a – 1/b)
Solution: (1/a + 1/b) = (b + a)/ab
(1/a – 1/b) = (b – a)/ab
LCD in this case would be ‘ab’
(b+a)/ab x ab = (b+a)
(b-a)/ab x ab = (b-a)
the simplified fraction is (b+a)/(b-a)
3.Simplify (x²/4)/(y/x)
Solution: x²/4 . x/y
= x³/4y
4.How to simplify complex fraction given below
(a+b)/(x-y) / (a² - b²)/(x² - y²)
Solution: We re-write the given complex fraction,
(a+b)/ (x-y) × (x² - y²)/(a² - b²)
we have, (a² - b²) = (a+b)(a-b)
(a+b)/ (x-y) × (x+y)(x-y)/(a+b)(a-b)
on simplification, we get (x+y)/(a-b)
5.simplify the complex fraction given,
4 ¾ /3 ½
Solution: Numerator = 4 ¾ = 19/4
Denominator = 3 ½ = 7/2
LCD of 4 and 2 is 4
19/4 x 4 = 19
7/2 x 4 = 14
the simplified fraction is 19/14
