Arithmetic With Fractions

Arithmetic with Fractions

 

When adding or subtracting fractions, multiply each fraction by a factor like:

 

  1=(2/2)=(3/3)=(4/4)=(5/5)=(6/6)=(7/7)=(8/8)=(9/9), etc.

 

so that all fractions end with the same denominator.
Once all fractions have the same denominator, you can add or subtract all the numerators to find the solution.

 

When multiplying or dividing fractions, factors common to both the numerator and denominator cancel out.

 

All solutions below are written as improper fractions with the numerators and denominators rescaled to be integers with the lowest possible magnitude.

 

Equation	Solution
(1/3) + (1/2)	5/6
(1/2) + (1/4)	3/4
(3/4) - (1/2)	1/4
(2/3) - (1/6)	1/2
(1/3) - (1/6)	1/6
(1/4) + (1/3)	7/12
(1/8) - (1/6)	-1/24
(5/6) - (3/4)	1/12
(3/10) + (2/5)	7/10
(3/5) + (-2/3)	-1/15
(5/8) - (-3/4)	11/8
(-12/7) - (-3/5)	-39/35
(-2/5) - (3/5)	-1
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Equation	Solution
(2/3) x (3/4)	1/2
(3/5) x (15/4)	9/4
(-3/5) / (-15/4)	4/25
(1/2) / (3/4)	2/3
(-5/3) x (-2/3)	10/9
(21/8) x (4/7)	3/2
(3/4) / (-1/6)	-9/2
(-5/2) / (2/3)	-15/4
(4/7) x (-3/8)	-3/14
(48/35) x (49/6)	56/5
(3/20) x (-5/6)	-1/8
(8/15) / (20/3)	2/25
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