Fraction Operations I

October 4, 2020

The most basic fraction operations are addition and multiplication. So let's start there. There are two simple rules to follow when we add or multiply fractions.

The rules are:

$$ \frac{a}{b} \, + \, \frac{c}{d}=\frac{a \, \times \, d + b \, \times \, c}{b \, \times \, d} $$

$$ \frac{a}{b} \, \times \, \frac{c}{d}= \frac{a \, \times \, c}{b \, \times \, d} $$

Whenever you want to add or multiply any fraction these rules will always work. These two rules simply mean this: when you are adding fractions, the sum of the fractions has a denominator equal to the product of the original two denominators and a numerator equal to sum of the two products resulting from cross-multiplying the numerator of one fraction with the denominator of the other fraction.

For multiplication, simply multiply across horizontally.

Let's try an example.

$$ \frac{1}{2}+\frac{3}{4}=\frac{1 \times 4\, + \, 2 \times 3}{2 \, \times \, 4}=\frac{4\, + \,6}{8}=\frac{10}{8}=\frac{5}{4}=1\frac{1}{4} $$

$$ \frac{1}{2}\times\frac{3}{4}=\frac{1 \, \times \, 3}{2 \, \times \, 4}=\frac{3}{8} $$