Fraction Operations I

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.

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

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