How do you subtract \frac { 2} { 3} - \frac { 1} { 5}?

Mar 9, 2018

$\frac{7}{15}$

Explanation:

When adding or subtracting fractions, you must find a common denominator for both. Adding or subtracting straight across breaks math rules.

So we need to find a number that both $3$ and $5$ go into. The fastest way is to just multiply the two together.

$5 \cdot 3 = 15$

Our common denominator is $15$ (meaning both fractions now have a bottom of $15$). However, that is not all we do to give us the ability to subtract. When we multiplied each denominator to get $15$, we need to multiply the numerator on each fraction by the corresponding number:

$\frac{2}{3} \implies \frac{2 \left(5\right)}{3 \left(5\right)} \implies \frac{10}{15}$

$\frac{1}{5} \implies \frac{1 \left(3\right)}{5 \left(3\right)} \implies \frac{3}{15}$

Now that our fractions have common denominators, we can subtract. The numerators are the only ones to change.

$\frac{10}{15} - \frac{3}{15}$

$\frac{7}{15}$