Subtract

Explanation

Since the smallest number the denominators 5 and 15 divide exactly is 15, the LCD is 15.  We will only need to build an equivalent fraction for \(\frac25\).

We do not have to build the fraction \(\frac{11}{15}\) because it already has a denominator of 15.

Solution

To build \(\frac25\) so that its denominator is 15, multiply it by a form of 1

$\frac25 - \frac{11}{15} = \frac25 \color{red}{\cdot \frac33} - \frac{11}{15}$

Multiply the numerators.  Multiply the denominators.  The denominators are now the same.

$= \frac{6}{15} - \frac{11}{15}$

Subtract the numerators and write the difference over the common denominator 15.

$= \frac{6 - 11}{15}$

If it is helpful, use the subtraction rule and add the opposite in the numerator: 6 + (-11) = -5.  Write the - sign in front of the fraction

$= \frac{5}{15}$

To simplify, factor 15 as 3 • 5.  Then remove the common factor of 5 from the numerator and denominator.

$\require{cancel} = \frac{\cancel{5}^1}{3 \cdot \cancel{5}_1}$

Multiply the remaining factors in the denominator: 3 • 1 = 3

$= - \frac13$