Add the following fractions

Explanation

We need to multiply the denominator of the second fraction by 5 to obtain 15.  it follows that \(\frac55\) should be the form of 1 used to build \(\frac13\)

We need to multiply the denominator of the first fraction by 3 to obtain 15.  It follows that \(\frac35\) should be the form of 1 that is used to build \(\frac35\)

$\frac35 + \frac13 = \frac35 \color{red}{\cdot \frac33} + \frac13 \color{blue}{\cdot \frac55}$

Multiply the numerators.  Multiply the denominators.  Note that the denominators are now the same.

$= \frac{9}{15} + \frac{5}{15}$

Add the numerators and write the sum over the common denominator 15

$= \frac{9 + 5}{15}$

Since 14 and 15 have no common factors other than 1, this fraction is in simplest form

$= \frac{14}{15}$