What Is 2/3 + 2/5?

Step-by-step solution

The problem

1. Write both fractions over 15. List multiples of each denominator until they meet:
   Multiples of 3: 3, 6, 9, 12, 15
   Multiples of 5: 5, 10, 15
   The least common denominator is 15. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.

   \begin{aligned} \frac{2}{3} &= \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \\[10pt] \frac{2}{5} &= \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \end{aligned}
   = \textcolor{#0b5c56}{\frac{10}{15}} + \textcolor{#0b5c56}{\frac{6}{15}}

2. Add the numerators. Keep the denominator 15.

   = \frac{10 + 6}{15} = \textcolor{#0b5c56}{\frac{16}{15}}

3. Check that it can't be simplified. 16 and 15 have no common factor other than 1, so this is the simplest form.

   \text{GCF}(16, 15) = 1

4. Write it as a mixed number. Divide: 15 goes into 16 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 15.

   16 \div 15 = 1\ \text{R}\ 1
   = \textcolor{#0b5c56}{1\frac{1}{15}}

All the working together