What Is 2/5 + 5/6?

Step-by-step solution

The problem

1. Write both fractions over 30. List multiples of each denominator until they meet:
   Multiples of 5: 5, 10, 15, 20, 25, 30
   Multiples of 6: 6, 12, 18, 24, 30
   The least common denominator is 30. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.

   \begin{aligned} \frac{2}{5} &= \frac{2 \times 6}{5 \times 6} = \frac{12}{30} \\[10pt] \frac{5}{6} &= \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \end{aligned}
   = \textcolor{#0b5c56}{\frac{12}{30}} + \textcolor{#0b5c56}{\frac{25}{30}}

2. Add the numerators. Keep the denominator 30.

   = \frac{12 + 25}{30} = \textcolor{#0b5c56}{\frac{37}{30}}

3. Check that it can't be simplified. 37 and 30 have no common factor other than 1, so this is the simplest form.

   \text{GCF}(37, 30) = 1

4. Write it as a mixed number. Divide: 30 goes into 37 1 time with 7 left over. The whole number is 1, the remainder 7 becomes the numerator, and the denominator stays 30.

   37 \div 30 = 1\ \text{R}\ 7
   = \textcolor{#0b5c56}{1\frac{7}{30}}

All the working together