What Is 2/3 + 7/8?

Step-by-step solution

The problem

1. Write both fractions over 24. List multiples of each denominator until they meet:
   Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24
   Multiples of 8: 8, 16, 24
   The least common denominator is 24. 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 8}{3 \times 8} = \frac{16}{24} \\[10pt] \frac{7}{8} &= \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \end{aligned}
   = \textcolor{#0b5c56}{\frac{16}{24}} + \textcolor{#0b5c56}{\frac{21}{24}}

2. Add the numerators. Keep the denominator 24.

   = \frac{16 + 21}{24} = \textcolor{#0b5c56}{\frac{37}{24}}

3. Check that it can't be simplified. 37 and 24 have no common factor other than 1, so this is the simplest form.

   \text{GCF}(37, 24) = 1

4. Write it as a mixed number. Divide: 24 goes into 37 1 time with 13 left over. The whole number is 1, the remainder 13 becomes the numerator, and the denominator stays 24.

   37 \div 24 = 1\ \text{R}\ 13
   = \textcolor{#0b5c56}{1\frac{13}{24}}

All the working together