What Is 1/2 + 2/3?

Step-by-step solution

The problem

1. Write both fractions over 6. List multiples of each denominator until they meet:
   Multiples of 2: 2, 4, 6
   Multiples of 3: 3, 6
   The least common denominator is 6. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.

   \begin{aligned} \frac{1}{2} &= \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \\[10pt] \frac{2}{3} &= \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \end{aligned}
   = \textcolor{#0b5c56}{\frac{3}{6}} + \textcolor{#0b5c56}{\frac{4}{6}}

2. Add the numerators. Keep the denominator 6.

   = \frac{3 + 4}{6} = \textcolor{#0b5c56}{\frac{7}{6}}

3. Check that it can't be simplified. 7 and 6 have no common factor other than 1, so this is the simplest form.

   \text{GCF}(7, 6) = 1

4. Write it as a mixed number. Divide: 6 goes into 7 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 6.

   7 \div 6 = 1\ \text{R}\ 1
   = \textcolor{#0b5c56}{1\frac{1}{6}}

All the working together