What Is 1/5 + 7/8?

Step-by-step solution

The problem

1. Write both fractions over 40. List multiples of each denominator until they meet:
   Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40
   Multiples of 8: 8, 16, 24, 32, 40
   The least common denominator is 40. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.

   \begin{aligned} \frac{1}{5} &= \frac{1 \times 8}{5 \times 8} = \frac{8}{40} \\[10pt] \frac{7}{8} &= \frac{7 \times 5}{8 \times 5} = \frac{35}{40} \end{aligned}
   = \textcolor{#0b5c56}{\frac{8}{40}} + \textcolor{#0b5c56}{\frac{35}{40}}

2. Add the numerators. Keep the denominator 40.

   = \frac{8 + 35}{40} = \textcolor{#0b5c56}{\frac{43}{40}}

3. Check that it can't be simplified. 43 and 40 have no common factor other than 1, so this is the simplest form.

   \text{GCF}(43, 40) = 1

4. Write it as a mixed number. Divide: 40 goes into 43 1 time with 3 left over. The whole number is 1, the remainder 3 becomes the numerator, and the denominator stays 40.

   43 \div 40 = 1\ \text{R}\ 3
   = \textcolor{#0b5c56}{1\frac{3}{40}}

All the working together