What Is 4/5 + 5/8?

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{4}{5} &= \frac{4 \times 8}{5 \times 8} = \frac{32}{40} \\[10pt] \frac{5}{8} &= \frac{5 \times 5}{8 \times 5} = \frac{25}{40} \end{aligned}
   = \textcolor{#0b5c56}{\frac{32}{40}} + \textcolor{#0b5c56}{\frac{25}{40}}

2. Add the numerators. Keep the denominator 40.

   = \frac{32 + 25}{40} = \textcolor{#0b5c56}{\frac{57}{40}}

3. Check that it can't be simplified. 57 and 40 have no common factor other than 1, so this is the simplest form.

   \text{GCF}(57, 40) = 1

4. Write it as a mixed number. Divide: 40 goes into 57 1 time with 17 left over. The whole number is 1, the remainder 17 becomes the numerator, and the denominator stays 40.

   57 \div 40 = 1\ \text{R}\ 17
   = \textcolor{#0b5c56}{1\frac{17}{40}}

All the working together