What Is 3/4 + 2/5?

Step-by-step solution

The problem

1. Write both fractions over 20. List multiples of each denominator until they meet:
   Multiples of 4: 4, 8, 12, 16, 20
   Multiples of 5: 5, 10, 15, 20
   The least common denominator is 20. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.

   \begin{aligned} \frac{3}{4} &= \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \\[10pt] \frac{2}{5} &= \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \end{aligned}
   = \textcolor{#0b5c56}{\frac{15}{20}} + \textcolor{#0b5c56}{\frac{8}{20}}

2. Add the numerators. Keep the denominator 20.

   = \frac{15 + 8}{20} = \textcolor{#0b5c56}{\frac{23}{20}}

3. Check that it can't be simplified. 23 and 20 have no common factor other than 1, so this is the simplest form.

   \text{GCF}(23, 20) = 1

4. Write it as a mixed number. Divide: 20 goes into 23 1 time with 3 left over. The whole number is 1, the remainder 3 becomes the numerator, and the denominator stays 20.

   23 \div 20 = 1\ \text{R}\ 3
   = \textcolor{#0b5c56}{1\frac{3}{20}}

All the working together