What Is 1/5 + 3/8?

Q: What is 1/5 + 3/8?

1/5 + 3/8 = 23/40 (0.575 as a decimal).

1/5 + 3/8 = 23/40, which is 0.575 as a decimal.

Result

Answer

\frac{1}{5} + \frac{3}{8} = \textcolor{#0b5c56}{\frac{23}{40}}

The sum is 23/40 in simplest form.

Decimal: \displaystyle 0.575
Percent: 57.5%

23 of 40 equal parts

Step-by-step solution

The problem

\frac{1}{5} + \frac{3}{8}

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{3}{8} &= \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \end{aligned}
= \textcolor{#0b5c56}{\frac{8}{40}} + \textcolor{#0b5c56}{\frac{15}{40}}
Add the numerators. Keep the denominator 40.
= \frac{8 + 15}{40} = \textcolor{#0b5c56}{\frac{23}{40}}
Check that it can't be simplified. 23 and 40 have no common factor other than 1, so this is the simplest form.
\text{GCF}(23, 40) = 1

All the working together

\begin{aligned} &\frac{1}{5} + \frac{3}{8} \\[8pt]  &= \frac{1 \times 8}{5 \times 8} + \frac{3 \times 5}{8 \times 5} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{8}{40} + \frac{15}{40} \\[8pt]  &= \frac{8 + 15}{40} && \textcolor{#5b6660}{\textsf{add}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{23}{40}}\end{aligned}

The answer in other forms

Simplest form	23/40
Decimal	0.575
Percent	57.5%
Same fractions	3/8 − 1/5, 1/5 × 3/8, 1/5 ÷ 3/8

1/5 plus other fractions

Sum	Answer
1/5 + 1/2	7/10
1/5 + 1/3	8/15
1/5 + 2/3	13/15
1/5 + 1/4	9/20
1/5 + 3/4	19/20
1/5 + 1/5	2/5
1/5 + 2/5	3/5
1/5 + 3/5	4/5
1/5 + 4/5	1
1/5 + 1/6	11/30
1/5 + 5/6	31/30
1/5 + 1/8	13/40
1/5 + 3/8	23/40
1/5 + 5/8	33/40
1/5 + 7/8	43/40