What Is 1/6 + 3/8?

Q: What is 1/6 + 3/8?

1/6 + 3/8 = 13/24 (0.5417 as a decimal).

1/6 + 3/8 = 13/24, about 0.542 as a decimal.

Result

Answer

\frac{1}{6} + \frac{3}{8} = \textcolor{#0b5c56}{\frac{13}{24}}

The sum is 13/24 in simplest form.

Decimal: \displaystyle 0.541\overline{6} (the 6 repeats forever, about 0.5417)
Percent: 54.17%

13 of 24 equal parts

Step-by-step solution

The problem

\frac{1}{6} + \frac{3}{8}

Write both fractions over 24. List multiples of each denominator until they meet:
Multiples of 6: 6, 12, 18, 24
Multiples of 8: 8, 16, 24
The least common denominator is 24. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\begin{aligned} \frac{1}{6} &= \frac{1 \times 4}{6 \times 4} = \frac{4}{24} \\[10pt] \frac{3}{8} &= \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \end{aligned}
= \textcolor{#0b5c56}{\frac{4}{24}} + \textcolor{#0b5c56}{\frac{9}{24}}
Add the numerators. Keep the denominator 24.
= \frac{4 + 9}{24} = \textcolor{#0b5c56}{\frac{13}{24}}
Check that it can't be simplified. 13 and 24 have no common factor other than 1, so this is the simplest form.
\text{GCF}(13, 24) = 1

All the working together

\begin{aligned} &\frac{1}{6} + \frac{3}{8} \\[8pt]  &= \frac{1 \times 4}{6 \times 4} + \frac{3 \times 3}{8 \times 3} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{4}{24} + \frac{9}{24} \\[8pt]  &= \frac{4 + 9}{24} && \textcolor{#5b6660}{\textsf{add}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{13}{24}}\end{aligned}

The answer in other forms

Simplest form	13/24
Decimal	0.541666… (the 6 repeats forever)
Percent	≈ 54.17%
Same fractions	3/8 − 1/6, 1/6 × 3/8, 1/6 ÷ 3/8

1/6 plus other fractions

Sum	Answer
1/6 + 1/2	2/3
1/6 + 1/3	1/2
1/6 + 2/3	5/6
1/6 + 1/4	5/12
1/6 + 3/4	11/12
1/6 + 1/5	11/30
1/6 + 2/5	17/30
1/6 + 3/5	23/30
1/6 + 4/5	29/30
1/6 + 1/6	1/3
1/6 + 5/6	1
1/6 + 1/8	7/24
1/6 + 3/8	13/24
1/6 + 5/8	19/24
1/6 + 7/8	25/24