What Is 1/3 + 5/8?

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

1/3 + 5/8 = 23/24 (0.9583 as a decimal).

1/3 + 5/8 = 23/24, about 0.958 as a decimal.

Result

Answer

\frac{1}{3} + \frac{5}{8} = \textcolor{#0b5c56}{\frac{23}{24}}

The sum is 23/24 in simplest form.

Decimal: \displaystyle 0.958\overline{3} (the 3 repeats forever, about 0.9583)
Percent: 95.83%

23 of 24 equal parts

Step-by-step solution

The problem

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

Write both fractions over 24. List multiples of each denominator until they meet:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 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}{3} &= \frac{1 \times 8}{3 \times 8} = \frac{8}{24} \\[10pt] \frac{5}{8} &= \frac{5 \times 3}{8 \times 3} = \frac{15}{24} \end{aligned}
= \textcolor{#0b5c56}{\frac{8}{24}} + \textcolor{#0b5c56}{\frac{15}{24}}
Add the numerators. Keep the denominator 24.
= \frac{8 + 15}{24} = \textcolor{#0b5c56}{\frac{23}{24}}
Check that it can't be simplified. 23 and 24 have no common factor other than 1, so this is the simplest form.
\text{GCF}(23, 24) = 1

All the working together

\begin{aligned} &\frac{1}{3} + \frac{5}{8} \\[8pt]  &= \frac{1 \times 8}{3 \times 8} + \frac{5 \times 3}{8 \times 3} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{8}{24} + \frac{15}{24} \\[8pt]  &= \frac{8 + 15}{24} && \textcolor{#5b6660}{\textsf{add}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{23}{24}}\end{aligned}

The answer in other forms

Simplest form	23/24
Decimal	0.958333… (the 3 repeats forever)
Percent	≈ 95.83%
Same fractions	5/8 − 1/3, 1/3 × 5/8, 1/3 ÷ 5/8

1/3 plus other fractions

Sum	Answer
1/3 + 1/2	5/6
1/3 + 1/3	2/3
1/3 + 2/3	1
1/3 + 1/4	7/12
1/3 + 3/4	13/12
1/3 + 1/5	8/15
1/3 + 2/5	11/15
1/3 + 3/5	14/15
1/3 + 4/5	17/15
1/3 + 1/6	1/2
1/3 + 5/6	7/6
1/3 + 1/8	11/24
1/3 + 3/8	17/24
1/3 + 5/8	23/24
1/3 + 7/8	29/24