What Is 1/3 + 1/5?

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

1/3 + 1/5 = 8/15 (0.5333 as a decimal).

1/3 + 1/5 = 8/15, about 0.533 as a decimal.

Result

Answer

\frac{1}{3} + \frac{1}{5} = \textcolor{#0b5c56}{\frac{8}{15}}

The sum is 8/15 in simplest form.

Decimal: \displaystyle 0.5\overline{3} (the 3 repeats forever, about 0.5333)
Percent: 53.33%

8 of 15 equal parts

Step-by-step solution

The problem

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

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

All the working together

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

The answer in other forms

Simplest form	8/15
Decimal	0.5333… (the 3 repeats forever)
Percent	≈ 53.33%
Same fractions	1/3 − 1/5, 1/3 × 1/5, 1/3 ÷ 1/5

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