What Is 3/5 + 1/6?

Q: What is 3/5 + 1/6?

3/5 + 1/6 = 23/30 (0.7667 as a decimal).

3/5 + 1/6 = 23/30, about 0.767 as a decimal.

Result

Answer

\frac{3}{5} + \frac{1}{6} = \textcolor{#0b5c56}{\frac{23}{30}}

The sum is 23/30 in simplest form.

Decimal: \displaystyle 0.7\overline{6} (the 6 repeats forever, about 0.7667)
Percent: 76.67%

23 of 30 equal parts

Step-by-step solution

The problem

\frac{3}{5} + \frac{1}{6}

Write both fractions over 30. List multiples of each denominator until they meet:
Multiples of 5: 5, 10, 15, 20, 25, 30
Multiples of 6: 6, 12, 18, 24, 30
The least common denominator is 30. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\begin{aligned} \frac{3}{5} &= \frac{3 \times 6}{5 \times 6} = \frac{18}{30} \\[10pt] \frac{1}{6} &= \frac{1 \times 5}{6 \times 5} = \frac{5}{30} \end{aligned}
= \textcolor{#0b5c56}{\frac{18}{30}} + \textcolor{#0b5c56}{\frac{5}{30}}
Add the numerators. Keep the denominator 30.
= \frac{18 + 5}{30} = \textcolor{#0b5c56}{\frac{23}{30}}
Check that it can't be simplified. 23 and 30 have no common factor other than 1, so this is the simplest form.
\text{GCF}(23, 30) = 1

All the working together

\begin{aligned} &\frac{3}{5} + \frac{1}{6} \\[8pt]  &= \frac{3 \times 6}{5 \times 6} + \frac{1 \times 5}{6 \times 5} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{18}{30} + \frac{5}{30} \\[8pt]  &= \frac{18 + 5}{30} && \textcolor{#5b6660}{\textsf{add}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{23}{30}}\end{aligned}

The answer in other forms

Simplest form	23/30
Decimal	0.7666… (the 6 repeats forever)
Percent	≈ 76.67%
Same fractions	3/5 − 1/6, 3/5 × 1/6, 3/5 ÷ 1/6

3/5 plus other fractions

Sum	Answer
3/5 + 1/2	11/10
3/5 + 1/3	14/15
3/5 + 2/3	19/15
3/5 + 1/4	17/20
3/5 + 3/4	27/20
3/5 + 1/5	4/5
3/5 + 2/5	1
3/5 + 3/5	6/5
3/5 + 4/5	7/5
3/5 + 1/6	23/30
3/5 + 5/6	43/30
3/5 + 1/8	29/40
3/5 + 3/8	39/40
3/5 + 5/8	49/40
3/5 + 7/8	59/40