What Is 1/3 + 5/6?

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

1/3 + 5/6 = 7/6 = 1 1/6 (1.1667 as a decimal).

1/3 + 5/6 = 7/6, or 1 1/6 as a mixed number.

Result

Answer

\frac{1}{3} + \frac{5}{6} = \textcolor{#0b5c56}{\frac{7}{6} = 1\frac{1}{6}}

The sum is 7/6 in simplest form, or 1 1/6 as a mixed number.

Decimal: \displaystyle 1.1\overline{6} (the 6 repeats forever, about 1.1667)
Percent: 116.67%

1 whole + 1 of 6 equal parts

Step-by-step solution

The problem

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

Write both fractions over 6. 6 is a multiple of 3:
3 × 2 = 6
So 6 is the least common denominator. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
= \textcolor{#0b5c56}{\frac{2}{6}} + \frac{5}{6}
Add the numerators. Keep the denominator 6.
= \frac{2 + 5}{6} = \textcolor{#0b5c56}{\frac{7}{6}}
Check that it can't be simplified. 7 and 6 have no common factor other than 1, so this is the simplest form.
\text{GCF}(7, 6) = 1
Write it as a mixed number. Divide: 6 goes into 7 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 6.
7 \div 6 = 1\ \text{R}\ 1
= \textcolor{#0b5c56}{1\frac{1}{6}}

All the working together

\begin{aligned} &\frac{1}{3} + \frac{5}{6} \\[8pt]  &= \frac{1 \times 2}{3 \times 2} + \frac{5}{6} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{2}{6} + \frac{5}{6} \\[8pt]  &= \frac{2 + 5}{6} && \textcolor{#5b6660}{\textsf{add}} \\[8pt]  &= \frac{7}{6} \\[8pt]  &= \textcolor{#0b5c56}{1\frac{1}{6}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}

The answer in other forms

Simplest form	7/6
Mixed number	1 1/6
Decimal	1.1666… (the 6 repeats forever)
Percent	≈ 116.67%
Same fractions	5/6 − 1/3, 1/3 × 5/6, 1/3 ÷ 5/6

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