What Is 2/3 + 5/6?

Q: What is 2/3 + 5/6?

2/3 + 5/6 = 3/2 = 1 1/2 (1.5 as a decimal).

2/3 + 5/6 = 3/2, or 1 1/2 as a mixed number.

Result

Answer

\frac{2}{3} + \frac{5}{6} = \textcolor{#0b5c56}{\frac{3}{2} = 1\frac{1}{2}}

The sum is 3/2 in simplest form, or 1 1/2 as a mixed number.

Decimal: \displaystyle 1.5
Percent: 150%

1 whole + 1 of 2 equal parts

Step-by-step solution

The problem

\frac{2}{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{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
= \textcolor{#0b5c56}{\frac{4}{6}} + \frac{5}{6}
Add the numerators. Keep the denominator 6.
= \frac{4 + 5}{6} = \textcolor{#0b5c56}{\frac{9}{6}}
Simplify. List the factors of each:
Factors of 9: 1, 3, 9
Factors of 6: 1, 2, 3, 6
The greatest common factor (GCF) is 3. Divide the top and bottom by 3.
= \frac{9 \div 3}{6 \div 3} = \textcolor{#0b5c56}{\frac{3}{2}}
Write it as a mixed number. Divide: 2 goes into 3 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 2.
3 \div 2 = 1\ \text{R}\ 1
= \textcolor{#0b5c56}{1\frac{1}{2}}

All the working together

\begin{aligned} &\frac{2}{3} + \frac{5}{6} \\[8pt]  &= \frac{2 \times 2}{3 \times 2} + \frac{5}{6} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{4}{6} + \frac{5}{6} \\[8pt]  &= \frac{4 + 5}{6} && \textcolor{#5b6660}{\textsf{add}} \\[8pt]  &= \frac{9}{6} \\[8pt]  &= \frac{9 \div 3}{6 \div 3} && \textcolor{#5b6660}{\textsf{simplify}} \\[8pt]  &= \frac{3}{2} \\[8pt]  &= \textcolor{#0b5c56}{1\frac{1}{2}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}

The answer in other forms

Simplest form	3/2
Mixed number	1 1/2
Decimal	1.5
Percent	150%
Same fractions	5/6 − 2/3, 2/3 × 5/6, 2/3 ÷ 5/6

2/3 plus other fractions

Sum	Answer
2/3 + 1/2	7/6
2/3 + 1/3	1
2/3 + 2/3	4/3
2/3 + 1/4	11/12
2/3 + 3/4	17/12
2/3 + 1/5	13/15
2/3 + 2/5	16/15
2/3 + 3/5	19/15
2/3 + 4/5	22/15
2/3 + 1/6	5/6
2/3 + 5/6	3/2
2/3 + 1/8	19/24
2/3 + 3/8	25/24
2/3 + 5/8	31/24
2/3 + 7/8	37/24