What Is 2/3 + 1/4?

Q: What is 2/3 + 1/4?

2/3 + 1/4 = 11/12 (0.9167 as a decimal).

2/3 + 1/4 = 11/12, about 0.917 as a decimal.

Result

Answer

\frac{2}{3} + \frac{1}{4} = \textcolor{#0b5c56}{\frac{11}{12}}

The sum is 11/12 in simplest form.

Decimal: \displaystyle 0.91\overline{6} (the 6 repeats forever, about 0.9167)
Percent: 91.67%

11 of 12 equal parts

Step-by-step solution

The problem

\frac{2}{3} + \frac{1}{4}

Write both fractions over 12. List multiples of each denominator until they meet:
Multiples of 3: 3, 6, 9, 12
Multiples of 4: 4, 8, 12
The least common denominator is 12. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\begin{aligned} \frac{2}{3} &= \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \\[10pt] \frac{1}{4} &= \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \end{aligned}
= \textcolor{#0b5c56}{\frac{8}{12}} + \textcolor{#0b5c56}{\frac{3}{12}}
Add the numerators. Keep the denominator 12.
= \frac{8 + 3}{12} = \textcolor{#0b5c56}{\frac{11}{12}}
Check that it can't be simplified. 11 and 12 have no common factor other than 1, so this is the simplest form.
\text{GCF}(11, 12) = 1

All the working together

\begin{aligned} &\frac{2}{3} + \frac{1}{4} \\[8pt]  &= \frac{2 \times 4}{3 \times 4} + \frac{1 \times 3}{4 \times 3} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{8}{12} + \frac{3}{12} \\[8pt]  &= \frac{8 + 3}{12} && \textcolor{#5b6660}{\textsf{add}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{11}{12}}\end{aligned}

The answer in other forms

Simplest form	11/12
Decimal	0.91666… (the 6 repeats forever)
Percent	≈ 91.67%
Same fractions	2/3 − 1/4, 2/3 × 1/4, 2/3 ÷ 1/4

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