What Is 3/4 + 1/6?

Q: What is 3/4 + 1/6?

3/4 + 1/6 = 11/12 (0.9167 as a decimal).

3/4 + 1/6 = 11/12, about 0.917 as a decimal.

Result

Answer

\frac{3}{4} + \frac{1}{6} = \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{3}{4} + \frac{1}{6}

Write both fractions over 12. List multiples of each denominator until they meet:
Multiples of 4: 4, 8, 12
Multiples of 6: 6, 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{3}{4} &= \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \\[10pt] \frac{1}{6} &= \frac{1 \times 2}{6 \times 2} = \frac{2}{12} \end{aligned}
= \textcolor{#0b5c56}{\frac{9}{12}} + \textcolor{#0b5c56}{\frac{2}{12}}
Add the numerators. Keep the denominator 12.
= \frac{9 + 2}{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{3}{4} + \frac{1}{6} \\[8pt]  &= \frac{3 \times 3}{4 \times 3} + \frac{1 \times 2}{6 \times 2} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{9}{12} + \frac{2}{12} \\[8pt]  &= \frac{9 + 2}{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	3/4 − 1/6, 3/4 × 1/6, 3/4 ÷ 1/6

3/4 plus other fractions

Sum	Answer
3/4 + 1/2	5/4
3/4 + 1/3	13/12
3/4 + 2/3	17/12
3/4 + 1/4	1
3/4 + 3/4	3/2
3/4 + 1/5	19/20
3/4 + 2/5	23/20
3/4 + 3/5	27/20
3/4 + 4/5	31/20
3/4 + 1/6	11/12
3/4 + 5/6	19/12
3/4 + 1/8	7/8
3/4 + 3/8	9/8
3/4 + 5/8	11/8
3/4 + 7/8	13/8