What Is 3/4 + 5/6?

3/4 + 5/6 = 19/12, or 1 7/12 as a mixed number.

Result

Answer

\frac{3}{4} + \frac{5}{6} = \textcolor{#0b5c56}{\frac{19}{12} = 1\frac{7}{12}}

The sum is 19/12 in simplest form, or 1 7/12 as a mixed number.

  • Decimal: \displaystyle 1.58\overline{3} (the 3 repeats forever, about 1.5833)
  • Percent: 158.33%

1 whole + 7 of 12 equal parts

Step-by-step solution

The problem

\frac{3}{4} + \frac{5}{6}

  1. 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{5}{6} &= \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \end{aligned}
    = \textcolor{#0b5c56}{\frac{9}{12}} + \textcolor{#0b5c56}{\frac{10}{12}}

  2. Add the numerators. Keep the denominator 12.

    = \frac{9 + 10}{12} = \textcolor{#0b5c56}{\frac{19}{12}}

  3. Check that it can't be simplified. 19 and 12 have no common factor other than 1, so this is the simplest form.

    \text{GCF}(19, 12) = 1

  4. Write it as a mixed number. Divide: 12 goes into 19 1 time with 7 left over. The whole number is 1, the remainder 7 becomes the numerator, and the denominator stays 12.

    19 \div 12 = 1\ \text{R}\ 7
    = \textcolor{#0b5c56}{1\frac{7}{12}}

All the working together

\begin{aligned} &\frac{3}{4} + \frac{5}{6} \\[8pt] &= \frac{3 \times 3}{4 \times 3} + \frac{5 \times 2}{6 \times 2} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt] &= \frac{9}{12} + \frac{10}{12} \\[8pt] &= \frac{9 + 10}{12} && \textcolor{#5b6660}{\textsf{add}} \\[8pt] &= \frac{19}{12} \\[8pt] &= \textcolor{#0b5c56}{1\frac{7}{12}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}

The answer in other forms

Simplest form19/12
Mixed number1 7/12
Decimal1.58333… (the 3 repeats forever)
Percent≈ 158.33%
Same fractions5/6 − 3/4, 3/4 × 5/6, 3/4 ÷ 5/6

3/4 plus other fractions

SumAnswer
3/4 + 1/25/4
3/4 + 1/313/12
3/4 + 2/317/12
3/4 + 1/41
3/4 + 3/43/2
3/4 + 1/519/20
3/4 + 2/523/20
3/4 + 3/527/20
3/4 + 4/531/20
3/4 + 1/611/12
3/4 + 5/619/12
3/4 + 1/87/8
3/4 + 3/89/8
3/4 + 5/811/8
3/4 + 7/813/8

Frequently asked questions

What is 3/4 + 5/6?

3/4 + 5/6 = 19/12 = 1 7/12 (1.5833 as a decimal).

How do you add 3/4 and 5/6?

Write both over a common denominator, add the numerators and simplify. The working above shows each step.

Other fractions, mixed numbers or up to five terms: use the Fraction Calculator.