What Is 5/6 + 7/8?

5/6 + 7/8 = 41/24, or 1 17/24 as a mixed number.

Result

Answer

\frac{5}{6} + \frac{7}{8} = \textcolor{#0b5c56}{\frac{41}{24} = 1\frac{17}{24}}

The sum is 41/24 in simplest form, or 1 17/24 as a mixed number.

  • Decimal: \displaystyle 1.708\overline{3} (the 3 repeats forever, about 1.7083)
  • Percent: 170.83%

1 whole + 17 of 24 equal parts

Step-by-step solution

The problem

\frac{5}{6} + \frac{7}{8}

  1. Write both fractions over 24. List multiples of each denominator until they meet:
    Multiples of 6: 6, 12, 18, 24
    Multiples of 8: 8, 16, 24
    The least common denominator is 24. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.

    \begin{aligned} \frac{5}{6} &= \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \\[10pt] \frac{7}{8} &= \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \end{aligned}
    = \textcolor{#0b5c56}{\frac{20}{24}} + \textcolor{#0b5c56}{\frac{21}{24}}

  2. Add the numerators. Keep the denominator 24.

    = \frac{20 + 21}{24} = \textcolor{#0b5c56}{\frac{41}{24}}

  3. Check that it can't be simplified. 41 and 24 have no common factor other than 1, so this is the simplest form.

    \text{GCF}(41, 24) = 1

  4. Write it as a mixed number. Divide: 24 goes into 41 1 time with 17 left over. The whole number is 1, the remainder 17 becomes the numerator, and the denominator stays 24.

    41 \div 24 = 1\ \text{R}\ 17
    = \textcolor{#0b5c56}{1\frac{17}{24}}

All the working together

\begin{aligned} &\frac{5}{6} + \frac{7}{8} \\[8pt] &= \frac{5 \times 4}{6 \times 4} + \frac{7 \times 3}{8 \times 3} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt] &= \frac{20}{24} + \frac{21}{24} \\[8pt] &= \frac{20 + 21}{24} && \textcolor{#5b6660}{\textsf{add}} \\[8pt] &= \frac{41}{24} \\[8pt] &= \textcolor{#0b5c56}{1\frac{17}{24}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}

The answer in other forms

Simplest form41/24
Mixed number1 17/24
Decimal1.708333… (the 3 repeats forever)
Percent≈ 170.83%
Same fractions7/8 − 5/6, 5/6 × 7/8, 5/6 ÷ 7/8

5/6 plus other fractions

SumAnswer
5/6 + 1/24/3
5/6 + 1/37/6
5/6 + 2/33/2
5/6 + 1/413/12
5/6 + 3/419/12
5/6 + 1/531/30
5/6 + 2/537/30
5/6 + 3/543/30
5/6 + 4/549/30
5/6 + 1/61
5/6 + 5/65/3
5/6 + 1/823/24
5/6 + 3/829/24
5/6 + 5/835/24
5/6 + 7/841/24

Frequently asked questions

What is 5/6 + 7/8?

5/6 + 7/8 = 41/24 = 1 17/24 (1.7083 as a decimal).

How do you add 5/6 and 7/8?

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.