What Is 1/6 + 7/8?

1/6 + 7/8 = 25/24, or 1 1/24 as a mixed number.

Result

Answer

\frac{1}{6} + \frac{7}{8} = \textcolor{#0b5c56}{\frac{25}{24} = 1\frac{1}{24}}

The sum is 25/24 in simplest form, or 1 1/24 as a mixed number.

  • Decimal: \displaystyle 1.041\overline{6} (the 6 repeats forever, about 1.0417)
  • Percent: 104.17%

1 whole + 1 of 24 equal parts

Step-by-step solution

The problem

\frac{1}{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{1}{6} &= \frac{1 \times 4}{6 \times 4} = \frac{4}{24} \\[10pt] \frac{7}{8} &= \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \end{aligned}
    = \textcolor{#0b5c56}{\frac{4}{24}} + \textcolor{#0b5c56}{\frac{21}{24}}

  2. Add the numerators. Keep the denominator 24.

    = \frac{4 + 21}{24} = \textcolor{#0b5c56}{\frac{25}{24}}

  3. Check that it can't be simplified. 25 and 24 have no common factor other than 1, so this is the simplest form.

    \text{GCF}(25, 24) = 1

  4. Write it as a mixed number. Divide: 24 goes into 25 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 24.

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

All the working together

\begin{aligned} &\frac{1}{6} + \frac{7}{8} \\[8pt] &= \frac{1 \times 4}{6 \times 4} + \frac{7 \times 3}{8 \times 3} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt] &= \frac{4}{24} + \frac{21}{24} \\[8pt] &= \frac{4 + 21}{24} && \textcolor{#5b6660}{\textsf{add}} \\[8pt] &= \frac{25}{24} \\[8pt] &= \textcolor{#0b5c56}{1\frac{1}{24}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}

The answer in other forms

Simplest form25/24
Mixed number1 1/24
Decimal1.041666… (the 6 repeats forever)
Percent≈ 104.17%
Same fractions7/8 − 1/6, 1/6 × 7/8, 1/6 ÷ 7/8

1/6 plus other fractions

SumAnswer
1/6 + 1/22/3
1/6 + 1/31/2
1/6 + 2/35/6
1/6 + 1/45/12
1/6 + 3/411/12
1/6 + 1/511/30
1/6 + 2/517/30
1/6 + 3/523/30
1/6 + 4/529/30
1/6 + 1/61/3
1/6 + 5/61
1/6 + 1/87/24
1/6 + 3/813/24
1/6 + 5/819/24
1/6 + 7/825/24

Frequently asked questions

What is 1/6 + 7/8?

1/6 + 7/8 = 25/24 = 1 1/24 (1.0417 as a decimal).

How do you add 1/6 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.