What Is 5/6 − 3/5?

Q: What is 5/6 − 3/5?

5/6 − 3/5 = 7/30 (0.2333 as a decimal).

5/6 − 3/5 = 7/30, about 0.233 as a decimal.

Result

Answer

\frac{5}{6} - \frac{3}{5} = \textcolor{#0b5c56}{\frac{7}{30}}

The difference is 7/30 in simplest form.

Decimal: \displaystyle 0.2\overline{3} (the 3 repeats forever, about 0.2333)
Percent: 23.33%

7 of 30 equal parts

Step-by-step solution

The problem

\frac{5}{6} - \frac{3}{5}

Write both fractions over 30. List multiples of each denominator until they meet:
Multiples of 6: 6, 12, 18, 24, 30
Multiples of 5: 5, 10, 15, 20, 25, 30
The least common denominator is 30. 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 5}{6 \times 5} = \frac{25}{30} \\[10pt] \frac{3}{5} &= \frac{3 \times 6}{5 \times 6} = \frac{18}{30} \end{aligned}
= \textcolor{#0b5c56}{\frac{25}{30}} - \textcolor{#0b5c56}{\frac{18}{30}}
Subtract the numerators. Keep the denominator 30.
= \frac{25 - 18}{30} = \textcolor{#0b5c56}{\frac{7}{30}}
Check that it can't be simplified. 7 and 30 have no common factor other than 1, so this is the simplest form.
\text{GCF}(7, 30) = 1

All the working together

\begin{aligned} &\frac{5}{6} - \frac{3}{5} \\[8pt]  &= \frac{5 \times 5}{6 \times 5} - \frac{3 \times 6}{5 \times 6} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt]  &= \frac{25}{30} - \frac{18}{30} \\[8pt]  &= \frac{25 - 18}{30} && \textcolor{#5b6660}{\textsf{subtract}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{7}{30}}\end{aligned}

The answer in other forms

Simplest form	7/30
Decimal	0.2333… (the 3 repeats forever)
Percent	≈ 23.33%
Same fractions	3/5 + 5/6, 3/5 × 5/6, 5/6 ÷ 3/5

5/6 minus other fractions

Sum	Answer
5/6 − 1/2	1/3
5/6 − 1/3	1/2
5/6 − 2/3	1/6
5/6 − 1/4	7/12
5/6 − 3/4	1/12
5/6 − 1/5	19/30
5/6 − 2/5	13/30
5/6 − 3/5	7/30
5/6 − 4/5	1/30
5/6 − 1/6	2/3
5/6 − 1/8	17/24
5/6 − 3/8	11/24
5/6 − 5/8	5/24