Answer
\frac{2}{3} - \frac{1}{5} = \textcolor{#0b5c56}{\frac{7}{15}}
The difference is 7/15 in simplest form.
- Decimal:
\displaystyle 0.4\overline{6} (the 6 repeats forever, about 0.4667) - Percent: 46.67%
Step-by-step solution
The problem
\frac{2}{3} - \frac{1}{5}
Write both fractions over 15. List multiples of each denominator until they meet:
Multiples of 3: 3, 6, 9, 12, 15
Multiples of 5: 5, 10, 15
The least common denominator is 15. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\begin{aligned} \frac{2}{3} &= \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \\[10pt] \frac{1}{5} &= \frac{1 \times 3}{5 \times 3} = \frac{3}{15} \end{aligned}
= \textcolor{#0b5c56}{\frac{10}{15}} - \textcolor{#0b5c56}{\frac{3}{15}}
Subtract the numerators. Keep the denominator 15.
= \frac{10 - 3}{15} = \textcolor{#0b5c56}{\frac{7}{15}}
Check that it can't be simplified. 7 and 15 have no common factor other than 1, so this is the simplest form.
\text{GCF}(7, 15) = 1
All the working together
\begin{aligned} &\frac{2}{3} - \frac{1}{5} \\[8pt] &= \frac{2 \times 5}{3 \times 5} - \frac{1 \times 3}{5 \times 3} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt] &= \frac{10}{15} - \frac{3}{15} \\[8pt] &= \frac{10 - 3}{15} && \textcolor{#5b6660}{\textsf{subtract}} \\[8pt] &= \textcolor{#0b5c56}{\frac{7}{15}}\end{aligned}