Answer
\frac{4}{5} - \frac{3}{8} = \textcolor{#0b5c56}{\frac{17}{40}}
The difference is 17/40 in simplest form.
- Decimal:
\displaystyle 0.425 - Percent: 42.5%
Step-by-step solution
The problem
\frac{4}{5} - \frac{3}{8}
Write both fractions over 40. List multiples of each denominator until they meet:
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40
Multiples of 8: 8, 16, 24, 32, 40
The least common denominator is 40. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\begin{aligned} \frac{4}{5} &= \frac{4 \times 8}{5 \times 8} = \frac{32}{40} \\[10pt] \frac{3}{8} &= \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \end{aligned}
= \textcolor{#0b5c56}{\frac{32}{40}} - \textcolor{#0b5c56}{\frac{15}{40}}
Subtract the numerators. Keep the denominator 40.
= \frac{32 - 15}{40} = \textcolor{#0b5c56}{\frac{17}{40}}
Check that it can't be simplified. 17 and 40 have no common factor other than 1, so this is the simplest form.
\text{GCF}(17, 40) = 1
All the working together
\begin{aligned} &\frac{4}{5} - \frac{3}{8} \\[8pt] &= \frac{4 \times 8}{5 \times 8} - \frac{3 \times 5}{8 \times 5} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt] &= \frac{32}{40} - \frac{15}{40} \\[8pt] &= \frac{32 - 15}{40} && \textcolor{#5b6660}{\textsf{subtract}} \\[8pt] &= \textcolor{#0b5c56}{\frac{17}{40}}\end{aligned}