Answer
\frac{3}{4} - \frac{1}{3} = \textcolor{#0b5c56}{\frac{5}{12}}
The difference is 5/12 in simplest form.
- Decimal:
\displaystyle 0.41\overline{6} (the 6 repeats forever, about 0.4167) - Percent: 41.67%
Step-by-step solution
The problem
\frac{3}{4} - \frac{1}{3}
Write both fractions over 12. List multiples of each denominator until they meet:
Multiples of 4: 4, 8, 12
Multiples of 3: 3, 6, 9, 12
The least common denominator is 12. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\begin{aligned} \frac{3}{4} &= \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \\[10pt] \frac{1}{3} &= \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \end{aligned}
= \textcolor{#0b5c56}{\frac{9}{12}} - \textcolor{#0b5c56}{\frac{4}{12}}
Subtract the numerators. Keep the denominator 12.
= \frac{9 - 4}{12} = \textcolor{#0b5c56}{\frac{5}{12}}
Check that it can't be simplified. 5 and 12 have no common factor other than 1, so this is the simplest form.
\text{GCF}(5, 12) = 1
All the working together
\begin{aligned} &\frac{3}{4} - \frac{1}{3} \\[8pt] &= \frac{3 \times 3}{4 \times 3} - \frac{1 \times 4}{3 \times 4} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt] &= \frac{9}{12} - \frac{4}{12} \\[8pt] &= \frac{9 - 4}{12} && \textcolor{#5b6660}{\textsf{subtract}} \\[8pt] &= \textcolor{#0b5c56}{\frac{5}{12}}\end{aligned}