Question

Simplify the following expression and
leave your answer as a mixed number.
5 1/8 - 1 3/8

Answer 1

To simplify the expression \( 5 \frac{1}{8} - 1 \frac{3}{8} \), we can follow these steps:

1. Convert the mixed numbers to improper fractions.

- For \( 5 \frac{1}{8} \):
\[
5 \frac{1}{8} = \frac{5 \times 8 + 1}{8} = \frac{40 + 1}{8} = \frac{41}{8}
\]

- For \( 1 \frac{3}{8} \):
\[
1 \frac{3}{8} = \frac{1 \times 8 + 3}{8} = \frac{8 + 3}{8} = \frac{11}{8}
\]

2. Now subtract the two improper fractions:
\[
\frac{41}{8} - \frac{11}{8} = \frac{41 - 11}{8} = \frac{30}{8}
\]

3. Simplify the fraction \( \frac{30}{8} \):
\[
\frac{30}{8} = \frac{15}{4} \quad \text{(dividing both the numerator and denominator by 2)}
\]

4. Convert \( \frac{15}{4} \) back to a mixed number:
- Divide \( 15 \) by \( 4 \), which equals \( 3 \) with a remainder of \( 3 \).
- Thus,
\[
\frac{15}{4} = 3 \frac{3}{4}
\]

5. Write the final answer as a mixed number:
\[
5 \frac{1}{8} - 1 \frac{3}{8} = 3 \frac{3}{4}
\]

Thus, the simplified expression is \( \boxed{3 \frac{3}{4}} \).