Question

simplify the following fraction
1.125+2/3/1.5

Answer 1

To simplify the expression \( 1.125 + \frac{2/3}{1.5} \), we will proceed step by step.

1. **Calculate \( \frac{2/3}{1.5} \)**:
- First, we need to convert \( 1.5 \) into a fraction. \( 1.5 = \frac{3}{2} \).
- Now, we can rewrite the division:
\[
\frac{2/3}{1.5} = \frac{2/3}{3/2} = \frac{2}{3} \times \frac{2}{3} = \frac{4}{9}
\]

2. **Add \( 1.125 \) and \( \frac{4}{9} \)**:
- First, convert \( 1.125 \) into a fraction. \( 1.125 = \frac{9}{8} \).
- Now, we need a common denominator to add \( \frac{9}{8} \) and \( \frac{4}{9} \). The least common multiple of 8 and 9 is 72.

Convert \( \frac{9}{8} \) to have a denominator of 72:
\[
\frac{9}{8} = \frac{9 \times 9}{8 \times 9} = \frac{81}{72}
\]

Convert \( \frac{4}{9} \) to have a denominator of 72:
\[
\frac{4}{9} = \frac{4 \times 8}{9 \times 8} = \frac{32}{72}
\]

3. **Now add the two fractions**:
\[
\frac{81}{72} + \frac{32}{72} = \frac{81 + 32}{72} = \frac{113}{72}
\]

Therefore, the simplified result of the expression \( 1.125 + \frac{2/3}{1.5} \) is:
\[
\frac{113}{72}
\]