Question

3/6 +8/9 round to a benchmark fraction

Answer 1

To round the sum of \( \frac{3}{6} + \frac{8}{9} \) to a benchmark fraction, we first find a common denominator and calculate the sum.

1. **Simplifying \( \frac{3}{6} \)**:
- \( \frac{3}{6} = \frac{1}{2} \)

Thus, the equation simplifies to:
\[
\frac{1}{2} + \frac{8}{9}
\]

2. **Finding a common denominator**:
- The least common multiple (LCM) of 2 and 9 is 18.

3. **Converting to a common denominator**:
- Convert \( \frac{1}{2} \) to have a denominator of 18:
\[
\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}
\]
- Convert \( \frac{8}{9} \) to have a denominator of 18:
\[
\frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18}
\]

4. **Adding the fractions**:
\[
\frac{9}{18} + \frac{16}{18} = \frac{25}{18}
\]

5. **Rounding to a benchmark fraction**:
- The fraction \( \frac{25}{18} \) is approximately \( 1.39 \), which can be rounded to the nearest benchmark fraction. The common benchmark fractions include \( \frac{1}{2}, \frac{1}{3}, \frac{2}{3}, 1, \frac{3}{2}, 2 \), etc.
- \( \frac{25}{18} \) is closest to \( \frac{1 \frac{7}{18}}{1} \) or approximately \( 1.5 \), which is \( \frac{3}{2} \).

Thus, the final rounded benchmark fraction is:
\[
\frac{3}{2}
\]