Question

6/7 × 9/16 by cancellation method

Answer 1

To multiply the fractions \( \frac{6}{7} \) and \( \frac{9}{16} \) using the cancellation method, we look for common factors in the numerators and denominators.

The fractions are:

\[
\frac{6}{7} \times \frac{9}{16}
\]

1. **Factor the numerators and denominators**:
- \( 6 = 2 \times 3 \)
- \( 9 = 3 \times 3 \)
- \( 7 \) is a prime number.
- \( 16 = 4 \times 4 = 2^4 \)

2. **Write the fractions with their factors**:
\[
\frac{2 \times 3}{7} \times \frac{3 \times 3}{2 \times 2 \times 2 \times 2}
\]

3. **Cancel common factors**:
- We see a \( 3 \) in the numerator of \( \frac{9}{16} \) and a \( 3 \) in the numerator of \( \frac{6}{7} \).
- We also see a \( 2 \) in \( 6 \) (which is \( 2 \times 3 \)) and a \( 2 \) in \( 16 \) (which is \( 2^4 \)).

After cancellation, we simplify:

\[
\frac{(2 \cancel{\times 3})}{7} \times \frac{\cancel{3} \times 3}{\cancel{2} \times 2 \times 2 \times 2}
\]

This simplifies to:

\[
\frac{(1)}{7} \times \frac{3}{8}
\]

Now we can multiply the remaining parts:

\[
\frac{1 \times 3}{7 \times 8} = \frac{3}{56}
\]

So, \( \frac{6}{7} \times \frac{9}{16} \) using the cancellation method yields:

\[
\frac{3}{56}
\]