Question

3/14 × 9/16 by cancellation method

Answer 1

To multiply the fractions \( \frac{3}{14} \) and \( \frac{9}{16} \) using the cancellation method, follow these steps:

1. **Write the multiplication of the fractions**:
\[
\frac{3}{14} \times \frac{9}{16}
\]

2. **Factor the numerators and denominators**:
- The numerator of the first fraction is \( 3 \).
- The numerator of the second fraction is \( 9 = 3 \times 3 \).
- The denominator of the first fraction is \( 14 = 2 \times 7 \).
- The denominator of the second fraction is \( 16 = 2^4 \) or \( 2 \times 2 \times 2 \times 2 \).

3. **Set up the multiplication with factors**:
\[
\frac{3 \cdot (3 \cdot 3)}{(2 \cdot 7) \cdot (2 \cdot 2 \cdot 2 \cdot 2)} = \frac{3 \cdot 3}{2 \cdot 7 \cdot 2 \cdot 2 \cdot 2}
\]

4. **Cancel common factors**:
- The \( 3 \) in the numerator and \( 3 \) from \( 9 \) can be used, but there are no common factors in that form.
- The \( 2 \) from the \( 16 \) and the \( 2 \) in the denominator gives:
\[
\frac{3}{14} \times \frac{9}{16} = \frac{3}{14} \times \frac{3 \times 3}{2 \times 2 \times 2 \times 2}
\]
- \( 9 \) (which is \( 3 \times 3 \)) can be simplified with \( 3 \) in numerator and denominator, however in this case nothing simplifies further with \( 14 \).

5. **Perform the multiplication**:
\[
\frac{3 \cdot 9}{14 \cdot 16} = \frac{27}{224}
\]

Thus, the simplified result of \( \frac{3}{14} \times \frac{9}{16} \) using the cancellation method is:
\[
\frac{27}{224}
\]