To solve the expression \((−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)\), we can break it down step by step.
First, we rewrite the expression by converting the division into multiplication by the reciprocal:
\[ (−3/5) × (5/16) × (7/12) × (-16/3) × (-7/5) \]
Now we can multiply the fractions together:
\[ = \left(−3 × 5 × 7 × -16 × -7\right) / \left(5 × 16 × 12 × -3 × 5\right) \]
We can start canceling out common factors in the numerator and denominator.
- The \(-3\) in the numerator cancels with \(-3\) in the denominator.
- The \(5\) in the numerator cancels with \(5\) in the denominator.
- The \(16\) in the numerator cancels with \(16\) in the denominator.
- The \(7\) in the numerator cancels with \(7\) in the denominator.
After canceling, the expression simplifies considerably:
\[ = \frac{(−1)(−1)}{1} = 1 \]
Now let's double-check the cancellation and products:
- The numerator from the product: \( (-3) \times (5) \times (7) \times (-16) \times (-7) = 3 \times 5 \times 7 \times 16 \times 7\).
- The denominator: \( 5 \times 16 \times 12 \times 3 \times 5 = 5 \times 5 \times 16 \times 3 \times 12\).
All these cancellations confirm that we have:
- \(3\) and \(3\) cancels,
- One \(5\) cancels,
- One \(16\) cancels,
- A \(7\) cancels.
Thus, the product simplifies down to 1, solidifying our conclusion that:
\[ \text{The answer is } 1. \]
1 answer