Use the properties of operations and rules for multiplying and dividing to solve:
(-3) / (3/4) × (2/7) × (-5/16) / (5/7)
To solve this expression, we will use the rules for multiplying and dividing fractions.
First, let's simplify the expression:
(-3) / (3/4) × (2/7) × (-5/16) / (5/7)
To divide fractions, we multiply by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3.
(-3) × (4/3) × (2/7) × (-5/16) / (5/7)
To multiply fractions, we multiply the numerators together and the denominators together.
(-3 * 4 * 2 * -5) / (3 * 7 * 16 * 5)
Simplifying the numerator and denominator separately:
Numerator: (-3 * 4 * 2 * -5) = 120
Denominator: (3 * 7 * 16 * 5) = 1680
Thus, the final simplified expression is:
120/1680
However, we can simplify further by dividing both the numerator and denominator by their greatest common divisor, which is 10.
120/10 = 12
1680/10 = 168
Therefore, the simplified expression is:
12/168
We can divide both the numerator and denominator by 12 to simplify further:
12/12 = 1
168/12 = 14
So the final simplified expression is:
1/14