Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(3/4)×(2/7)×(−5/16)÷(5/7)
(1 point)
To solve this expression, let's break it down step by step using the properties of operations and rules for multiplying and dividing:
Step 1: Simplify the expression within the parentheses.
(−3) ÷ (3/4) × (2/7) × (−5/16) ÷ (5/7)
Step 2: Divide -3 by the fraction 3/4.
-3 ÷ (3/4) = -3 × (4/3) = -12/3 = -4
Step 3: Multiply -4 by the fraction 2/7.
-4 × (2/7) = -8/7
Step 4: Multiply -8/7 by the fraction -5/16.
(-8/7) × (-5/16) = 40/112 = 5/14
Step 5: Divide 5/14 by the fraction 5/7.
(5/14) ÷ (5/7) = (5/14) × (7/5) = 35/70 = 1/2
Thus, the result of the expression (-3) ÷ (3/4) × (2/7) × (−5/16) ÷ (5/7) is 1/2.
To solve this expression, we can follow the order of operations (also known as PEMDAS):
Step 1: Simplify the division of negative numbers:
(−3) ÷ (3/4) = -3 * 4/3 = -12/3 = -4
Step 2: Multiply all the fractions together:
-4 × (2/7) × (-5/16) × (5/7)
Multiplying the numerators: -4 * 2 * -5 * 5 = 400
Multiplying the denominators: 7 * 16 * 7 = 784
The result is 400/784.
Step 3: Simplify the fraction, if possible:
400/784 = 25/49.
So the final answer is 25/49.