Question

Use the properties of operations and rules for multiplying and dividing to solve:
(-3) divide (3/4) x (2/7) x (-5/16) divide (5/7)

Answer 1

To solve this expression, we will follow the order of operations and apply the properties of operations and rules for multiplying and dividing. First, let's simplify the expression inside the parentheses:
(-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)

To simplify (-3) ÷ (3/4), we multiply -3 by the reciprocal of 3/4, which is 4/3:
(-3) ÷ (3/4) = -3 × (4/3) = -12/3 = -4

Now we have:
-4 × (2/7) × (-5/16) ÷ (5/7)

Multiplying -4 by (2/7) gives:
-4 × (2/7) = -8/7

Now we have:
-8/7 × (-5/16) ÷ (5/7)

Multiplying -8/7 by (-5/16) gives:
-8/7 × (-5/16) = 40/112 = 5/14

Now we have:
5/14 ÷ (5/7)

Dividing 5/14 by (5/7) gives:
(5/14) ÷ (5/7) = 5/14 × (7/5) = (5*7)/(14*5) = 35/70 = 1/2

Therefore, (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to 1/2.