Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(3/4)×(2/7)×(−5/16)÷(5/7) = ?
To calculate this expression, we can simplify step by step using the properties of operations and the rules for multiplying and dividing fractions.
First, let's simplify the division:
(-3) ÷ (3/4) = (-3) × (4/3) = -12/3 = -4
Next, let's simplify the multiplication:
-4 × (2/7) × (-5/16) × (5/7)
We can cancel out factors that appear in both the numerator and denominator:
(-4) × (2/1) × (-1/16) × (1/1)
Now, let's multiply:
(-4) × (2/1) × (-1/16) × (1/1) = -8/16
Simplifying further, we can simplify the fraction:
-8/16 = -1/2
Therefore, (-3)÷(3/4)×(2/7)×(−5/16)÷(5/7) = -1/2
To solve this expression, we will follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Let's simplify the expression step by step:
Step 1: Simplify inside the parentheses first:
(-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)
Step 2: Divide -3 by (3/4):
(-3) ÷ (3/4) = -3 × (4/3) = -4
Step 3: Multiply -4 by (2/7):
-4 × (2/7) = -8/7
Step 4: Multiply -8/7 by (-5/16):
-8/7 × (-5/16) = 40/112 = 5/14
Step 5: Finally, divide 5/14 by (5/7):
(5/14) ÷ (5/7) = (5/14) × (7/5) = 35/70 = 1/2
So, the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to 1/2.