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, we'll follow the order of operations: parentheses, multiplication and division from left to right, and finally addition and subtraction from left to right.
First, let's simplify the expression inside the parentheses.
(-3) ÷ (3/4) = -3 * (4/3) = -12/3 = -4
Now, let's multiply the remaining fractions.
(-4) × (2/7) × (-5/16) = (-4 * 2 * -5) / (7 * 16) = 40 / 112
Finally, let's simplify the division:
40 / 112 = 5/14
Therefore, the answer is 5/14.
To solve the expression: (−3)÷(3/4)×(2/7)×(−5/16)÷(5/7), we can use the properties of operations and the rules for multiplying and dividing.
Step 1: Simplify the division: (−3)÷(3/4) = (−3)×(4/3)
Multiply the numerator by the reciprocal of the denominator:
(−3)×(4/3) = (−3)×(4/3) = −12/3 = −4
Step 2: Multiply all the fractions together:
−4 × (2/7) × (−5/16) × (5/7)
Step 3: Cancel out common factors:
In the given expression, we can cancel out the common factor of 7 between the denominators of the second and fourth fraction:
−4 × (2/1) × (−5/16) × (5/1)
Step 4: Simplify the multiplication:
Multiply the numerators together and the denominators together:
−4 × 2 × (−5) × 5 / 1 × 1 × 16 × 1
Step 5: Perform the multiplication:
−4 × 2 × (−5) × 5 = −400
Step 6: Simplify further, if possible:
−400/1 × 1/16 = -400/16 = -25
Therefore, the solution to the expression (−3)÷(3/4)×(2/7)×(−5/16)÷(5/7) is -25.