Use the properties of operations and rules for multiplying and dividing to solve: (−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7). Show your work.
To solve the expression using the properties of operations and rules for multiplying and dividing, we can simplify the expression step by step.
First, we will multiply the fractions together.
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
= (-3 × 5 × 7 × -5) / (5 × 16 × 12 × -3 × -7)
= (-525) / (10080)
Next, we will divide the simplified fraction.
(-525) / (10080)
= -525 ÷ 10080
To divide, we can simplify the fraction by finding any common factors in the numerator and denominator. In this case, both -525 and 10080 are divisible by 105.
= (-525 ÷ 105) / (10080 ÷ 105)
= -5 / 96
Thus, the solution to the expression is -5/96.
To solve the given expression:
(−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)
We can simplify the expression step by step.
Step 1: Multiply across the numerators and denominators:
((-3)(5)(7))/((5)(16)(12))/((-3)(16)(-5)(-7))
Step 2: Simplify the expression inside the numerator:
-3 × 5 × 7 = -105
Step 3: Simplify the expression inside the denominator:
5 × 16 × 12 = 960
Step 4: Divide the numerator and denominator:
-105/960
Step 5: Simplify the fraction:
-105 ÷ 960 = -7/64
Therefore, the solution to the expression (-3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7) is -7/64.