no Use the properties of operations and rules for multiplying and dividing to solve: (−3/5) × (5/16) × (7/12) ÷ (−3/16) ×( −5/7) (1 point)
To solve this expression, we need to simplify the given expression using the properties of operations.
First, let's simplify the numerators:
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
(-3 × 5 × 7) / (5 × 16 × 12) ÷ (-3/16) × (-5/7)
-105/960 ÷ (-3/16) × (-5/7)
Next, let's simplify the denominators:
-105/960 ÷ (-3/16) × (-5/7) = -105/(960 × 16 × 7/3) × (-5/7)
Now, let's simplify the expression:
-105/(960 × 16 × 7/3) × (-5/7) = -105/(960 × 16 × 7/3) × (-5/7)
Finally, we can multiply the fractions together:
-105/(960 × 16 × 7/3) × (-5/7) = -105/ ((960 × 16 × 7) / (3 × 7))
Now, we can simplify the expression further:
-105/ ((960 × 16 × 7) / (3 × 7)) = -105/ ((960 × 16) / 3)
This expression cannot be simplified further without knowing the value of the numerator and denominator.
To solve the expression, we can apply the properties of operations and rules for multiplying and dividing.
Step 1: Multiply the numerators of the fractions together:
(-3/5) × (5/16) × (7/12) = (-3 × 5 × 7) / (5 × 16 × 12)
Step 2: Multiply the denominators of the fractions together:
(-3/5) × (5/16) × (7/12) = (-3 × 5 × 7) / (5 × 16 × 12)
Step 3: Cancel out any common factors between the numerator and denominator:
In this case, there are no common factors, so we can proceed to step 4.
Step 4: Multiply all the numerators together and multiply all the denominators together:
(-3 × 5 × 7) / (5 × 16 × 12) = - 105 / 960
Step 5: Simplify the fraction if possible:
The fraction -105/960 can be simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 15:
-105 ÷ 15 / 960 ÷ 15 = -7/64
Therefore, the result of (−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7) is -7/64.
To solve the expression (-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7), we can follow these steps:
Step 1: Simplify the expression using the commutative property of multiplication. Rearrange the terms if necessary.
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7) = (-3/5) × (5/16) × (7/12) × (-1) × (-1) ÷ (16/3) × (7/5)
Step 2: Apply the associative property of multiplication to group the terms together.
[(-3/5) × (5/16) × (7/12) × (-1) × (-1)] ÷ [(16/3) × (7/5)]
Step 3: Multiply the numerators and denominators separately.
[-3 × 5 × 7 × 1 × 1] ÷ [5 × 16 × 12 × 16 × 1 × 7 × 3 × 5]
Step 4: Simplify the numerator and denominator separately.
[-105] ÷ [268,800]
Step 5: Divide the numerator by the denominator to evaluate the expression.
-105 ÷ 268,800 = -0.000390625
So, (-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7) is approximately equal to -0.000390625.