Use the properties of operations and rules for multiplying and dividing signed numbers to solve:
(−4)×(7/5)×(−3/4)÷(71/5)
(1 point)
Responses
−147/75
−9
9
147/75
To solve the expression (−4)×(7/5)×(−3/4)÷(71/5), we first simplify the multiplication and division operations separately.
First, multiply the numbers:
(−4) × (7/5) × (−3/4) = (-4) × (-3/4) × (7/5) = (12/4) × (7/5) = 84/20
Next, divide the result by (71/5):
(84/20) ÷ (71/5) = (84/20) × (5/71) = (420/1420) = 147/75
Therefore, the simplified expression is 147/75.
To solve the expression (-4)×(7/5)×(-3/4)÷(71/5), follow these steps:
Step 1: Multiply the first two numbers: (-4)×(7/5) = -28/5.
Step 2: Multiply the result from step 1 by the next number: (-28/5)×(-3/4) = 84/20.
Step 3: Divide the result from step 2 by the last number: (84/20) ÷ (71/5).
To divide fractions, you need to multiply by the reciprocal of the divisor. The reciprocal of (71/5) is (5/71). Therefore:
(84/20) ÷ (71/5) = (84/20) × (5/71).
Step 4: Multiply the numerators together: 84 × 5 = 420.
Step 5: Multiply the denominators together: 20 × 71 = 1420.
Step 6: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which in this case is 20: 420/1420 = 21/71.
Therefore, the final answer is 21/71.
To solve the expression (−4)×(7/5)×(−3/4)÷(71/5), we need to apply the properties of operations and rules for multiplying and dividing signed numbers. Follow these steps to get the answer:
Step 1: Simplify the multiplication and division operations separately.
Start with the multiplication:
(−4) × (7/5) × (−3/4)
Multiply the numerators together: -4 × 7 × -3 = 84.
Multiply the denominators together: 5 × 4 = 20.
Simplified multiplication: 84/20.
Now, perform the division:
84/20 ÷ (71/5)
To divide two fractions, we can multiply the first fraction by the reciprocal of the second fraction:
84/20 × (5/71)
Step 2: Simplify the division by multiplying the two fractions together.
Multiply the numerators together: 84 × 5 = 420.
Multiply the denominators together: 20 × 71 = 1420.
Simplified division: 420/1420.
Step 3: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).
The GCD of 420 and 1420 is 140. Divide both numerator and denominator by 140 to simplify the fraction:
420 ÷ 140 = 3 (numerator)
1420 ÷ 140 = 10 (denominator)
Simplified fraction: 3/10.
So, the final answer is 3/10.