Use the properties of operations and rules for multiplying and dividing signed numbers to solve: (−4)×(7/5)×(−3/4)÷(7 1/5) (1 point) Responses −14775 negative Start Fraction 147 over 75 End Fraction 9
To solve this expression, we can apply the properties of operations and rules for multiplying and dividing signed numbers.
First, let's simplify the expression step by step.
(−4)×(7/5)×(−3/4)÷(7 1/5)
Step 1: Multiply the numerators and denominators of the fractions:
(-4)×7×(-3)÷(5×4)÷(7 1/5)
Step 2: Perform the multiplication and division from left to right:
-4×7×(-3)÷20÷(7 1/5)
Step 3: Multiply -4 and 7:
-28×(-3)÷20÷(7 1/5)
Step 4: Multiply -28 and -3:
84÷20÷(7 1/5)
Step 5: Divide 84 by 20:
4.2÷(7 1/5)
Step 6: Convert the mixed number (7 1/5) to an improper fraction:
4.2÷(36/5)
Step 7: Divide 4.2 by 36/5:
4.2÷(36/5) = 4.2 * (5/36) = 0.7
Therefore, the final result is 0.7.
Answer: 0.7
To solve the expression (-4)×(7/5)×(-3/4)÷(7 1/5), we can follow the order of operations:
Step 1: Evaluate the multiplication and division from left to right.
(-4)×(7/5)×(-3/4)÷(7 1/5)
= (-28/5) × (-3/4) ÷ (36/5)
Step 2: Simplify the multiplication and division of fractions.
= [(-28) × (-3)] / [(5) × (4)] ÷ [(36/5)]
= [84] / [20] ÷ [(36/5)]
Step 3: Simplify the division of fractions by multiplying the numerator by the reciprocal of the denominator.
= [84] / [20] × [(5/36)]
Step 4: Simplify the multiplication of fractions.
= [(84) × (5)] / [(20) × (36)]
= 420 / 720
Step 5: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 120.
= (420 ÷ 120) / (720 ÷ 120)
= 7/12
So, the final answer is 7/12.
To solve the given expression, we can follow these steps using the properties of operations and rules for multiplying and dividing signed numbers:
Step 1: Start by multiplying the first three numbers: (-4) × (7/5) × (-3/4).
Start Fraction (-4) End Fraction × Start Fraction (7/5) End Fraction × Start Fraction (-3/4) End Fraction
To multiply fractions, we multiply the numerators together and the denominators together:
(-4) × (7/5) × (-3/4) = (-4 × 7 × -3) / (5 × 4)
Simplified: (84 / 20)
Step 2: Next, divide the result from Step 1 by the fourth number: (84/20) ÷ (7 1/5).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(84/20) ÷ (7 1/5) = (84/20) × (5/36)
Simplified: (84 × 5) / (20 × 36) = 420 / 720
Step 3: Simplify the fraction.
Both 420 and 720 are divisible by 60, so we can divide them by 60 to simplify the fraction further:
420 / 720 = (420 ÷ 60) / (720 ÷ 60) = 7 / 12
Therefore, (-4) × (7/5) × (-3/4) ÷ (7 1/5) equals 7/12 or 0.5833.
Note: If you need the decimal answer, divide 7 by 12 to get 0.5833.