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 the expression (−3/5) × (5/16) × (7/12) ÷ (−3/16) ×( −5/7), we need to follow the properties of operations and rules for multiplying and dividing fractions.
Step 1: Multiply the numerators.
(-3) × (5) × (7) × (-5) = 525
Step 2: Multiply the denominators.
(5) × (16) × (12) × (3) × (16) × (7) = 120960
Step 3: Divide the numerator by the denominator.
525 ÷ 120960
Step 4: Simplify the fraction if possible.
To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD is 105 because both 525 and 120960 are divisible by 105.
525 ÷ 105 = 5
120960 ÷ 105 = 1152
So, the simplified fraction is 5/1152 or 5 ÷ 1152.
Therefore, the result of (−3/5) × (5/16) × (7/12) ÷ (−3/16) ×( −5/7) is 5/1152.
To solve the expression, we can use the properties of operations and rules for multiplying and dividing.
First, we can simplify the expression by canceling out the common factors in the numerator and denominator of the different fractions:
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
We can cancel out the common factor of 5 in the first and second fraction:
(-3/1) × (1/16) × (7/12) ÷ (-3/16) × (-1/7)
Next, we can cancel out the common factor of 3 in the first and fourth fraction:
(-1/1) × (1/16) × (7/12) ÷ (-1/16) × (-1/7)
Further simplifying, we can cancel out the common factor of 16 in the first and fourth fraction:
(-1/1) × (1/1) × (7/12) ÷ (-1/1) × (-1/7)
Now, we can multiply the fractions:
(-1) × (1) × (7/12) ÷ (-1) × (-1/7)
Simplifying the expression further, we can cancel out the common factor of 7:
(-1) × (1) × (1/12) ÷ (-1) × (-1)
Finally, we can simplify the expression by multiplying the fractions:
(-1/12) ÷ (1)
The division of -1/12 by 1 is equal to -1/12.
So the solution to the expression (-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7) is -1/12.
To solve the expression (−3/5) × (5/16) × (7/12) ÷ (−3/16) ×( −5/7), we can use the properties of operations and rules for multiplying and dividing.
Step 1: Simplify the numerator and denominator separately:
Numerator: (−3/5) × (5/16) × (7/12) = (-3*5*7) / (5*16*12) = -105 / 960
Denominator: (−3/16) × (−5/7) = (-3*-5) / (16*7) = 15 / 112
Step 2: Divide the simplified numerator by the simplified denominator:
-105 / 960 ÷ 15 / 112 = (-105*112) / (960*15) = -11760 / 14400
Step 3: Simplify the fraction:
-11760 / 14400 = -49 / 60
Therefore, the final result is -49/60.