Use the properties of operations and rules for multiplying and dividing to solve:
(−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7).
To solve this expression, we can simplify it step by step following the properties of operations and the rules for multiplying and dividing fractions.
First, let's multiply the numerators and the denominators together:
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
= (-3 × 5 × 7) / (5 × 16 × 12) ÷ (-3 × 16 × -5 / 7)
Next, we can simplify the numerator and denominator separately:
Numerator: -3 × 5 × 7 = -105
Denominator: 5 × 16 × 12 = 960
Now, let's divide the numerator by the denominator:
-105 / 960
Finally, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor:
-105 ÷ 15 / 960 ÷ 15
= -7 / 64
Therefore, the simplified result is -7/64.
To solve the expression (−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7), we can follow these steps using the properties of operations and rules for multiplying and dividing:
Step 1: Simplify each fraction:
(−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7)
= (-3 × 5 × 7) / (5 × 16 × 12) ÷ (-3 × 16 ×(-5) / 7)
= (-3 × 5 × 7) / (5 × 4 × 4 × 3) ÷ (-3 × 16 ×(-1))
= (-3 × 5 × 7) / (5 × 4 × 4 × 3) ÷ (3 × 16)
= (-15 × 7) / (20 × 3) ÷ (48)
= (-105) / (60) ÷ (48)
Step 2: Divide the numerator and the denominator of the fraction by their greatest common divisor (GCD) to simplify the fraction:
GCD of (-105) and (60) is 15.
GCD of (60) and (48) is 12.
(-105) / (60) ÷ (48)
= (-7) / (4) ÷ (4)
Step 3: Divide the numerator by the denominator and multiply the result by the reciprocal of the denominator:
(-7) / (4) ÷ (4)
= (-7/4) × (1/4)
= (−7/16)
Therefore, the solution to the expression (−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7) is −7/16.
To solve the given expression, we can make use of the properties of operations and rules for multiplying and dividing fractions.
Let's break down the expression step by step:
Step 1:
Start by simplifying each fraction separately.
- (-3/5) = -3 ÷ 5 = -0.6
- (5/16) = 5 ÷ 16 = 0.3125
- (7/12) = 7 ÷ 12 = 0.5833
- (-3/16) = -3 ÷ 16 = -0.1875
- (-5/7) = -5 ÷ 7 = -0.7143
Step 2:
Now substitute the simplified fractions back into the expression:
(-0.6) × (0.3125) × (0.5833) ÷ (-0.1875) × (-0.7143)
Step 3:
Next, multiply the numerators together and multiply the denominators together separately:
-0.6 × 0.3125 × 0.5833 ÷ -0.1875 × -0.7143
(-0.6 × 0.3125 × 0.5833) ÷ (-0.1875 × -0.7143)
Step 4:
Multiply the numerators together and multiply the denominators together:
-0.6 × 0.3125 × 0.5833 = -0.10798625
-0.1875 × -0.7143 = 0.133748125
Step 5:
Finally, divide the numerator by the denominator:
-0.10798625 ÷ 0.133748125 = -0.806718915
Therefore, the value of the expression (-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7) is approximately -0.8067.