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 the expression:
(−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7),
we can follow the order of operations and simplify step by step:
1. Multiply the fractions from left to right:
(-3/5) × (5/16) = (-15/80) = (-3/16)
2. Multiply the remaining fractions:
(-3/16) × (7/12) = (-21/192) = (-7/64)
3. Divide the fractions:
(-7/64) ÷ (-3/16) = (-7/64) × (-16/3) = (112/192) = (7/12)
4. Multiply the fraction by the last fraction:
(7/12) × (-5/7) = (-35/84) = (-5/12)
Therefore, the expression (−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7) simplifies to (-5/12).
First, let's simplify the expression:
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
To simplify this expression, we can cancel out any common factors between the numerator and denominator. Let's look for common factors:
((-3) × 5 × 7 × (-5)) / ((5) × (4) × 3 × (-3)) × (-5)
Next, we can simplify the numerator and denominator separately before dividing:
= (105 × (-5)) / ((1 × 4 × 3 × (-1)) × (-5))
= (-525) / ((-12) × (-1) × (-5))
= (-525) / (60)
Finally, we can divide -525 by 60:
= -525 / 60
Simplifying further, we can divide both the numerator and denominator by their greatest common divisor, which is 5:
= -105 / 12
So, the simplified expression is -105/12.
Wrong
Apologies for the mistake. Let's examine the expression again:
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
To solve this expression, we can start by multiplying the numerators together and the denominators together. Let's simplify this step:
((-3) × (5) × (7) × (-5)) / ((5) × (16) × (12) × (-3)) × (-5) × (7)
Multiplying the numerators together gives us -525, and multiplying the denominators together gives us -5,760.
Now, let's simplify the expression further:
-525 / (-5,760)
Since the numerator and denominator both have negatives, they cancel each other out:
525 / 5,760
This expression cannot be simplified any further, so the final answer is 525/5,760.
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 fractions. Here's a step-by-step process on how to do it:
Step 1: Multiply the numerators together.
Numerator = (−3) × (5) × (7) × (−5) = 525
Step 2: Multiply the denominators together.
Denominator = (5) × (16) × (12) × (−3) × (−7) = 10080
Step 3: Simplify the fraction if possible by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
GCD(525, 10080) = 105
Simplified numerator = 525 ÷ 105 = 5
Simplified denominator = 10080 ÷ 105 = 96
Therefore, the expression (−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7) simplifies to 5/96.