Use the properties of operations and rules for multiplying and dividing to solve:
(−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)
please show me how you got the answer
To solve this expression, we can simplify step by step using the properties of operations and rules for multiplying and dividing fractions.
First, let's start by canceling out the common factors in the numerator and denominator:
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
= (-3/5) × (1/16) × (7/12) ÷ (1/16) × (5/7)
= (-3/5) × (7/12) ÷ (5/7)
Next, we can simplify the multiplication and division:
= (-3/5) × (7/12) ÷ (5/7)
= (-3/5) × (7/12) × (7/5)
= (-3 × 7) / (5 × 12) × (7/5)
= -21/60 × 7/5
Now, we can simplify the expression further by canceling out common factors:
= -21/60 × 7/5
= -7/20 × 7/5
= (-7 × 7)/(20 × 5)
= -49/100
Therefore, the final answer is -49/100.
wrong
Apologies for the mistake. Let's do the calculations again:
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
First, we simplify the numerator and denominator:
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
Now, we can divide the numerator by the denominator:
(-105/960) ÷ (15/112)
When dividing fractions, we can multiply the first fraction by the reciprocal of the second fraction:
(-105/960) × (112/15) = (-105 × 112) / (960 × 15) = -11760/14400
Next, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (which is 240):
(-11760/14400) ÷ 240/240 = (-49/60) ÷ 1 = -49/60
Therefore, the final answer is -49/60.
To solve the given expression, let's break it down step-by-step:
Step 1: Simplify within parentheses:
(−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7)
Step 2: Simplify the multiplications:
For multiplying fractions, you multiply the numerators to get the new numerator, and you multiply the denominators to get the new denominator.
(-3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7) = [-3 × 5 × 7 × (-5)] / [5 × 16 × 12 × (-3) × (-7)]
Step 3: Simplify within the numerator and denominator:
-3 × 5 × 7 × (-5) = -525
5 × 16 × 12 × (-3) × (-7) = -10080
Therefore, the expression simplifies to:
(-3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7) = -525 / -10080
Step 4: Simplify the fraction:
To simplify the fraction -525 / -10080, we can cancel out common factors. Both -525 and -10080 are divisible by 105:
-525 ÷ 105 = -5
-10080 ÷ 105 = -96
So, the expression simplifies further to:
(-3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7) = -5 / -96
Step 5: Further simplify the fraction:
To simplify the fraction -5 / -96, we find that both -5 and -96 are divisible by -1:
-5 ÷ -1 = 5
-96 ÷ -1 = 96
Therefore, the final result is:
(-3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7) = 5 / 96