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 multiply and divide the fractions in the order they appear, while applying the properties of operations and the rules for multiplying and dividing fractions:
(−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7)
First, let's start by multiplying the fractions:
(−3/5) * (5/16) * (7/12) ÷ (−3/16) * (−5/7)
(-3 * 5 * 7) / (5 * 16 * 12) ÷ (-3 * -5) / (16 * 7)
(-105) / (960) ÷ (15) / (112)
Next, let's simplify each fraction:
(-105) / (960) = -7/64
(15) / (112) = 5/37
Now we can divide the fractions:
(-7/64) ÷ (5/37)
To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
(-7/64) * (37/5)
(-7 * 37) / (64 * 5)
(-259) / (320)
Therefore, the expression (-3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7) simplifies to -259/320.
Are you sure
Apologies for the mistake. Let's go through the calculation again.
(−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7)
First, we can simplify the negative signs:
(-3/5) × (5/16) × (7/12) ÷ (3/16) × (5/7)
Next, let's multiply the fractions together:
((-3)(5)(7))/((5)(16)(12)) ÷ ((3)(5))/(16)(7)
(-105)/(960) ÷ (15)/(112)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(-105)/(960) * (112)/(15)
Simplify the multiplication:
(-105)(112)/(960)(15)
(-11760)/(14400)
Now, we can simplify the fraction:
(-392)/(480)
Finally, we can simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 8:
(-392 ÷ 8)/(480 ÷ 8)
(-49)/(60)
Therefore, the expression (-3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7) simplifies to -49/60.
Are either of them correct
I apologize for the mistakes in my previous responses. Let's go through the calculation again:
(−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7)
First, let's simplify the negative signs:
(-3/5) × (5/16) × (7/12) ÷ (3/16) × (5/7)
Next, let's multiply the fractions together:
((-3)(5)(7))/((5)(16)(12)) ÷ ((3)(5))/(16)(7)
(-105)/(960) ÷ (15)/(112)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(-105)/(960) * (112)/(15)
Simplify the multiplication:
(-105)(112)/(960)(15)
(-11760)/(14400)
Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 240:
(-11760 ÷ 240)/(14400 ÷ 240)
(-49)/(60)
Therefore, the correct answer is -49/60.
That not right
Apologies for the confusion. Let's solve the expression again:
(−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7)
First, let's simplify the negative signs:
(3/5) × (5/16) × (7/12) ÷ (3/16) × (5/7)
Next, let's multiply the fractions together:
(3 * 5 * 7) / (5 * 16 * 12) ÷ (3 * 5) / (16 * 7)
(105) / (960) ÷ (15) / (112)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(105) / (960) * (112) / (15)
Simplify the multiplication:
(105 * 112) / (960 * 15)
11760 / 14400
Now, let's simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 240:
(11760 ÷ 240) / (14400 ÷ 240)
49 / 60
Therefore, the expression (−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7) simplifies to 49/60.
Not that either
Apologies for the mistakes in my previous responses. Let's go through the calculation again:
(−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7)
First, we can simplify the negative signs:
(-3/5) × (5/16) × (7/12) ÷ (3/16) × (5/7)
Next, let's multiply the fractions together:
((-3)(5)(7))/((5)(16)(12)) ÷ ((3)(16))/(16)(7)
(-105)/(960) ÷ (48)/(112)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(-105)/(960) * (112)/(48)
Simplify the multiplication:
(-105)(112)/(960)(48)
(-11760)/(46080)
Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 240:
(-11760 ÷ 240)/(46080 ÷ 240)
(-49)/(192)
Therefore, the expression (-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7) simplifies to -49/192.