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 (- 3/5)(5/16)(7/12) / (- 3/16) * (- 5/7), we can simplify the expression step by step using the properties of multiplication and division.
First, let's simplify the numerator:
(- 3/5)(5/16)(7/12) = (3*5*7) / (5*16*12) = 105 / 960
Now let's simplify the denominator:
(- 3/16) * (- 5/7) = (3*5) / (16*7) = 15 / 112
Now we can simplify the whole expression:
(105 / 960) / (15 / 112) = (105 / 960) * (112 / 15) = (105 * 112) / (960 * 15) = 11760 / 14400
Finally, we can simplify the fraction:
11760 / 14400 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 240.
11760 / 14400 = (11760 / 240) / (14400 / 240) = 49 / 60
Therefore, (- 3/5)(5/16)(7/12) / (- 3/16) * (- 5/7) simplifies to 49/60.
To solve this expression step by step, we can follow the order of operations (also known as PEMDAS or BODMAS).
Step 1: Multiply the numerators of the fractions together and multiply the denominators of the fractions together separately.
(-3/5)(5/16)(7/12) / (-3/16) * (-5/7)
Numerator: (-3)(5)(7) = -105
Denominator: (5)(16)(12) = 960
The expression now becomes:
-105/960 / (-3/16) * (-5/7)
Step 2: Divide the fractions by multiplying by the reciprocal of the divisor.
To divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction.
(-105/960) * (16/-3) * (-7/5)
Step 3: Simplify the expression by canceling out common factors.
The numerator (-105) has a common factor of 5 with the denominator (960), and the numerator (-7) has a common factor of 7 with the denominator (5).
(-21/192) * (16/-1) * (-1/1)
The expression now becomes:
(-21/192) * (-16)
Step 4: Multiply the numerators together and the denominators together.
Numerator: (-21)(-16) = 336
Denominator: (192)(1) = 192
The expression now becomes:
336/192
Step 5: Simplify the fraction if possible.
The numerator (336) and denominator (192) have a common factor of 4.
336/192 = (336/4)/(192/4) = 84/48
Step 6: Simplify the fraction further by canceling out common factors.
Both the numerator (84) and denominator (48) have a common factor of 12.
84/48 = (84/12)/(48/12) = 7/4
So the final simplified answer is 7/4.