Use the properties of operations and rules for multiplying and dividing signed numbers to solve.
(-4) x (7/5) x (-3/4) divided by (7/15)
A. 9
B. -147/75
C. -9
D. 147/75
To solve this problem, start by simplifying the expression given.
(-4) x (7/5) x (-3/4) divided by (7/15)
Step 1: Multiply the numerators together and the denominators together:
(-4 x 7 x -3) / (5 x 4) / (7/15)
Step 2: Multiply the numbers:
(-84) / (20) / (7/15)
Step 3: Divide by the reciprocal of the fraction in the denominator:
(-84) / (20) x (15/7)
Step 4: Simplify the expression further:
-84 x 15 / 20 x 7
Step 5: Multiply the numerators and denominators:
-1260 / 140
Step 6: Simplify the fraction:
-9
Therefore, the solution is C. -9.
To solve this expression, we need to apply the properties of operations and rules for multiplying and dividing signed numbers.
First, let's simplify the expression:
(-4) x (7/5) x (-3/4) divided by (7/15)
To multiply the numbers:
(-4) x (7/5) = -28/5
Next, we multiply the result by (-3/4):
(-28/5) x (-3/4) = 84/20 = 21/5
Finally, we divide the result by (7/15):
(21/5) divided by (7/15) = (21/5) x (15/7)
Now, we can cancel out common factors:
(21/5) x (15/7) = (21/1) x (3/1) = 63
Therefore, the simplified expression is 63.
The correct answer is not among the options provided.
To solve the given expression (-4) x (7/5) x (-3/4) divided by (7/15), we can follow these steps:
Step 1: Simplify all the individual multiplications:
(-4) x (7/5) x (-3/4) = (-4) x (-3) x (7/5) x (1/4)
Step 2: Multiply the whole numbers first:
(-4) x (-3) = 12
Step 3: Multiply the fractions:
(7/5) x (1/4) = 7/20
Step 4: Divide the result by the fraction (7/15):
12 x (7/20) divided by (7/15)
Step 5: Dividing by a fraction is the same as multiplying by its reciprocal, so we will multiply by the reciprocal of (7/15):
12 x (7/20) x (15/7)
Step 6: Simplify the multiplication:
12 x (7/20) x (15/7) = (12 x 7 x 15) / (20 x 7)
Step 7: Cancel out common factors between the numerator and denominator:
The numerator has a factor of 7 that cancels out with the denominator, leaving:
12 x 15 / 20 = 180 / 20
Step 8: Simplify the division:
180 / 20 = 9
Therefore, the value of (-4) x (7/5) x (-3/4) divided by (7/15) is 9.
So, the correct answer is A. 9.