use the properties of operations and rules for multiplying and dividing signed numbers to solve:
(-4) x (7/5) x (-3/4) ÷ (7/15)
A. 9
B. 147/75
C. -147/75
D. -9
To solve this problem, we will apply the properties of operations and rules for multiplying and dividing signed numbers.
First, let's simplify the expression step by step:
(-4) x (7/5) x (-3/4) ÷ (7/15)
Step 1: Simplify the multiplication.
(-4) x (-3) = 12
Step 2: Simplify the division.
(7/5) ÷ (7/15) = (7/5) x (15/7) = (7 x 15) / (5 x 7) = 105/35
Step 3: Combine the multiplication and division.
12 x (105/35) = 12 x (3/1) = 12 x 3 = 36
Therefore, the solution is 36.
None of the answer choices provide 36 as an option. But we can simplify 36 to get the correct answer:
36 = 36/1
So, the solution is 36/1.
Comparing the answer choices, we can see that:
36/1 = 36/1
Thus, the correct answer is not listed among the given options.
To solve the given expression, we will follow the properties of operations and rules for multiplying and dividing signed numbers step-by-step.
Step 1: Multiply the numbers together, ignoring the signs for now:
(-4) x (7/5) x (-3/4) x (7/15) = (4) x (7/5) x (3/4) x (7/15)
Step 2: Simplify the expression:
(4) x (7/5) x (3/4) x (7/15) = (4 x 7 x 3 x 7) / (5 x 4 x 15)
Step 3: Perform the multiplication:
(4 x 7 x 3 x 7) / (5 x 4 x 15) = (588) / (300)
Step 4: Reduce the fraction to simplest form:
588/300 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 12:
(588 ÷ 12) / (300 ÷ 12) = 49/25
Step 5: Take into account the signs of the numbers:
Since there are an odd number of negative signs in the given expression, the final answer will be negative. Thus, the answer is:
C. -147/75
To solve the given expression (-4) x (7/5) x (-3/4) ÷ (7/15), we can apply the properties of operations and rules for multiplying and dividing signed numbers.
Step 1: Simplify the multiplication of the numbers: (-4) x (7/5) x (-3/4) = (-28/5) x (-3/4)
To multiply fractions, we multiply the numerators together and the denominators together:
= (-28 x -3) / (5 x 4) = (84) / (20)
Step 2: Simplify the division of the resulting fraction by (7/15): (84/20) ÷ (7/15)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
= (84/20) x (15/7)
Simplify the multiplication of the fractions by multiplying the numerators and denominators together:
= (84 x 15) / (20 x 7) = 1260 / 140
Step 3: Simplify the resulting fraction: 1260 / 140
To simplify a fraction, we can cancel out any common factors between the numerator and the denominator. In this case, both the numerator and denominator have a common factor of 140.
Divide both the numerator and the denominator by 140:
= 1260 ÷ 140 / 140 ÷ 140
= 9 / 1
Therefore, the final solution is 9, which corresponds to option A.