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 expression, we can follow the order of operations (PEMDAS).
First, let's simplify the multiplication and division.
(-4) x (7/5) x (-3/4) ÷ (7/15)
=(-4) x (-7/5) x (-3/4) ÷ (7/15)
Now, let's multiply the numbers together.
=(-4)(-7)(-3)/(5)(4)(7)/(15)
=84/20/7/15
Next, let's simplify the division by multiplying by the reciprocal.
=(84/20)(1/7)(15/1)
= (84/20)(15/7)
= (84)(15)/(20)(7)
= 1260/140
= 9
Therefore, the answer is A. 9.
To solve this problem, we will follow the properties of operations and rules for multiplying and dividing signed numbers.
Step 1: Multiply the numbers from left to right, regardless of the signs.
(-4) × (7/5) × (-3/4) ÷ (7/15)
= -4 × 7/5 × -3/4 ÷ 7/15
Step 2: Multiply the numerators together and the denominators together.
= (-4 × 7 × -3) / (5 × 4) ÷ 7/15
= (-84) / 20 ÷ 7/15
Step 3: Divide the fraction by multiplying by the reciprocal.
= (-84) / 20 × 15/7
= (-12) × (3/1)
Step 4: Multiply the numerators and denominators.
= (-12 × 3) / 1
= -36 / 1
= -36
Therefore, the solution is -36, which corresponds to option D.
To solve the given expression (-4) x (7/5) x (-3/4) ÷ (7/15), we can follow these steps:
Step 1: Apply the multiplication of signed numbers rule, which states that the product of two negative numbers or two positive numbers is positive, and the product of a negative number and a positive number is negative.
(-4) x (7/5) x (-3/4) ÷ (7/15)
= (-1 x 4) x (7/5) x (-1 x 3/4) ÷ (7/15)
= -1 x 4 x 7/5 x -1 x 3/4 ÷ 7/15
= -4 x 7/5 x 3/4 ÷ 7/15
Step 2: Simplify the multiplication and division by canceling out common factors.
= (-4 x 7 x 3) / (5 x 4) ÷ 7/15
= -84 / 20 ÷ 7/15
Step 3: Apply the division of fractions rule, which states that dividing by a fraction is equivalent to multiplying by its reciprocal.
= -84 / 20 x 15/7
= -3.36 x 2.143
≈ -7.2
Therefore, the answer to the given expression (-4) x (7/5) x (-3/4) ÷ (7/15) is approximately -7.2.
So, the correct option is not provided among the answer choices.