Use the properties of operations and rules for multiplying dividing signed numbers to solve:
(-4)×(7/5)×(-3/4)÷(7/15)
A. 9
B. -147/75
C. 147/75
D. -9
To solve (-4)×(7/5)×(-3/4)÷(7/15), we can simplify step by step using the properties of operations and rules for multiplying and dividing signed numbers.
First, let's multiply (-4) with (7/5):
(-4)×(7/5) = (-4*7)/(5*1) = -28/5
Now, we multiply the result (-28/5) with (-3/4):
(-28/5)×(-3/4) = (-28*-3)/(5*4) = 84/20
Next, we divide the obtained fraction (84/20) by (7/15):
(84/20) ÷ (7/15) = (84/20) * (15/7) = (84*15)/(20*7) = 1260/140 = 9
Therefore, (-4)×(7/5)×(-3/4)÷(7/15) simplifies to 9, which means the correct option is:
A. 9
To solve this expression step-by-step, we will follow the rules for multiplying and dividing signed numbers, as well as the properties of operations.
First, let's simplify the expression step by step:
(-4) × (7/5) × (-3/4) ÷ (7/15)
Step 1: Multiplication of -4 and 7/5:
When multiplying a negative number by a positive number, the product will be negative.
So, (-4) × (7/5) = -28/5
The expression becomes:
(-28/5) × (-3/4) ÷ (7/15)
Step 2: Multiplication of -28/5 and -3/4:
When multiplying two negative numbers, the product will be positive.
So, (-28/5) × (-3/4) = 84/20 = 21/5
The expression becomes:
(21/5) ÷ (7/15)
Step 3: Division of 21/5 by 7/15:
To divide by a fraction, we can multiply by its reciprocal.
So,
(21/5) ÷ (7/15) = (21/5) × (15/7) = 315/35 = 9
Therefore, the answer is 9.
The correct option is A. 9.
To solve the expression (-4) × (7/5) × (-3/4) ÷ (7/15), we need to follow the properties of operations and rules for multiplying and dividing signed numbers.
Step 1: Simplify each division and multiplication operation, from left to right.
First, we have (-4) × (7/5). To multiply a negative number and a positive number, we simply multiply the absolute values and take the negative sign. So, (-4) × (7/5) = -(4 × 7/5) = -(28/5).
Next, we have -(28/5) × (-3/4). When we multiply two negative numbers, the result is positive. So, -(28/5) × (-3/4) = (28/5) × (3/4) = (28 × 3)/(5 × 4) = 84/20 = 21/5.
Now, we have 21/5 ÷ (7/15). To divide fractions, we multiply by the reciprocal of the second fraction. Therefore, 21/5 ÷ (7/15) = 21/5 × (15/7).
Step 2: Simplify the last division by canceling out common factors.
In this case, we can cancel out the factors of 5 and 7:
21/5 × (15/7) = (21/1) × (3/1) = (21 × 3)/(1 × 1) = 63/1 = 63.
So, the final answer to the expression (-4) × (7/5) × (-3/4) ÷ (7/15) is 63.
Therefore, the correct answer is A. 9.