Use the properties of operations and rules for multiplying and dividing signed numbers to solve:
(−4) × (7/5) × (−3/4 ) ÷ (7/15)
A −9
B −147/75
C 147/75
D 9
To solve this problem, we follow the order of operations: parentheses, multiplication/division (from left to right), and addition/subtraction (from left to right).
First, we simplify within the parentheses:
(−4) × (7/5) × (−3/4) ÷ (7/15) = (−4) × (7/5) × (−3/4) ÷ (7/15)
= (−4) × (7/5) × (−3/4) × (15/7)
= (−4) × (7 × 15) / (5 × 4 × 7)
= (−4) × (105) / (20 × 7)
= −420 / 140
Next, we simplify the division:
−420 / 140 = (−420) ÷ (140)
= (−420) × (1/140)
= (−420/1) × (1/140)
Finally, we multiply the numerators and the denominators:
= (−420 × 1) / (1 × 140)
= −420/140.
Simplifying further, we get:
−420/140 = −3/1 = −3.
Therefore, the answer is D) 9.
To simplify the expression (−4) × (7/5) × (−3/4) ÷ (7/15), we will follow the order of operations, which is parentheses, multiplication and division (from left to right), and addition and subtraction (from left to right).
First, we will simplify the multiplication and division operations.
(−4) × (7/5) × (−3/4) ÷ (7/15)
= (−4) × (7/5) × (−3/4) × (15/7) (Flipping the divisor and multiplying by its reciprocal)
= [(−4) × (7) × (−3) × (15)] / [(5) × (4) × (7)] (Multiplying the numerators and denominators separately)
= [−4 × 7 × −3 × 15] / [5 × 4 × 7] (Simplifying further)
= [84 × 45] / [140] (Performing the multiplications)
= 3780 / 140
= 27
Therefore, the simplified expression is 27.
The correct answer is not among the options provided.
To solve this problem, we can follow the order of operations and apply the properties and rules for multiplying and dividing signed numbers.
Step 1: Multiply the numbers from left to right.
Product = (−4) × (7/5) × (−3/4 ) ÷ (7/15)
Let's start with the first multiplication: (−4) × (7/5)
When multiplying two numbers with different signs, the product is negative.
(−4) × (7/5) = −(4 × 7)/5 = −28/5
We now have: Product = −28/5 × (−3/4 ) ÷ (7/15)
Now, let's do the second multiplication: (−28/5) × (−3/4)
When multiplying two negative numbers, the product is positive.
(−28/5) × (−3/4) = (28/5) × (3/4) = (28 × 3)/(5 × 4) = 84/20
We now have: Product = 84/20 ÷ (7/15)
Step 2: Divide the result by (7/15).
When dividing by a fraction, we can multiply by its reciprocal.
Reciprocal of (7/15) is (15/7).
So, we can rewrite the expression as multiplication instead of division:
Product = 84/20 × (15/7)
Now, let's multiply: (84/20) × (15/7)
When multiplying two fractions, we multiply the numerators together and the denominators together.
(84/20) × (15/7) = (84 × 15)/(20 × 7) = 1260/140
Step 3: Simplify the result.
We can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor.
The greatest common divisor of 1260 and 140 is 140. Dividing both by 140 gives us:
1260/140 = 9/1
Therefore, the solution is 9.
The correct option is D) 9.