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.) 9
D.) 147/75
To solve the expression, we need to simplify step by step using the properties of operations.
First, we can simplify the multiplication of the signed numbers: (-4) × (-3) = 12 because the product of two negative numbers is positive.
Next, we can simplify the multiplication of the fractions: (7/5) × (7/15) = 49/75 because multiplying two fractions is done by multiplying the numerators together and the denominators together.
Finally, we can simplify the division by multiplying by the reciprocal of the fraction: 12 ÷ (49/75) = 12 × (75/49).
To multiply fractions, multiply the numerators together and the denominators together: 12 × 75 = 900, 49.
Therefore, the final answer is 900/49 or 18 36/49.
D.) 147/75 is the correct answer.
To solve the expression (−4)×(7/5)×(−3/4)÷(7/15), we can apply the properties of operations and rules for multiplying and dividing signed numbers.
Step 1: Multiply the numbers with the same sign together.
(−4) × (−3) = 12
Step 2: Multiply the numbers with different signs together.
(7/5) × (7/15) = 49/75
Step 3: Divide the result from step 1 by the result from step 2.
12 ÷ (49/75)
To divide by a fraction, we can multiply by the reciprocal of the fraction.
12 × (75/49) = 900/49
So the final answer is 900/49, which is equivalent to 18 and 18/49.
Therefore, the correct answer is D) 147/75.
To solve the expression (-4)×(7/5)×(-3/4)÷(7/15), we can follow the order of operations (also known as PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, let's simplify the multiplication and division operations. We'll start from left to right.
(-4) × (7/5) = -28/5
Now we have (-28/5) × (-3/4).
When multiplying two negative numbers, the result is positive. Therefore, we have:
(-28/5) × (-3/4) = 84/20 = 21/5
Next, let's divide by (7/15).
To divide fractions, we can multiply by the reciprocal of the divisor. The reciprocal of (7/15) is (15/7).
So, we have:
(21/5) ÷ (7/15) = (21/5) × (15/7)
Now, let's simplify this multiplication.
To multiply fractions, we simply multiply the numerators together and the denominators together.
(21/5) × (15/7) = (21 × 15)/(5 × 7) = 315/35 = 9
Therefore, the answer is C.) 9.
To summarize:
(-4) × (7/5) × (-3/4) ÷ (7/15) simplifies to 9.