Question

Use the properties of operations and rules for multiplying and dividing to solve:

(9)÷(5/4)×(7/9)×(−5)÷(7/2)

(1 point)
Responses

−8


1,225/8


8


−1,225/8

Answer 1

To solve the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2), we can simplify step by step:

Step 1: Perform the division (9) ÷ (5/4) by multiplying the numerator (9) by the reciprocal of the denominator (5/4). The reciprocal of 5/4 is 4/5.

(9) ÷ (5/4) = (9) × (4/5) = 36/5

Step 2: Multiply the result from Step 1, 36/5, by (7/9).

(36/5) × (7/9) = (36 × 7) / (5 × 9) = 252/45

Step 3: Multiply the result from Step 2, 252/45, by (-5).

(252/45) × (-5) = -1260/45

Step 4: Perform the division -1260/45 by multiplying the numerator (-1260) by the reciprocal of the denominator (45/1). The reciprocal of 45/1 is 1/45.

(-1260/45) ÷ (45/1) = (-1260/45) × (1/45) = -1260/2025

Simplifying the fraction -1260/2025 gives the final answer:

-1260/2025 = -14/25

Therefore, the value of the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) is -14/25.