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

(9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2)

1 answer

To solve this expression using the properties of operations and rules for multiplying and dividing, let's follow the order of operations (PEMDAS/BODMAS) and solve step by step.

First, let's simplify the multiplication and division from left to right:
(9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2)
9 ÷ (5/4) = 9 x (4/5) = 36/5
(36/5) x (7/9) = (36 x 7) / (5 x 9) = 252/45
(-5) ÷ (7/2) = -5 x (2/7) = -10/7

Now, let's multiply the remaining fractions:
(252/45) x (-10/7) = (252 x -10) / (45 x 7) = -2520/315 = -8

So, the final answer to the expression (9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2) is -8.