Use the properties of operations and rules for multiplying and dividing to solve:
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
To solve this expression, we can apply the properties of operations and rules for multiplying and dividing.
First, let's simplify the expression from left to right using the division property of equality:
(9) ÷ (5/4) = (9) × (4/5) = 36/5
Now, let's continue simplifying the expression by multiplying the fractions and the number:
(36/5) × (7/9) × (-5) ÷ (7/2)
= (36/5) × (7/9) × (-5) × (2/7)
Next, we can multiply the fractions and the numbers together:
(36/5) × (7/9) × (-5) × (2/7) = (36 × 7 × (-5) × 2) / (5 × 9 × 7) = -40/3
Therefore, (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) simplifies to -40/3.
Step 1: Simplify the division and multiplication from left to right.
(9) ÷ (5/4) = 9 * (4/5) = 36/5
(36/5) × (7/9) = (36 * 7) / (5 * 9) = 252/45
(252/45) × (-5) = (252 * -5) / 45 = -1260/45
(-1260/45) ÷ (7/2) = (-1260/45) * (2/7) = -2520/315
Step 2: Simplify the resulting fraction.
-2520/315 = (-2520/9) / (315/9) = -280/35
Step 3: Simplify the fraction further.
-280/35 = -8
Therefore, (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) is equal to -8.