(9)÷(5/4)×(7/9)×(-5)÷(7/2)
To evaluate the expression (9)÷(5/4)×(7/9)×(-5)÷(7/2), we follow the order of operations, which is parentheses, multiplication and division from left to right.
First, let's simplify the expression within the parentheses.
(9)÷(5/4) = 9 ÷ (5/4) = 9 × (4/5) = 9 × 4/5 = 36/5
Now, let's simplify the multiplication and division from left to right.
(36/5) × (7/9) × (-5) ÷ (7/2)
Cancel out common factors:
(36/5) × (1/9) × (-1) ÷ (1/2)
Multiply the numerators:
(36 ×1 ×(-1)) / (5 × 9 × 1/2)
Multiply the denominators:
(36 × -1) / (5 × 9 × 1/2)
Simplify:
-36 / (45 × 1/2)
= -36 / (45/2)
To divide by a fraction, we multiply by its reciprocal:
= -36 × (2/45)
= -72/45
Simplify the fraction:
= -8/5
To solve this expression step-by-step, let's start with the division:
(9) ÷ (5/4)
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 5/4 is 4/5, so we have:
(9) × (4/5)
Multiplying 9 by 4 gives us 36:
36/5
Next, let's multiply this result by (7/9):
(36/5) × (7/9)
When multiplying fractions, we multiply the numerators together and the denominators together, which gives us:
(36 * 7)/(5 * 9)
252/45
Simplifying this fraction, we can see that both 252 and 45 are divisible by 9:
(252 ÷ 9) / (45 ÷ 9)
28/5
Finally, let's multiply this fraction by (-5) and divide it by (7/2):
(28/5) × (-5) ÷ (7/2)
To multiply fractions, we simply multiply the numerators and multiply the denominators:
(28 * -5) / (5 * 1) ÷ (7/2)
-140/5 ÷ (7/2)
To divide by a fraction, we can multiply by the reciprocal:
(-140/5) × (2/7)
Multiplying -140 by 2 gives us -280:
-280/5
This fraction can be simplified by dividing both the numerator and denominator by 5:
(-280 ÷ 5) / (5 ÷ 5)
-56/1
Therefore, the final result is -56.