Use the properties of operations and rules for multiplying and dividing to solve:
(8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5)
(1 point)
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To solve this problem, we will need to simplify the expression by applying the rules for multiplying and dividing fractions.
First, we can simplify the multiplication:
(8/9) × (-3/4) = (-24/36).
Next, let's simplify the division:
(-24/36) ÷ (1/9) = (-24/36) × (9/1) = (-24/4) = -6.
Now, let's simplify the last division:
-6 × (-4/5) ÷ (3/5) = (-6 × -4/5) ÷ (3/5) = (24/5) ÷ (3/5) = (24/5) × (5/3) = (24/3) = 8.
Therefore, the final result is 8.
To solve this expression, you can follow the order of operations (PEMDAS/BODMAS) which states to perform multiplication and division from left to right before addition and subtraction.
Let's simplify the expression step by step:
Step 1: Multiply the fractions
(8/9) × (-3/4) = -24/36
Step 2: Divide by another fraction
Now divide -24/36 by (1/9):
(-24/36) ÷ (1/9)
To divide fractions, you should multiply by the reciprocal of the second fraction.
(-24/36) × (9/1) = -216/36
Step 3: Multiply by another fraction
Now multiply -216/36 by (-4/5):
(-216/36) × (-4/5)
To multiply fractions, you can multiply the numerators together and the denominators together.
(-216 × -4) / (36 × 5) = 864 / 180
Step 4: Simplify the fraction
To simplify the fraction, find the greatest common divisor (GCD) of 864 and 180, which is 36:
864 ÷ 36 = 24
180 ÷ 36 = 5
So, the simplified fraction is:
24/5
Therefore, the solution to the expression (8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5) is 24/5.