To solve this expression, we will work from left to right following the order of operations (parentheses, exponents, multiplication/division from left to right, and finally addition/subtraction from left to right).
First, we have:
8/9 x (-3/4) ÷ (1/90 x (-4/5) ÷ (3/5)
Next, let's simplify the division inside the parentheses on the right:
8/9 x (-3/4) ÷ (1/90 x (-4/5) ÷ 3/5)
The division of fractions is the same as multiplying by the reciprocal, so:
8/9 x (-3/4) ÷ (1/90 x (-4/5) x 5/3)
Now, we can simplify the multiplication inside the parentheses on the right:
8/9 x (-3/4) ÷ (-4/18)
Next, multiply the fractions on the left:
-24/36 ÷ (-4/18)
Simplifying further, we have:
-2/3 ÷ (-2/9)
Again, division of fractions is the same as multiplying by the reciprocal, so:
-2/3 x (-9/2)
Finally, we multiply the fractions:
(2 x 9) / (3 x 2) = 18/6 = 3
Therefore, (8/9) x (-3/4) ÷ (1/90) x (-4/5) ÷ (3/5) = 3
(8/9) x (-3/4) divide (1/90 x (-4/5) divide (3/5)
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