(8/9) x (-3/4) divide (1/90 x (-4/5) divide (3/5)
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
To solve this expression step-by-step, first let's simplify the expression inside the first set of parentheses:
(8/9) x (-3/4) = -24/36 = -2/3
Next, let's simplify the expression inside the second set of parentheses:
(1/90 x (-4/5)) = -4/450 = -1/112.5
Finally, let's divide the result from the second set of parentheses by the expression inside the third pair of parentheses:
(-1/112.5) ÷ (3/5) = (-1/112.5) x (5/3) = -5/337.5
Therefore, the final simplified expression is -5/337.5.
To solve this expression, you need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
First, let's simplify each division separately.
1. (8/9) x (-3/4) = -24/36 = -2/3
2. (1/90 x (-4/5)) = -4/450 = -1/112.5
Now, we have:
(-2/3) ÷ (-1/112.5) ÷ (3/5)
To divide by a fraction, we can multiply by its reciprocal:
(-2/3) x (112.5/-1) ÷ (3/5) = (-2/3) x (-112.5/1) ÷ (3/5)
Now, we can simplify the multiplication:
(-2 x -112.5) / (3 x 3/5) = 225 / (9/5)
To divide by a fraction, we can multiply by its reciprocal:
225 x (5/9) = 1125/9 = 125
Therefore, the answer is 125.