Use the properties of operations and rules for multiplying and dividing to solve:
(8/9) x (-3/4) divide (1/9) x (-4/5) divide (3/5)
To solve this expression, we can use the properties of operations and rules for multiplying and dividing fractions.
First, determine the numerator of the fraction:
(8/9) x (-3/4) = (8 x -3) / (9 x 4) = -24/36
Next, determine the numerator of the second fraction and divide it by the denominator:
(-24/36) ÷ (1/9) = (-24/36) x (9/1) = (-24 x 9) / (36 x 1) = -216/36
Finally, determine the numerator of the third fraction and divide it by the denominator:
(-216/36) ÷ (3/5) = (-216/36) x (5/3) = (-216 x 5) / (36 x 3) = -1080/108
Simplifying the fractional result:
-1080/108 = -10
Therefore, the solution to the expression (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5) is -10.
To solve the expression (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5), we will follow the order of operations, which is parentheses, multiplications and divisions from left to right.
Step 1: Simplify the multiplications
Multiply the fractions together from left to right:
(8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5) = (-24/36) ÷ (-4/45) ÷ (3/5)
Simplify the fraction multiplication using the property of multiplication of fractions: numerator x numerator divided by denominator x denominator:
(-24/36) ÷ (-4/45) ÷ (3/5) = (-24 x -4 x 5) / (36 x 45 x 3)
Step 2: Simplify the divisions
Divide the numerator by the denominator:
(-24 x -4 x 5) / (36 x 45 x 3) = (480) / (4860)
Step 3: Simplify the fraction
Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor:
(480) / (4860) = (80) / (810)
The simplified answer for the given expression is 80/810.
To solve the given expression using the properties of operations and rules for multiplying and dividing, we can simplify each multiplication and division separately, and then combine the results.
First, let's simplify each expression individually:
(8/9) x (-3/4) = (8 x -3) / (9 x 4)
= -24 / 36
= -2/3 (multiply the numerators and denominators separately)
(1/9) x (-4/5) = (1 x -4) / (9 x 5)
= -4 / 45 (multiply the numerators and denominators separately)
(3/5) = 3/5 (this expression doesn't require simplification)
Now, let's multiply and divide the simplified expressions:
(-2/3) ÷ (-4/45) ÷ (3/5)
When dividing, we can multiply by the reciprocal of the divisor, which means we need to take the reciprocal of the second fraction:
(-2/3) ÷ (-4/45) x (5/3)
Now, we can multiply across:
= (-2/3) x (5/3) x (-4/45)
= (-2 x 5 x -4) / (3 x 3 x 45)
= 40 / 405 (multiply the numerators and denominators separately)
= 8/81
Therefore, the final simplified result of the expression (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5) is 8/81.