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)
To solve this expression, we will use the properties of operations and rules for multiplying and dividing:
Step 1: Multiply the numerators together and the denominators together:
[(8)(-3)(-4)]/[(9)(4)(9)(-5)(3)(5)]
Step 2: Simplify the expression by canceling out common factors between the numerator and denominator:
[96]/[(9)(9)(5)(3)(5)]
Step 3: Multiply the remaining terms in the denominator together:
[96]/[4050]
Step 4: Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 6:
[16]/[675]
Therefore, the simplified expression is 16/675.
To solve this expression using the properties of operations and rules for multiplying and dividing, we follow these steps:
Step 1: Simplify by performing the multiplications and divisions from left to right, one at a time.
(8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5)
Step 2: Multiply the fractions:
(8/9) × (-3/4) = -24/36
Step 3: Simplify the fraction, if possible:
-24/36 = -2/3
Step 4: Divide the fractions:
(-2/3) ÷ (1/9) = -18/3
Step 5: Simplify the fraction:
-18/3 = -6
Step 6: Divide the fractions:
(-6) ÷ (4/5) ÷ (3/5)
Step 7: Multiply the fractions:
(-6) ÷ (4/5) = (-6) × (5/4) = -30/4
Step 8: Simplify the fraction:
-30/4 = -15/2
Step 9: Divide the fractions:
(-15/2) ÷ (3/5) = (-15/2) × (5/3) = -75/6
Step 10: Simplify the fraction:
-75/6 = -25/2
Therefore, the final result of the given expression is -25/2.
To solve the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5), we can use the properties of operations and rules for multiplying and dividing.
Step 1: Start with the multiplication and division operations from left to right.
First, let's multiply the first two fractions: (8/9) × (-3/4).
To multiply fractions, multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
(8/9) × (-3/4) = (8 × -3) / (9 × 4) = -24/36.
Next, let's divide the result by the next fraction: -24/36 ÷ (1/9).
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by switching the numerator and denominator.
-24/36 ÷ (1/9) = -24/36 × (9/1) = -24/4.
Step 2: Simplify the obtained fraction further.
To simplify the fraction -24/4, we can divide both the numerator and the denominator by their greatest common divisor, which is 4.
-24/4 = -6.
Finally, let's multiply the remaining fraction with the next fraction: -6 × (-4/5) ÷ (3/5).
-6 × (-4/5) ÷ (3/5) = (-6 × -4) / 5 × 1/3.
To multiply fractions, multiply the numerators together and the denominators together.
((-6) × (-4)) / (5 × 1) × 1/3 = (24/5) × 1/3.
24/5 × 1/3 = (24 × 1) / (5 × 3) = 24/15.
Step 3: Simplify the obtained fraction further.
To simplify the fraction 24/15, we can divide both the numerator and the denominator by their greatest common divisor, which is 3.
24/15 = 8/5.
Therefore, the value of the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) is 8/5.