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 can use the associative property of multiplication and division to rearrange the terms:
(8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5)
= [(8/9) × (-3/4) × (-4/5)] ÷ [(1/9) × (3/5)]
= [(8 × -3 × -4)/ (9 × 4 × 5)] ÷ [(1 × 3) / (9 × 5)]
= [(8 × 3 × 4)/ (9 × 4 × 5)] ÷ [(1 × 3) / (9 × 5)]
= [96/(180)] ÷ [3/45]
= 96/180 ÷ 3/45
Now, we can simplify the fractions by dividing the numerators and denominators:
= (96 ÷ 180) ÷ (3 ÷ 45)
= (2/5) ÷ (1/15)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
= (2/5) × (15/1)
= 30/5
= 6
Therefore, (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) equals 6.
To solve the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5), we can simplify it step by step by using the properties of operations and rules for multiplying and dividing.
Step 1: Multiply the fractions from left to right.
(8/9) × (-3/4) = -24/36
Step 2: Divide the result by the next fraction from left to right.
-24/36 ÷ (1/9) = -24/36 × 9/1 = -24/4 = -6
Step 3: Multiply the result by the next fraction from left to right.
-6 × (-4/5) = 24/5
Step 4: Divide the result by the last fraction.
24/5 ÷ (3/5) = 24/5 × 5/3 = 120/15 = 8
So, the final result is 8.
To solve the given expression, we can follow these steps using the properties of operations and rules for multiplying and dividing:
Step 1: Simplify multiplication and division from left to right.
- Start by multiplying the first two fractions: (8/9) × (-3/4).
- To multiply fractions, multiply the numerators (top numbers) and the denominators (bottom numbers).
- (8/9) × (-3/4) = (8 × -3) / (9 × 4) = -24/36.
- The fraction -24/36 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 12.
- -24/36 = -2/3.
Step 2: Continue simplifying the expression by performing division.
- Next, divide -2/3 by (1/9).
- To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction.
- -2/3 ÷ (1/9) = -2/3 × (9/1) = -2 × 9 / 3 × 1 = -18/3.
- The fraction -18/3 can be simplified by dividing both the numerator and denominator by their GCD, which is 3.
- -18/3 = -6/1 = -6.
Step 3: Continue simplifying the expression by multiplying and dividing the remaining fractions.
- Multiply -6 by (-4/5): -6 × (-4/5) = 24/5.
- Divide 24/5 by (3/5): 24/5 ÷ (3/5) = 24/5 × (5/3) = 24/3.
- The fraction 24/3 can be simplified by dividing both the numerator and denominator by their GCD, which is 3.
- 24/3 = 8/1 = 8.
Therefore, the solution to the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) is 8.