Use the properties of operations and rules for multiplying and dividing to solve: (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4) (1 point)
First, let's simplify the expression step by step using the rules for multiplying and dividing.
Step 1: Multiply -2 and 1/5:
(-2) × (1/5) = -2/5
Step 2: Divide -2/5 by 2/3:
(-2/5) ÷ (2/3) = (-2/5) × (3/2) = -6/10 = -3/5
Step 3: Multiply -3/5 by -5/6:
(-3/5) × (-5/6) = (3/5) × (5/6) = 15/30 = 1/2
Step 4: Divide 1/2 by 3/4:
(1/2) ÷ (3/4) = (1/2) × (4/3) = 4/6 = 2/3
Therefore, the value of the expression (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) is 2/3.
To solve the expression: (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4), we can follow the order of operations, which is parentheses first, then multiplication and division from left to right.
Let's simplify each operation step-by-step:
1. Multiply (-2) by (1/5):
(-2) × (1/5) = -2/5
2. Divide the previous result by (2/3):
(-2/5) ÷ (2/3)
To divide by a fraction, we can multiply by its reciprocal:
(-2/5) × (3/2)
3. Multiply the result by (-5/6):
(-2/5) × (3/2) × (-5/6)
To multiply fractions, we multiply the numerators and denominators separately:
(-2 × 3) / (5 × 2) × (-5/6)
(-6) / (10) × (-5/6)
4. Finally, divide by (3/4):
(-6/10) × (-5/6) ÷ (3/4)
Again, to divide by a fraction, we multiply by its reciprocal:
(-6/10) × (-5/6) × (4/3)
Now, let's simplify the fractions:
(-6 × -5) / (10 × 6) × (4/3)
(30) / (60) × (4/3)
Reducing the fraction 30/60:
(1/2) × (4/3)
1/2 × 4/3
Finally, let's multiply the fractions together:
(1 × 4) / (2 × 3)
4/6
The final answer is 4/6, which simplifies to 2/3.
To solve this expression, we need to follow the properties of operations and rules for multiplying and dividing.
Let's break down the expression step by step:
Step 1: Start by multiplying the first two numbers.
(-2) × (1/5) = -2/5
Step 2: Next, multiply the result from step 1 by the next number.
-2/5 × (2/3) = (-2/5) × (2/3)
To multiply fractions, multiply the numerators and multiply the denominators:
(-2/5) × (2/3) = (-2 × 2) / (5 × 3) = -4/15
Step 3: Now, multiply the result from step 2 by the next number.
-4/15 × (-5/6) = (-4/15) × (-5/6)
To multiply fractions, multiply the numerators and multiply the denominators:
(-4/15) × (-5/6) = (-4 × -5) / (15 × 6) = 20/90
Step 4: Finally, divide the result from step 3 by the last number.
20/90 ÷ (3/4) = (20/90) ÷ (3/4)
To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
(20/90) ÷ (3/4) = (20/90) × (4/3)
To simplify, multiply the numerators and multiply the denominators:
(20/90) × (4/3) = (20 × 4) / (90 × 3) = 80/270
To further simplify, reduce the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 10:
80/270 = (80 ÷ 10) / (270 ÷ 10) = 8/27
Therefore, the value of the given expression (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) is 8/27.