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.