(4)/(5)div [(1)/(5)+((3)/(4)-(1)/(3))cdot 2]

Question

(4)/(5)div [(1)/(5)+((3)/(4)-(1)/(3))cdot 2]

Answer 1

## Step 1: Simplify the expression inside the parentheses### The expression inside the parentheses is \(\left( \frac{3}{4} - \frac{1}{3} \right)\). To simplify this, we need a common denominator. The least common multiple of 4 and 3 is 12. Convert each fraction:

Subtract these fractions:

## Step 2: Multiply the result by 2### Now multiply the result from Step 1 by 2:

## Step 3: Add the result to

### Add

to the result from Step 2. Find a common denominator for 5 and 6, which is 30:

Add these fractions:

## Step 4: Divide

by the result from Step 3### The original expression is

. Dividing by a fraction is equivalent to multiplying by its reciprocal:

Simplify

by finding the greatest common divisor, which is 5:

Question

(4)/(5)div [(1)/(5)+((3)/(4)-(1)/(3))cdot 2]

Solution

Answer

Explanation