(1+2/3-1/4)x(4/5-3/4)^2

2 min read Jun 16, 2024

Simplifying the Expression: (1 + 2/3 - 1/4) x (4/5 - 3/4)^2

This article will walk you through the steps of simplifying the expression: (1 + 2/3 - 1/4) x (4/5 - 3/4)^2. We'll break it down into manageable steps to make the process clear.

Step 1: Simplifying the Parentheses

First, we need to simplify the expressions within the parentheses.

(1 + 2/3 - 1/4) To add and subtract fractions, we need a common denominator. The least common denominator for 3 and 4 is 12.
- 1 = 12/12
- 2/3 = 8/12
- 1/4 = 3/12
- (12/12 + 8/12 - 3/12) = 17/12
(4/5 - 3/4) The least common denominator for 5 and 4 is 20.
- 4/5 = 16/20
- 3/4 = 15/20
- (16/20 - 15/20) = 1/20

Step 2: Squaring the Second Parenthesis

Now, we need to square the simplified expression from the second parenthesis:

(1/20)^2 = 1/400

Step 3: Multiplying the Results

Finally, we multiply the results from the simplified parentheses:

(17/12) x (1/400) = 17/4800

Conclusion

The simplified form of the expression (1 + 2/3 - 1/4) x (4/5 - 3/4)^2 is 17/4800.