Question

The value of \(\frac{0.325 \ \times \ 0.325\ + \ 0.175 \ \times\ 0.175\ + \ 25\ \times \ 0.00455}{5 \ \times \ 0.0065 \ \times \ 3.25\ - \ 7\ \times \ 0.175\ \times\ 0.025}\ + \ \frac{0.5}{1.5}\) is:

Answer 1

Correct Answer - Option 4 : \(\frac{11}{3}\)

Given:

\(\frac{0.325 \ \times \ 0.325\ + \ 0.175 \ \times\ 0.175\ + \ 25\ \times \ 0.00455}{5 \ \times \ 0.0065 \ \times \ 3.25\ - \ 7\ \times \ 0.175\ \times\ 0.025}\ + \ \frac{0.5}{1.5}\)

Formula Used:

(a + b)² = a² + b² + 2ab

(a² – b²) = (a + b) (a - b)

Concept Used:

We need to identify the numbers to fit them into the above stated formula.

Calculation:

Let a = 0.325 and b = 0.175

In the numerator,

25 × 0.00455 = 2 × 0.325 × 0.175

In the denominator,

5 × 0.0065 × 3.25 = (0.325)²

7 × 0.175 × 0.025 = (0.175)²

On Comparing Formulas with given equation we get,

\(\Rightarrow \frac{{{{\left( {0.325\ + \ 0.175} \right)}^2}}}{{\left( {0.325\ +\ 0.175} \right)\left( {0.325\ -\ 0.175} \right)}} + \frac{{0.5}}{{1.5}} \)

\(= \frac{{0.5}}{{0.15}} + \frac{{0.5}}{{1.5}} \)

= (5.5)/(1.5)

= 11/3

∴ The simplified Value of this Expression is 11/3