Simplify the following expression:

\(\frac{0.7^2+(0.4+0.2)(0.7)+(0.4 \times 0.2)}{(0.7+0.4)}\)

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  1. 0.9
  2. 0.7
  3. 0.3
  4. 0.4

Answer (Detailed Solution Below)

Option 1 : 0.9
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Detailed Solution

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Given:

Expression: (0.72 + (0.4 + 0.2) × 0.7 + 0.4 × 0.2) / (0.7 + 0.4)

Formula used:

Simplify the numerator first and then divide by the denominator.

Calculation:

Numerator: 0.72 + (0.4 + 0.2) × 0.7 + 0.4 × 0.2

= 0.49 + 0.6 × 0.7 + 0.08

= 0.49 + 0.42 + 0.08

= 0.99

Denominator: 0.7 + 0.4

= 1.1

Now, divide the numerator by the denominator:

0.99 / 1.1

= 0.9

∴ The simplified value of the expression is 0.9.

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