To solve the expression

$-\frac{5}{9} - \left(\frac{2}{5}\right)^2 + 3$

we’ll go through each term step-by-step:

1. Square the fraction: $\left(\frac{2}{5}\right)^2 = \frac{4}{25}$.

   Now, the expression becomes: $-\frac{5}{9} - \frac{4}{25} + 3$

2. Convert 3 to a fraction: To combine these terms, it helps to express $3$ as a fraction: $3 = \frac{75}{25}$

   This allows us to add the fractions more easily.

3. Find a common denominator for $-\frac{5}{9}$, $-\frac{4}{25}$, and $3$ (expressed as $\frac{75}{25}$) if we want to combine them directly. Alternatively, we could solve each component separately and add them up, but it’s simplest to approximate.

Calculation

• $-\frac{5}{9} \approx -0.555$
• $-\frac{4}{25} = -0.16$
• $3 = 3.0$

Summing these: $-0.555 - 0.16 + 3 = 2.285$

Thus, the result is approximately: $2.285$

Would you like a detailed breakdown of each fractional calculation or have further questions?

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Related Questions

1. How would you solve expressions with mixed fractions?
2. How do you add and subtract fractions with different denominators?
3. What are common ways to approximate decimals?
4. How do you express whole numbers as fractions?
5. How does order of operations apply to fractions?

Tip

When dealing with mixed expressions, converting all terms to a common form (like decimals or fractions) can make calculations smoother.