Pre-Algebra Examples

$\frac{3}{5} - 4 + {(\frac{2}{3})}^{2} \cdot 9$

Step 1

Find the common denominator.

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Step 1.1

Write $- 4$ as a fraction with denominator $1$ .

$\frac{3}{5} + \frac{- 4}{1} + {(\frac{2}{3})}^{2} \cdot 9$

Step 1.2

Multiply $\frac{- 4}{1}$ by $\frac{5}{5}$ .

$\frac{3}{5} + \frac{- 4}{1} \cdot \frac{5}{5} + {(\frac{2}{3})}^{2} \cdot 9$

Step 1.3

Multiply $\frac{- 4}{1}$ by $\frac{5}{5}$ .

$\frac{3}{5} + \frac{- 4 \cdot 5}{5} + {(\frac{2}{3})}^{2} \cdot 9$

Step 1.4

Write ${(\frac{2}{3})}^{2} \cdot 9$ as a fraction with denominator $1$ .

$\frac{3}{5} + \frac{- 4 \cdot 5}{5} + \frac{{(\frac{2}{3})}^{2} \cdot 9}{1}$

Step 1.5

Multiply $\frac{{(\frac{2}{3})}^{2} \cdot 9}{1}$ by $\frac{5}{5}$ .

$\frac{3}{5} + \frac{- 4 \cdot 5}{5} + \frac{{(\frac{2}{3})}^{2} \cdot 9}{1} \cdot \frac{5}{5}$

Step 1.6

Multiply $\frac{{(\frac{2}{3})}^{2} \cdot 9}{1}$ by $\frac{5}{5}$ .

$\frac{3}{5} + \frac{- 4 \cdot 5}{5} + \frac{{(\frac{2}{3})}^{2} \cdot 9 \cdot 5}{5}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 - 4 \cdot 5 + {(\frac{2}{3})}^{2} \cdot 9 \cdot 5}{5}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 4$ by $5$ .

$\frac{3 - 20 + {(\frac{2}{3})}^{2} \cdot 9 \cdot 5}{5}$

Step 3.2

Apply the product rule to $\frac{2}{3}$ .

$\frac{3 - 20 + \frac{2^{2}}{3^{2}} \cdot 9 \cdot 5}{5}$

Step 3.3

Raise $2$ to the power of $2$ .

$\frac{3 - 20 + \frac{4}{3^{2}} \cdot 9 \cdot 5}{5}$

Step 3.4

Raise $3$ to the power of $2$ .

$\frac{3 - 20 + \frac{4}{9} \cdot 9 \cdot 5}{5}$

Step 3.5

Cancel the common factor of $9$ .

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Step 3.5.1

Cancel the common factor.

$\frac{3 - 20 + \frac{4}{9} \cdot 9 \cdot 5}{5}$

Step 3.5.2

Rewrite the expression.

$\frac{3 - 20 + 4 \cdot 5}{5}$

Step 3.6

Multiply $4$ by $5$ .

$\frac{3 - 20 + 20}{5}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Subtract $20$ from $3$ .

$\frac{- 17 + 20}{5}$

Step 4.2

Add $- 17$ and $20$ .

$\frac{3}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{5}$

Decimal Form:

$0.6$