Basic Math Examples

$\frac{\frac{10}{5} - {(- 2)}^{2}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 1

To write $- {(- 2)}^{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{10}{5} - {(- 2)}^{2} \cdot \frac{5}{5}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 2

Combine $- {(- 2)}^{2}$ and $\frac{5}{5}$ .

$\frac{\frac{10}{5} + \frac{- {(- 2)}^{2} \cdot 5}{5}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{\frac{10 - {(- 2)}^{2} \cdot 5}{5}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{\frac{10 - 1 \cdot 4 \cdot 5}{5}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 4.2

Multiply $- 1$ by $4$ .

$\frac{\frac{10 - 4 \cdot 5}{5}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 4.3

Multiply $- 4$ by $5$ .

$\frac{\frac{10 - 20}{5}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 4.4

Subtract $20$ from $10$ .

$\frac{\frac{- 10}{5}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5

Simplify each term.

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Step 5.1

Cancel the common factor of $- 10$ and $5$ .

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Step 5.1.1

Factor $5$ out of $- 10$ .

$\frac{\frac{5 \cdot - 2}{5}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $5$ out of $5$ .

$\frac{\frac{5 \cdot - 2}{5 (1)}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.1.2.2

Cancel the common factor.

$\frac{\frac{5 \cdot - 2}{5 \cdot 1}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.1.2.3

Rewrite the expression.

$\frac{\frac{- 2}{1}}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.1.2.4

Divide $- 2$ by $1$ .

$\frac{- 2}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.2

Cancel the common factor of $- 2$ and $(2 \cdot 5 - 6) - 2$ .

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Step 5.2.1

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{(2 \cdot 5 - 6) - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $2$ out of $2 \cdot 5$ .

$\frac{2 (- 1)}{2 (5) - 6 - 2} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.2.2.2

Factor $2$ out of $- 6$ .

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

Step 5.2.2.3

Factor $2$ out of $2 (5) + 2 (- 3)$ .

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

Step 5.2.2.4

Factor $2$ out of $- 2$ .

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

Step 5.2.2.5

Factor $2$ out of $2 (5 - 3) + 2 (- 1)$ .

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

Step 5.2.2.6

Cancel the common factor.

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

Step 5.2.2.7

Rewrite the expression.

$\frac{- 1}{5 - 3 - 1} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.3

Simplify the denominator.

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Step 5.3.1

Subtract $3$ from $5$ .

$\frac{- 1}{2 - 1} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.3.2

Subtract $1$ from $2$ .

$\frac{- 1}{1} + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.4

Divide $- 1$ by $1$ .

$- 1 + \frac{5^{2} - 4^{2}}{3^{2}}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Raise $5$ to the power of $2$ .

$- 1 + \frac{25 - 4^{2}}{3^{2}}$

Step 5.5.2

Raise $4$ to the power of $2$ .

$- 1 + \frac{25 - 1 \cdot 16}{3^{2}}$

Step 5.5.3

Multiply $- 1$ by $16$ .

$- 1 + \frac{25 - 16}{3^{2}}$

Step 5.5.4

Subtract $16$ from $25$ .

$- 1 + \frac{9}{3^{2}}$

Step 5.6

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

$- 1 + \frac{9}{9}$

Step 5.7

Divide $9$ by $9$ .

$- 1 + 1$

Step 6

Add $- 1$ and $1$ .

$0$