Basic Math Examples

${(\frac{4}{3})}^{2} \div (- \frac{- {1.2}^{2}}{\frac{- 3^{2}}{- 5}}) - \frac{2}{9}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

${(\frac{4}{3})}^{2} (- \frac{\frac{- 3^{2}}{- 5}}{- {1.2}^{2}}) - \frac{2}{9}$

Step 1.2

Apply the product rule to $\frac{4}{3}$ .

$\frac{4^{2}}{3^{2}} (- \frac{\frac{- 3^{2}}{- 5}}{- {1.2}^{2}}) - \frac{2}{9}$

Step 1.3

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

$\frac{16}{3^{2}} (- \frac{\frac{- 3^{2}}{- 5}}{- {1.2}^{2}}) - \frac{2}{9}$

Step 1.4

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

$\frac{16}{9} (- \frac{\frac{- 3^{2}}{- 5}}{- {1.2}^{2}}) - \frac{2}{9}$

Step 1.5

Multiply the numerator by the reciprocal of the denominator.

$\frac{16}{9} (- (\frac{- 3^{2}}{- 5} \cdot \frac{1}{- {1.2}^{2}})) - \frac{2}{9}$

Step 1.6

Combine.

$\frac{16}{9} (- \frac{- 3^{2} \cdot 1}{- 5 (- {1.2}^{2})}) - \frac{2}{9}$

Step 1.7

Dividing two negative values results in a positive value.

$\frac{16}{9} (- \frac{3^{2}}{- 5 \cdot ({1.2}^{2})}) - \frac{2}{9}$

Step 1.8

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

$\frac{16}{9} (- \frac{9}{- 5 \cdot {1.2}^{2}}) - \frac{2}{9}$

Step 1.9

Raise $1.2$ to the power of $2$ .

$\frac{16}{9} (- \frac{9}{- 5 \cdot 1.44}) - \frac{2}{9}$

Step 1.10

Multiply $- 5$ by $1.44$ .

$\frac{16}{9} (- \frac{9}{- 7.2}) - \frac{2}{9}$

Step 1.11

Cancel the common factor of $9$ .

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Step 1.11.1

Move the leading negative in $- \frac{9}{- 7.2}$ into the numerator.

$\frac{16}{9} \cdot \frac{- 9}{- 7.2} - \frac{2}{9}$

Step 1.11.2

Factor $9$ out of $- 9$ .

$\frac{16}{9} \cdot \frac{9 (- 1)}{- 7.2} - \frac{2}{9}$

Step 1.11.3

Cancel the common factor.

$\frac{16}{9} \cdot \frac{9 \cdot - 1}{- 7.2} - \frac{2}{9}$

Step 1.11.4

Rewrite the expression.

$16 (\frac{- 1}{- 7.2}) - \frac{2}{9}$

Step 1.12

Combine $16$ and $\frac{- 1}{- 7.2}$ .

$\frac{16 \cdot - 1}{- 7.2} - \frac{2}{9}$

Step 1.13

Multiply $16$ by $- 1$ .

$\frac{- 16}{- 7.2} - \frac{2}{9}$

Step 1.14

Divide $- 16$ by $- 7.2$ .

$2.\overline{2} - \frac{2}{9}$

Step 2

To write $2.\overline{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$2.\overline{2} \cdot \frac{9}{9} - \frac{2}{9}$

Step 3

Combine $2.\overline{2}$ and $\frac{9}{9}$ .

$\frac{2.\overline{2} \cdot 9}{9} - \frac{2}{9}$

Step 4

Combine the numerators over the common denominator.

$\frac{2.\overline{2} \cdot 9 - 2}{9}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2.\overline{2}$ by $9$ .

$\frac{20 - 2}{9}$

Step 5.2

Subtract $2$ from $20$ .

$\frac{18}{9}$

Step 6

Divide $18$ by $9$ .

$2$