Basic Math Examples

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

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Raise $- 1$ to the power of $2$ .

$1 \frac{2^{2}}{3^{2}} - \frac{3}{4} \cdot 2 \frac{1}{3}$

Step 3

Multiply $\frac{2^{2}}{3^{2}}$ by $1$ .

$\frac{2^{2}}{3^{2}} - \frac{3}{4} \cdot 2 \frac{1}{3}$

Step 4

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

$\frac{4}{3^{2}} - \frac{3}{4} \cdot 2 \frac{1}{3}$

Step 5

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

$\frac{4}{9} - \frac{3}{4} \cdot 2 \frac{1}{3}$

Step 6

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 6.1

A mixed number is an addition of its whole and fractional parts.

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

Step 6.2

Add $2$ and $\frac{1}{3}$ .

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Step 6.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 6.2.2

Combine $2$ and $\frac{3}{3}$ .

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

Step 6.2.3

Combine the numerators over the common denominator.

$\frac{4}{9} - \frac{3}{4} \cdot \frac{2 \cdot 3 + 1}{3}$

Step 6.2.4

Simplify the numerator.

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Step 6.2.4.1

Multiply $2$ by $3$ .

$\frac{4}{9} - \frac{3}{4} \cdot \frac{6 + 1}{3}$

Step 6.2.4.2

Add $6$ and $1$ .

$\frac{4}{9} - \frac{3}{4} \cdot \frac{7}{3}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{4}{9} + \frac{- 3}{4} \cdot \frac{7}{3}$

Step 7.2

Factor $3$ out of $- 3$ .

$\frac{4}{9} + \frac{3 (- 1)}{4} \cdot \frac{7}{3}$

Step 7.3

Cancel the common factor.

$\frac{4}{9} + \frac{3 \cdot - 1}{4} \cdot \frac{7}{3}$

Step 7.4

Rewrite the expression.

$\frac{4}{9} + \frac{- 1}{4} \cdot 7$

Step 8

Combine $\frac{- 1}{4}$ and $7$ .

$\frac{4}{9} + \frac{- 1 \cdot 7}{4}$

Step 9

Multiply $- 1$ by $7$ .

$\frac{4}{9} + \frac{- 7}{4}$

Step 10

Move the negative in front of the fraction.

$\frac{4}{9} - \frac{7}{4}$

Step 11

To write $\frac{4}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{4}{9} \cdot \frac{4}{4} - \frac{7}{4}$

Step 12

To write $- \frac{7}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{4}{9} \cdot \frac{4}{4} - \frac{7}{4} \cdot \frac{9}{9}$

Step 13

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 13.1

Multiply $\frac{4}{9}$ by $\frac{4}{4}$ .

$\frac{4 \cdot 4}{9 \cdot 4} - \frac{7}{4} \cdot \frac{9}{9}$

Step 13.2

Multiply $9$ by $4$ .

$\frac{4 \cdot 4}{36} - \frac{7}{4} \cdot \frac{9}{9}$

Step 13.3

Multiply $\frac{7}{4}$ by $\frac{9}{9}$ .

$\frac{4 \cdot 4}{36} - \frac{7 \cdot 9}{4 \cdot 9}$

Step 13.4

Multiply $4$ by $9$ .

$\frac{4 \cdot 4}{36} - \frac{7 \cdot 9}{36}$

Step 14

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 - 7 \cdot 9}{36}$

Step 15

Simplify the numerator.

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Step 15.1

Multiply $4$ by $4$ .

$\frac{16 - 7 \cdot 9}{36}$

Step 15.2

Multiply $- 7$ by $9$ .

$\frac{16 - 63}{36}$

Step 15.3

Subtract $63$ from $16$ .

$\frac{- 47}{36}$

Step 16

Move the negative in front of the fraction.

$- \frac{47}{36}$