Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the product rule to $- \frac{1}{3}$ .

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

Step 1.1.2

Apply the product rule to $\frac{1}{3}$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

One to any power is one.

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

Step 1.5

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

$\frac{1}{9} + \frac{5}{6} \cdot (- \frac{2}{5})$

Step 1.6

Cancel the common factor of $5$ .

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Step 1.6.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{1}{9} + \frac{5}{6} \cdot \frac{- 2}{5}$

Step 1.6.2

Cancel the common factor.

$\frac{1}{9} + \frac{5}{6} \cdot \frac{- 2}{5}$

Step 1.6.3

Rewrite the expression.

$\frac{1}{9} + \frac{1}{6} \cdot - 2$

Step 1.7

Cancel the common factor of $2$ .

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Step 1.7.1

Factor $2$ out of $6$ .

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

Step 1.7.2

Factor $2$ out of $- 2$ .

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

Step 1.7.3

Cancel the common factor.

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

Step 1.7.4

Rewrite the expression.

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

Step 1.8

Combine $\frac{1}{3}$ and $- 1$ .

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

Step 1.9

Move the negative in front of the fraction.

$\frac{1}{9} - \frac{1}{3}$

Step 2

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Multiply $3$ by $3$ .

$\frac{1}{9} - \frac{3}{9}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 - 3}{9}$

Step 5

Subtract $3$ from $1$ .

$\frac{- 2}{9}$

Step 6

Move the negative in front of the fraction.

$- \frac{2}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{9}$

Decimal Form:

$- 0.\overline{2}$