Basic Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Combine $6^{2}$ and $\frac{2}{5}$ .

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

Step 1.2

Combine $\frac{6^{2} \cdot 2}{5}$ and $- 1$ .

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

Step 1.3

Multiply $\frac{6^{2} \cdot 2 \cdot - 1}{5}$ by $\frac{1}{3}$ .

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

Step 2

Simplify the expression.

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Step 2.1

Multiply $- 1$ by $2$ .

$\frac{5}{\frac{6^{2} \cdot - 2}{5 \cdot 3}}$

Step 2.2

Multiply $5$ by $3$ .

$\frac{5}{\frac{6^{2} \cdot - 2}{15}}$

Step 2.3

Raise $6$ to the power of $2$ .

$\frac{5}{\frac{36 \cdot - 2}{15}}$

Step 2.4

Multiply $36$ by $- 2$ .

$\frac{5}{\frac{- 72}{15}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $- 72$ and $15$ .

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Step 3.1.1

Factor $3$ out of $- 72$ .

$\frac{5}{\frac{3 (- 24)}{15}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $3$ out of $15$ .

$\frac{5}{\frac{3 \cdot - 24}{3 \cdot 5}}$

Step 3.1.2.2

Cancel the common factor.

$\frac{5}{\frac{3 \cdot - 24}{3 \cdot 5}}$

Step 3.1.2.3

Rewrite the expression.

$\frac{5}{\frac{- 24}{5}}$

Step 3.2

Move the negative in front of the fraction.

$\frac{5}{- \frac{24}{5}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$5 (- \frac{5}{24})$

Step 5

Multiply $5 (- \frac{5}{24})$ .

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Step 5.1

Multiply $- 1$ by $5$ .

$- 5 (\frac{5}{24})$

Step 5.2

Combine $- 5$ and $\frac{5}{24}$ .

$\frac{- 5 \cdot 5}{24}$

Step 5.3

Multiply $- 5$ by $5$ .

$\frac{- 25}{24}$

Step 6

Move the negative in front of the fraction.

$- \frac{25}{24}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{25}{24}$

Decimal Form:

$- 1.041\overline{6}$

Mixed Number Form:

$- 1 \frac{1}{24}$