Basic Math Examples

$\frac{13}{20} \div \frac{3}{40} \cdot {(\frac{2}{3})}^{2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{13}{20} \cdot \frac{40}{3} \cdot {(\frac{2}{3})}^{2}$

Step 2

Cancel the common factor of $20$ .

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Step 2.1

Factor $20$ out of $40$ .

$\frac{13}{20} \cdot \frac{20 (2)}{3} \cdot {(\frac{2}{3})}^{2}$

Step 2.2

Cancel the common factor.

$\frac{13}{20} \cdot \frac{20 \cdot 2}{3} \cdot {(\frac{2}{3})}^{2}$

Step 2.3

Rewrite the expression.

$13 (\frac{2}{3}) \cdot {(\frac{2}{3})}^{2}$

Step 3

Combine $13$ and $\frac{2}{3}$ .

$\frac{13 \cdot 2}{3} \cdot {(\frac{2}{3})}^{2}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $13$ by $2$ .

$\frac{26}{3} \cdot {(\frac{2}{3})}^{2}$

Step 4.2

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

$\frac{26}{3} \cdot \frac{2^{2}}{3^{2}}$

Step 5

Combine.

$\frac{26 \cdot 2^{2}}{3 \cdot 3^{2}}$

Step 6

Multiply $3$ by $3^{2}$ by adding the exponents.

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Step 6.1

Multiply $3$ by $3^{2}$ .

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Step 6.1.1

Raise $3$ to the power of $1$ .

$\frac{26 \cdot 2^{2}}{3^{1} \cdot 3^{2}}$

Step 6.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{26 \cdot 2^{2}}{3^{1 + 2}}$

Step 6.2

Add $1$ and $2$ .

$\frac{26 \cdot 2^{2}}{3^{3}}$

Step 7

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

$\frac{26 \cdot 4}{3^{3}}$

Step 8

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

$\frac{26 \cdot 4}{27}$

Step 9

Multiply $26$ by $4$ .

$\frac{104}{27}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{104}{27}$

Decimal Form:

$3.\overline{851}$

Mixed Number Form:

$3 \frac{23}{27}$