Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{5}{6}$ .

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

Step 1.2

Raise $5$ to the power of $2$ .

$\frac{25}{6^{2}} + \frac{1}{3} \cdot \frac{2}{5}$

Step 1.3

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

$\frac{25}{36} + \frac{1}{3} \cdot \frac{2}{5}$

Step 1.4

Multiply $\frac{1}{3} \cdot \frac{2}{5}$ .

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Step 1.4.1

Multiply $\frac{1}{3}$ by $\frac{2}{5}$ .

$\frac{25}{36} + \frac{2}{3 \cdot 5}$

Step 1.4.2

Multiply $3$ by $5$ .

$\frac{25}{36} + \frac{2}{15}$

Step 2

To write $\frac{25}{36}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{25}{36} \cdot \frac{5}{5} + \frac{2}{15}$

Step 3

To write $\frac{2}{15}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{25}{36} \cdot \frac{5}{5} + \frac{2}{15} \cdot \frac{12}{12}$

Step 4

Write each expression with a common denominator of $180$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{25}{36}$ by $\frac{5}{5}$ .

$\frac{25 \cdot 5}{36 \cdot 5} + \frac{2}{15} \cdot \frac{12}{12}$

Step 4.2

Multiply $36$ by $5$ .

$\frac{25 \cdot 5}{180} + \frac{2}{15} \cdot \frac{12}{12}$

Step 4.3

Multiply $\frac{2}{15}$ by $\frac{12}{12}$ .

$\frac{25 \cdot 5}{180} + \frac{2 \cdot 12}{15 \cdot 12}$

Step 4.4

Multiply $15$ by $12$ .

$\frac{25 \cdot 5}{180} + \frac{2 \cdot 12}{180}$

Step 5

Combine the numerators over the common denominator.

$\frac{25 \cdot 5 + 2 \cdot 12}{180}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $25$ by $5$ .

$\frac{125 + 2 \cdot 12}{180}$

Step 6.2

Multiply $2$ by $12$ .

$\frac{125 + 24}{180}$

Step 6.3

Add $125$ and $24$ .

$\frac{149}{180}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{149}{180}$

Decimal Form:

$0.82\overline{7}$