Basic Math Examples

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

Step 1

Move $2^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify each term.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 5

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

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

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

Step 5.2

Multiply $3$ by $5$ .

$(\frac{5}{15} + \frac{1}{5} \cdot \frac{3}{3}) \cdot 2$

Step 5.3

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

$(\frac{5}{15} + \frac{3}{5 \cdot 3}) \cdot 2$

Step 5.4

Multiply $5$ by $3$ .

$(\frac{5}{15} + \frac{3}{15}) \cdot 2$

Step 6

Combine the numerators over the common denominator.

$\frac{5 + 3}{15} \cdot 2$

Step 7

Add $5$ and $3$ .

$\frac{8}{15} \cdot 2$

Step 8

Multiply $\frac{8}{15} \cdot 2$ .

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Step 8.1

Combine $\frac{8}{15}$ and $2$ .

$\frac{8 \cdot 2}{15}$

Step 8.2

Multiply $8$ by $2$ .

$\frac{16}{15}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{15}$

Decimal Form:

$1.0\overline{6}$

Mixed Number Form:

$1 \frac{1}{15}$