Basic Math Examples

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

Step 1

Convert $1 \frac{1}{2}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.2

Add $1$ and $\frac{1}{2}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $2$ and $1$ .

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

Step 2

Convert $1 \frac{1}{3}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

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

Step 2.2

Add $1$ and $\frac{1}{3}$ .

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

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

Step 2.2.2

Combine the numerators over the common denominator.

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

Step 2.2.3

Add $3$ and $1$ .

${(\frac{3}{2})}^{- 1} + \frac{4}{3}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{2}{3} + \frac{4}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 + 4}{3}$

Step 5

Simplify the expression.

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Step 5.1

Add $2$ and $4$ .

$\frac{6}{3}$

Step 5.2

Divide $6$ by $3$ .

$2$