Basic Math Examples

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

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.

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

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.

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $2$ and $1$ .

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

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.

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

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.

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

Step 2.2.2

Combine the numerators over the common denominator.

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

Step 2.2.3

Add $3$ and $1$ .

$\frac{1}{2} + \frac{3}{2} - \frac{4}{3}$

Step 3

Combine fractions.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{1 + 3}{2} + \frac{- 4}{3}$

Step 3.2

Add $1$ and $3$ .

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

Step 4

Simplify each term.

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Step 4.1

Divide $4$ by $2$ .

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

Step 4.2

Move the negative in front of the fraction.

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

Step 5

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 \cdot \frac{3}{3} - \frac{4}{3}$

Step 6

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

$\frac{2 \cdot 3}{3} - \frac{4}{3}$

Step 7

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 - 4}{3}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $2$ by $3$ .

$\frac{6 - 4}{3}$

Step 8.2

Subtract $4$ from $6$ .

$\frac{2}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$