Basic Math Examples

$\frac{1 - \frac{1}{3}}{1 + \frac{1}{2}} + \frac{5}{9}$

Step 1

Simplify the expression.

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Step 1.1

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

$\frac{\frac{3}{3} - \frac{1}{3}}{1 + \frac{1}{2}} + \frac{5}{9}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{\frac{3 - 1}{3}}{1 + \frac{1}{2}} + \frac{5}{9}$

Step 1.3

Subtract $1$ from $3$ .

$\frac{\frac{2}{3}}{1 + \frac{1}{2}} + \frac{5}{9}$

Step 2

Simplify each term.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} \cdot \frac{1}{1 + \frac{1}{2}} + \frac{5}{9}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

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

$\frac{2}{3} \cdot \frac{1}{\frac{2}{2} + \frac{1}{2}} + \frac{5}{9}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{2}{3} \cdot \frac{1}{\frac{2 + 1}{2}} + \frac{5}{9}$

Step 2.2.3

Add $2$ and $1$ .

$\frac{2}{3} \cdot \frac{1}{\frac{3}{2}} + \frac{5}{9}$

Step 2.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{3} (1 (\frac{2}{3})) + \frac{5}{9}$

Step 2.4

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

$\frac{2}{3} \cdot \frac{2}{3} + \frac{5}{9}$

Step 2.5

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

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Step 2.5.1

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

$\frac{2 \cdot 2}{3 \cdot 3} + \frac{5}{9}$

Step 2.5.2

Multiply $2$ by $2$ .

$\frac{4}{3 \cdot 3} + \frac{5}{9}$

Step 2.5.3

Multiply $3$ by $3$ .

$\frac{4}{9} + \frac{5}{9}$

Step 3

Combine fractions.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{4 + 5}{9}$

Step 3.2

Simplify the expression.

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Step 3.2.1

Add $4$ and $5$ .

$\frac{9}{9}$

Step 3.2.2

Divide $9$ by $9$ .

$1$