Pre-Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $3$ and $1$ .

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

Step 2

Multiply $\frac{2}{3} \cdot \frac{4}{3}$ .

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Step 2.1

Multiply $\frac{2}{3}$ by $\frac{4}{3}$ .

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

Step 2.2

Multiply $2$ by $4$ .

$\frac{1}{2} + \frac{8}{3 \cdot 3}$

Step 2.3

Multiply $3$ by $3$ .

$\frac{1}{2} + \frac{8}{9}$

Step 3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{1}{2} \cdot \frac{9}{9} + \frac{8}{9}$

Step 4

To write $\frac{8}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} \cdot \frac{9}{9} + \frac{8}{9} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{1}{2}$ by $\frac{9}{9}$ .

$\frac{9}{2 \cdot 9} + \frac{8}{9} \cdot \frac{2}{2}$

Step 5.2

Multiply $2$ by $9$ .

$\frac{9}{18} + \frac{8}{9} \cdot \frac{2}{2}$

Step 5.3

Multiply $\frac{8}{9}$ by $\frac{2}{2}$ .

$\frac{9}{18} + \frac{8 \cdot 2}{9 \cdot 2}$

Step 5.4

Multiply $9$ by $2$ .

$\frac{9}{18} + \frac{8 \cdot 2}{18}$

Step 6

Combine the numerators over the common denominator.

$\frac{9 + 8 \cdot 2}{18}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $8$ by $2$ .

$\frac{9 + 16}{18}$

Step 7.2

Add $9$ and $16$ .

$\frac{25}{18}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{18}$

Decimal Form:

$1.3\overline{8}$

Mixed Number Form:

$1 \frac{7}{18}$