Pre-Algebra Examples

$3 \frac{2}{9} - 1 \frac{8}{9}$

Step 1

Convert $3 \frac{2}{9}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{2}{9} - 1 \frac{8}{9}$

Step 1.2

Add $3$ and $\frac{2}{9}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$3 \cdot \frac{9}{9} + \frac{2}{9} - 1 \frac{8}{9}$

Step 1.2.2

Combine $3$ and $\frac{9}{9}$ .

$\frac{3 \cdot 9}{9} + \frac{2}{9} - 1 \frac{8}{9}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 9 + 2}{9} - 1 \frac{8}{9}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $9$ .

$\frac{27 + 2}{9} - 1 \frac{8}{9}$

Step 1.2.4.2

Add $27$ and $2$ .

$\frac{29}{9} - 1 \frac{8}{9}$

Step 2

Convert $1 \frac{8}{9}$ to an improper fraction.

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Step 2.1

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

$\frac{29}{9} - (1 + \frac{8}{9})$

Step 2.2

Add $1$ and $\frac{8}{9}$ .

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Step 2.2.1

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

$\frac{29}{9} - (\frac{9}{9} + \frac{8}{9})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{29}{9} - \frac{9 + 8}{9}$

Step 2.2.3

Add $9$ and $8$ .

$\frac{29}{9} - \frac{17}{9}$

Step 3

Combine the numerators over the common denominator.

$\frac{29 - 17}{9}$

Step 4

Subtract $17$ from $29$ .

$\frac{12}{9}$

Step 5

Cancel the common factor of $12$ and $9$ .

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Step 5.1

Factor $3$ out of $12$ .

$\frac{3 (4)}{9}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $9$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$