Pre-Algebra Examples

$3 \frac{4}{6} + \frac{9}{18}$

Step 1

Convert $3 \frac{4}{6}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{4}{6} + \frac{9}{18}$

Step 1.2

Add $3$ and $\frac{4}{6}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$3 \cdot \frac{6}{6} + \frac{4}{6} + \frac{9}{18}$

Step 1.2.2

Combine $3$ and $\frac{6}{6}$ .

$\frac{3 \cdot 6}{6} + \frac{4}{6} + \frac{9}{18}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 6 + 4}{6} + \frac{9}{18}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $6$ .

$\frac{18 + 4}{6} + \frac{9}{18}$

Step 1.2.4.2

Add $18$ and $4$ .

$\frac{22}{6} + \frac{9}{18}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $22$ and $6$ .

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Step 2.1.1

Factor $2$ out of $22$ .

$\frac{2 (11)}{6} + \frac{9}{18}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 11}{2 \cdot 3} + \frac{9}{18}$

Step 2.1.2.2

Cancel the common factor.

$\frac{2 \cdot 11}{2 \cdot 3} + \frac{9}{18}$

Step 2.1.2.3

Rewrite the expression.

$\frac{11}{3} + \frac{9}{18}$

Step 2.2

Cancel the common factor of $9$ and $18$ .

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Step 2.2.1

Factor $9$ out of $9$ .

$\frac{11}{3} + \frac{9 (1)}{18}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $9$ out of $18$ .

$\frac{11}{3} + \frac{9 \cdot 1}{9 \cdot 2}$

Step 2.2.2.2

Cancel the common factor.

$\frac{11}{3} + \frac{9 \cdot 1}{9 \cdot 2}$

Step 2.2.2.3

Rewrite the expression.

$\frac{11}{3} + \frac{1}{2}$

Step 3

To write $\frac{11}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11}{3} \cdot \frac{2}{2} + \frac{1}{2}$

Step 4

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{11}{3} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{11}{3}$ by $\frac{2}{2}$ .

$\frac{11 \cdot 2}{3 \cdot 2} + \frac{1}{2} \cdot \frac{3}{3}$

Step 5.2

Multiply $3$ by $2$ .

$\frac{11 \cdot 2}{6} + \frac{1}{2} \cdot \frac{3}{3}$

Step 5.3

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

$\frac{11 \cdot 2}{6} + \frac{3}{2 \cdot 3}$

Step 5.4

Multiply $2$ by $3$ .

$\frac{11 \cdot 2}{6} + \frac{3}{6}$

Step 6

Combine the numerators over the common denominator.

$\frac{11 \cdot 2 + 3}{6}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $11$ by $2$ .

$\frac{22 + 3}{6}$

Step 7.2

Add $22$ and $3$ .

$\frac{25}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{6}$

Decimal Form:

$4.1\overline{6}$

Mixed Number Form:

$4 \frac{1}{6}$