Basic Math Examples

$\frac{6}{9} + \frac{5}{18} + 1 \frac{3}{6}$

Step 1

Convert $1 \frac{3}{6}$ to an improper fraction.

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Step 1.1

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

$\frac{6}{9} + \frac{5}{18} + 1 + \frac{3}{6}$

Step 1.2

Add $1$ and $\frac{3}{6}$ .

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Step 1.2.1

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

$\frac{6}{9} + \frac{5}{18} + \frac{6}{6} + \frac{3}{6}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{6}{9} + \frac{5}{18} + \frac{6 + 3}{6}$

Step 1.2.3

Add $6$ and $3$ .

$\frac{6}{9} + \frac{5}{18} + \frac{9}{6}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{6}{9}$ by $\frac{2}{2}$ .

$\frac{6}{9} \cdot \frac{2}{2} + \frac{5}{18} + \frac{9}{6}$

Step 2.2

Multiply $\frac{6}{9}$ by $\frac{2}{2}$ .

$\frac{6 \cdot 2}{9 \cdot 2} + \frac{5}{18} + \frac{9}{6}$

Step 2.3

Multiply $\frac{9}{6}$ by $\frac{3}{3}$ .

$\frac{6 \cdot 2}{9 \cdot 2} + \frac{5}{18} + \frac{9}{6} \cdot \frac{3}{3}$

Step 2.4

Multiply $\frac{9}{6}$ by $\frac{3}{3}$ .

$\frac{6 \cdot 2}{9 \cdot 2} + \frac{5}{18} + \frac{9 \cdot 3}{6 \cdot 3}$

Step 2.5

Reorder the factors of $9 \cdot 2$ .

$\frac{6 \cdot 2}{2 \cdot 9} + \frac{5}{18} + \frac{9 \cdot 3}{6 \cdot 3}$

Step 2.6

Multiply $2$ by $9$ .

$\frac{6 \cdot 2}{18} + \frac{5}{18} + \frac{9 \cdot 3}{6 \cdot 3}$

Step 2.7

Reorder the factors of $6 \cdot 3$ .

$\frac{6 \cdot 2}{18} + \frac{5}{18} + \frac{9 \cdot 3}{3 \cdot 6}$

Step 2.8

Multiply $3$ by $6$ .

$\frac{6 \cdot 2}{18} + \frac{5}{18} + \frac{9 \cdot 3}{18}$

Step 3

Combine the numerators over the common denominator.

$\frac{6 \cdot 2 + 5 + 9 \cdot 3}{18}$

Step 4

Simplify each term.

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Step 4.1

Multiply $6$ by $2$ .

$\frac{12 + 5 + 9 \cdot 3}{18}$

Step 4.2

Multiply $9$ by $3$ .

$\frac{12 + 5 + 27}{18}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Add $12$ and $5$ .

$\frac{17 + 27}{18}$

Step 5.2

Add $17$ and $27$ .

$\frac{44}{18}$

Step 5.3

Cancel the common factor of $44$ and $18$ .

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Step 5.3.1

Factor $2$ out of $44$ .

$\frac{2 (22)}{18}$

Step 5.3.2

Cancel the common factors.

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Step 5.3.2.1

Factor $2$ out of $18$ .

$\frac{2 \cdot 22}{2 \cdot 9}$

Step 5.3.2.2

Cancel the common factor.

$\frac{2 \cdot 22}{2 \cdot 9}$

Step 5.3.2.3

Rewrite the expression.

$\frac{22}{9}$