Algebra Examples

$(\frac{1}{2} + \frac{1}{3} + \frac{1}{6}) \div 2 \frac{1}{2}$

Step 1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$(\frac{1}{2} + \frac{1}{3} + \frac{1}{6}) \div (2 + \frac{1}{2})$

Step 1.2

Add $2$ and $\frac{1}{2}$ .

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Step 1.2.1

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

$(\frac{1}{2} + \frac{1}{3} + \frac{1}{6}) \div (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 1.2.2

Combine $2$ and $\frac{2}{2}$ .

$(\frac{1}{2} + \frac{1}{3} + \frac{1}{6}) \div (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{1}{2} + \frac{1}{3} + \frac{1}{6}) \div \frac{2 \cdot 2 + 1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $2$ .

$(\frac{1}{2} + \frac{1}{3} + \frac{1}{6}) \div \frac{4 + 1}{2}$

Step 1.2.4.2

Add $4$ and $1$ .

$(\frac{1}{2} + \frac{1}{3} + \frac{1}{6}) \div \frac{5}{2}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$(\frac{1}{2} + \frac{1}{3} + \frac{1}{6}) \frac{2}{5}$

Step 3

Find the common denominator.

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Step 3.1

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

$(\frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3} + \frac{1}{6}) \frac{2}{5}$

Step 3.2

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

$(\frac{3}{2 \cdot 3} + \frac{1}{3} + \frac{1}{6}) \frac{2}{5}$

Step 3.3

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

$(\frac{3}{2 \cdot 3} + \frac{1}{3} \cdot \frac{2}{2} + \frac{1}{6}) \frac{2}{5}$

Step 3.4

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

$(\frac{3}{2 \cdot 3} + \frac{2}{3 \cdot 2} + \frac{1}{6}) \frac{2}{5}$

Step 3.5

Multiply $2$ by $3$ .

$(\frac{3}{6} + \frac{2}{3 \cdot 2} + \frac{1}{6}) \frac{2}{5}$

Step 3.6

Reorder the factors of $3 \cdot 2$ .

$(\frac{3}{6} + \frac{2}{2 \cdot 3} + \frac{1}{6}) \frac{2}{5}$

Step 3.7

Multiply $2$ by $3$ .

$(\frac{3}{6} + \frac{2}{6} + \frac{1}{6}) \frac{2}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 + 2 + 1}{6} \cdot \frac{2}{5}$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $3$ and $2$ .

$\frac{5 + 1}{6} \cdot \frac{2}{5}$

Step 5.2

Add $5$ and $1$ .

$\frac{6}{6} \cdot \frac{2}{5}$

Step 6

Cancel the common factor of $6$ .

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Step 6.1

Cancel the common factor.

$\frac{6}{6} \cdot \frac{2}{5}$

Step 6.2

Rewrite the expression.

$1 (\frac{2}{5})$

Step 7

Multiply $\frac{2}{5}$ by $1$ .

$\frac{2}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{5}$

Decimal Form:

$0.4$