Basic Math Examples

$5 \frac{1}{2} - \frac{1}{4} - \frac{1}{3}$

Step 1

Convert $5 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$5 + \frac{1}{2} - \frac{1}{4} - \frac{1}{3}$

Step 1.2

Add $5$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 \cdot \frac{2}{2} + \frac{1}{2} - \frac{1}{4} - \frac{1}{3}$

Step 1.2.2

Combine $5$ and $\frac{2}{2}$ .

$\frac{5 \cdot 2}{2} + \frac{1}{2} - \frac{1}{4} - \frac{1}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 + 1}{2} - \frac{1}{4} - \frac{1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $2$ .

$\frac{10 + 1}{2} - \frac{1}{4} - \frac{1}{3}$

Step 1.2.4.2

Add $10$ and $1$ .

$\frac{11}{2} - \frac{1}{4} - \frac{1}{3}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{11}{2}$ by $\frac{6}{6}$ .

$\frac{11}{2} \cdot \frac{6}{6} - \frac{1}{4} - \frac{1}{3}$

Step 2.2

Multiply $\frac{11}{2}$ by $\frac{6}{6}$ .

$\frac{11 \cdot 6}{2 \cdot 6} - \frac{1}{4} - \frac{1}{3}$

Step 2.3

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{11 \cdot 6}{2 \cdot 6} - (\frac{1}{4} \cdot \frac{3}{3}) - \frac{1}{3}$

Step 2.4

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{11 \cdot 6}{2 \cdot 6} - \frac{3}{4 \cdot 3} - \frac{1}{3}$

Step 2.5

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{11 \cdot 6}{2 \cdot 6} - \frac{3}{4 \cdot 3} - (\frac{1}{3} \cdot \frac{4}{4})$

Step 2.6

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{11 \cdot 6}{2 \cdot 6} - \frac{3}{4 \cdot 3} - \frac{4}{3 \cdot 4}$

Step 2.7

Multiply $2$ by $6$ .

$\frac{11 \cdot 6}{12} - \frac{3}{4 \cdot 3} - \frac{4}{3 \cdot 4}$

Step 2.8

Reorder the factors of $4 \cdot 3$ .

$\frac{11 \cdot 6}{12} - \frac{3}{3 \cdot 4} - \frac{4}{3 \cdot 4}$

Step 2.9

Multiply $3$ by $4$ .

$\frac{11 \cdot 6}{12} - \frac{3}{12} - \frac{4}{3 \cdot 4}$

Step 2.10

Multiply $3$ by $4$ .

$\frac{11 \cdot 6}{12} - \frac{3}{12} - \frac{4}{12}$

Step 3

Combine the numerators over the common denominator.

$\frac{11 \cdot 6 - 3 - 4}{12}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $11$ by $6$ .

$\frac{66 - 3 - 4}{12}$

Step 4.2

Subtract $3$ from $66$ .

$\frac{63 - 4}{12}$

Step 4.3

Subtract $4$ from $63$ .

$\frac{59}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{59}{12}$

Decimal Form:

$4.91\overline{6}$

Mixed Number Form:

$4 \frac{11}{12}$