Basic Math Examples

$12 \frac{2}{3} - 4 \frac{5}{6}$

Step 1

Convert $12 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$12 + \frac{2}{3} - 4 \frac{5}{6}$

Step 1.2

Add $12$ and $\frac{2}{3}$ .

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Step 1.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$12 \cdot \frac{3}{3} + \frac{2}{3} - 4 \frac{5}{6}$

Step 1.2.2

Combine $12$ and $\frac{3}{3}$ .

$\frac{12 \cdot 3}{3} + \frac{2}{3} - 4 \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{12 \cdot 3 + 2}{3} - 4 \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $12$ by $3$ .

$\frac{36 + 2}{3} - 4 \frac{5}{6}$

Step 1.2.4.2

Add $36$ and $2$ .

$\frac{38}{3} - 4 \frac{5}{6}$

Step 2

Convert $4 \frac{5}{6}$ to an improper fraction.

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Step 2.1

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

$\frac{38}{3} - (4 + \frac{5}{6})$

Step 2.2

Add $4$ and $\frac{5}{6}$ .

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{38}{3} - (4 \cdot \frac{6}{6} + \frac{5}{6})$

Step 2.2.2

Combine $4$ and $\frac{6}{6}$ .

$\frac{38}{3} - (\frac{4 \cdot 6}{6} + \frac{5}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{38}{3} - \frac{4 \cdot 6 + 5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $6$ .

$\frac{38}{3} - \frac{24 + 5}{6}$

Step 2.2.4.2

Add $24$ and $5$ .

$\frac{38}{3} - \frac{29}{6}$

Step 3

To write $\frac{38}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{38}{3} \cdot \frac{2}{2} - \frac{29}{6}$

Step 4

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

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Step 4.1

Multiply $\frac{38}{3}$ by $\frac{2}{2}$ .

$\frac{38 \cdot 2}{3 \cdot 2} - \frac{29}{6}$

Step 4.2

Multiply $3$ by $2$ .

$\frac{38 \cdot 2}{6} - \frac{29}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{38 \cdot 2 - 29}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $38$ by $2$ .

$\frac{76 - 29}{6}$

Step 6.2

Subtract $29$ from $76$ .

$\frac{47}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{47}{6}$

Decimal Form:

$7.8\overline{3}$

Mixed Number Form:

$7 \frac{5}{6}$