Basic Math Examples

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

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

Step 1

Convert

12 \frac{2}{3}

$12 \frac{2}{3}$ 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}

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

Step 1.2

Add

12

$12$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

To write

12

$12$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.2

Combine

12

$12$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

12

$12$ by

3

$3$ .

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

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

Step 1.2.4.2

Add

36

$36$ and

2

$2$ .

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

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

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

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

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

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

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

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

Step 2

Convert

4 \frac{5}{6}

$4 \frac{5}{6}$ 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})

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

Step 2.2

Add

4

$4$ and

\frac{5}{6}

$\frac{5}{6}$ .

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Step 2.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 2.2.2

Combine

4

$4$ and

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

4

$4$ by

6

$6$ .

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

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

Step 2.2.4.2

Add

24

$24$ and

5

$5$ .

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

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

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

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

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

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

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

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

Step 3

To write

\frac{38}{3}

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

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4

Write each expression with a common denominator of

6

$6$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{38}{3}

$\frac{38}{3}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4.2

Multiply

3

$3$ by

2

$2$ .

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

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

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

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

Step 5

Combine the numerators over the common denominator.

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

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply

38

$38$ by

2

$2$ .

\frac{76 - 29}{6}

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

Step 6.2

Subtract

29

$29$ from

76

$76$ .

\frac{47}{6}

$\frac{47}{6}$

\frac{47}{6}

$\frac{47}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{47}{6}

$\frac{47}{6}$

Decimal Form:

7.8 ¯ 3

$7.8\overline{3}$

Mixed Number Form:

7 \frac{5}{6}

$7 \frac{5}{6}$