Basic Math Examples

6 \frac{1}{3} - 2 \frac{2}{3}

$6 \frac{1}{3} - 2 \frac{2}{3}$

Step 1

Convert

6 \frac{1}{3}

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

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Step 1.1

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

6 + \frac{1}{3} - 2 \frac{2}{3}

$6 + \frac{1}{3} - 2 \frac{2}{3}$

Step 1.2

Add

6

$6$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

6 \cdot \frac{3}{3} + \frac{1}{3} - 2 \frac{2}{3}

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

Step 1.2.2

Combine

6

$6$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{6 \cdot 3}{3} + \frac{1}{3} - 2 \frac{2}{3}

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

Step 1.2.3

Combine the numerators over the common denominator.

\frac{6 \cdot 3 + 1}{3} - 2 \frac{2}{3}

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

3

$3$ .

\frac{18 + 1}{3} - 2 \frac{2}{3}

$\frac{18 + 1}{3} - 2 \frac{2}{3}$

Step 1.2.4.2

Add

18

$18$ and

1

$1$ .

\frac{19}{3} - 2 \frac{2}{3}

$\frac{19}{3} - 2 \frac{2}{3}$

\frac{19}{3} - 2 \frac{2}{3}

$\frac{19}{3} - 2 \frac{2}{3}$

\frac{19}{3} - 2 \frac{2}{3}

$\frac{19}{3} - 2 \frac{2}{3}$

\frac{19}{3} - 2 \frac{2}{3}

$\frac{19}{3} - 2 \frac{2}{3}$

Step 2

Convert

2 \frac{2}{3}

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

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Step 2.1

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

\frac{19}{3} - (2 + \frac{2}{3})

$\frac{19}{3} - (2 + \frac{2}{3})$

Step 2.2

Add

2

$2$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 2.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{19}{3} - (2 \cdot \frac{3}{3} + \frac{2}{3})

$\frac{19}{3} - (2 \cdot \frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{19}{3} - (\frac{2 \cdot 3}{3} + \frac{2}{3})

$\frac{19}{3} - (\frac{2 \cdot 3}{3} + \frac{2}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{19}{3} - \frac{2 \cdot 3 + 2}{3}

$\frac{19}{3} - \frac{2 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

3

$3$ .

\frac{19}{3} - \frac{6 + 2}{3}

$\frac{19}{3} - \frac{6 + 2}{3}$

Step 2.2.4.2

Add

6

$6$ and

2

$2$ .

\frac{19}{3} - \frac{8}{3}

$\frac{19}{3} - \frac{8}{3}$

\frac{19}{3} - \frac{8}{3}

$\frac{19}{3} - \frac{8}{3}$

\frac{19}{3} - \frac{8}{3}

$\frac{19}{3} - \frac{8}{3}$

\frac{19}{3} - \frac{8}{3}

$\frac{19}{3} - \frac{8}{3}$

Step 3

Combine the numerators over the common denominator.

\frac{19 - 8}{3}

$\frac{19 - 8}{3}$

Step 4

Subtract

8

$8$ from

19

$19$ .

\frac{11}{3}

$\frac{11}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{11}{3}

$\frac{11}{3}$

Decimal Form:

3.\overline{6}

$3.\overline{6}$

Mixed Number Form:

3 \frac{2}{3}

$3 \frac{2}{3}$