Basic Math Examples

2 \frac{5}{6} - 2 \frac{1}{3}

$2 \frac{5}{6} - 2 \frac{1}{3}$

Step 1

Convert

2 \frac{5}{6}

$2 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

2 + \frac{5}{6} - 2 \frac{1}{3}

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

Step 1.2

Add

2

$2$ and

\frac{5}{6}

$\frac{5}{6}$ .

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Step 1.2.1

To write

2

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

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

6

$6$ .

\frac{12 + 5}{6} - 2 \frac{1}{3}

$\frac{12 + 5}{6} - 2 \frac{1}{3}$

Step 1.2.4.2

Add

12

$12$ and

5

$5$ .

\frac{17}{6} - 2 \frac{1}{3}

$\frac{17}{6} - 2 \frac{1}{3}$

\frac{17}{6} - 2 \frac{1}{3}

$\frac{17}{6} - 2 \frac{1}{3}$

\frac{17}{6} - 2 \frac{1}{3}

$\frac{17}{6} - 2 \frac{1}{3}$

\frac{17}{6} - 2 \frac{1}{3}

$\frac{17}{6} - 2 \frac{1}{3}$

Step 2

Convert

2 \frac{1}{3}

$2 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

\frac{17}{6} - (2 + \frac{1}{3})

$\frac{17}{6} - (2 + \frac{1}{3})$

Step 2.2

Add

2

$2$ and

\frac{1}{3}

$\frac{1}{3}$ .

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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{17}{6} - (2 \cdot \frac{3}{3} + \frac{1}{3})

$\frac{17}{6} - (2 \cdot \frac{3}{3} + \frac{1}{3})$

Step 2.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{17}{6} - (\frac{2 \cdot 3}{3} + \frac{1}{3})

$\frac{17}{6} - (\frac{2 \cdot 3}{3} + \frac{1}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{17}{6} - \frac{2 \cdot 3 + 1}{3}

$\frac{17}{6} - \frac{2 \cdot 3 + 1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

3

$3$ .

\frac{17}{6} - \frac{6 + 1}{3}

$\frac{17}{6} - \frac{6 + 1}{3}$

Step 2.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{17}{6} - \frac{7}{3}

$\frac{17}{6} - \frac{7}{3}$

\frac{17}{6} - \frac{7}{3}

$\frac{17}{6} - \frac{7}{3}$

\frac{17}{6} - \frac{7}{3}

$\frac{17}{6} - \frac{7}{3}$

\frac{17}{6} - \frac{7}{3}

$\frac{17}{6} - \frac{7}{3}$

Step 3

To write

- \frac{7}{3}

$- \frac{7}{3}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{17}{6} - \frac{7}{3} \cdot \frac{2}{2}

$\frac{17}{6} - \frac{7}{3} \cdot \frac{2}{2}$

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{7}{3}

$\frac{7}{3}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{17}{6} - \frac{7 \cdot 2}{3 \cdot 2}

$\frac{17}{6} - \frac{7 \cdot 2}{3 \cdot 2}$

Step 4.2

Multiply

3

$3$ by

2

$2$ .

\frac{17}{6} - \frac{7 \cdot 2}{6}

$\frac{17}{6} - \frac{7 \cdot 2}{6}$

\frac{17}{6} - \frac{7 \cdot 2}{6}

$\frac{17}{6} - \frac{7 \cdot 2}{6}$

Step 5

Combine the numerators over the common denominator.

\frac{17 - 7 \cdot 2}{6}

$\frac{17 - 7 \cdot 2}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

- 7

$- 7$ by

2

$2$ .

\frac{17 - 14}{6}

$\frac{17 - 14}{6}$

Step 6.2

Subtract

14

$14$ from

17

$17$ .

\frac{3}{6}

$\frac{3}{6}$

\frac{3}{6}

$\frac{3}{6}$

Step 7

Cancel the common factor of

3

$3$ and

6

$6$ .

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Step 7.1

Factor

3

$3$ out of

3

$3$ .

\frac{3 (1)}{6}

$\frac{3 (1)}{6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor

3

$3$ out of

6

$6$ .

\frac{3 \cdot 1}{3 \cdot 2}

$\frac{3 \cdot 1}{3 \cdot 2}$

Step 7.2.2

Cancel the common factor.

$\frac{3 \cdot 1}{3 \cdot 2}$

Step 7.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$