Basic Math Examples

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

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

Step 1

Convert

2 \frac{1}{6}

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

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

Step 1.2

Add

2

$2$ and

\frac{1}{6}

$\frac{1}{6}$ .

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

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

Step 1.2.2

Combine

2

$2$ and

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

6

$6$ .

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

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

Step 1.2.4.2

Add

12

$12$ and

1

$1$ .

\frac{13}{6} - 5 \frac{2}{3}

$\frac{13}{6} - 5 \frac{2}{3}$

\frac{13}{6} - 5 \frac{2}{3}

$\frac{13}{6} - 5 \frac{2}{3}$

\frac{13}{6} - 5 \frac{2}{3}

$\frac{13}{6} - 5 \frac{2}{3}$

\frac{13}{6} - 5 \frac{2}{3}

$\frac{13}{6} - 5 \frac{2}{3}$

Step 2

Convert

5 \frac{2}{3}

$5 \frac{2}{3}$ to an improper fraction.

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Step 2.1

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

\frac{13}{6} - (5 + \frac{2}{3})

$\frac{13}{6} - (5 + \frac{2}{3})$

Step 2.2

Add

5

$5$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 2.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{13}{6} - (5 \cdot \frac{3}{3} + \frac{2}{3})

$\frac{13}{6} - (5 \cdot \frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine

$5$ and

$\frac{3}{3}$ .

$\frac{13}{6} - (\frac{5 \cdot 3}{3} + \frac{2}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{13}{6} - \frac{5 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$5$ by

$3$ .

$\frac{13}{6} - \frac{15 + 2}{3}$

Step 2.2.4.2

Add

$15$ and

$2$ .

$\frac{13}{6} - \frac{17}{3}$

Step 3

To write

$- \frac{17}{3}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{13}{6} - \frac{17}{3} \cdot \frac{2}{2}$

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

$\frac{17}{3}$ by

$\frac{2}{2}$ .

$\frac{13}{6} - \frac{17 \cdot 2}{3 \cdot 2}$

Step 4.2

Multiply

$3$ by

$2$ .

$\frac{13}{6} - \frac{17 \cdot 2}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{13 - 17 \cdot 2}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$- 17$ by

$2$ .

$\frac{13 - 34}{6}$

Step 6.2

Subtract

$34$ from

$13$ .

$\frac{- 21}{6}$

Step 7

Cancel the common factor of

$- 21$ and

$6$ .

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Step 7.1

Factor

$3$ out of

$- 21$ .

$\frac{3 (- 7)}{6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor

$3$ out of

$6$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$\frac{- 7}{2}$

Step 8

Move the negative in front of the fraction.

$- \frac{7}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{2}$

Decimal Form:

$- 3.5$

Mixed Number Form:

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