Basic Math Examples

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

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

Step 1

Convert

1 \frac{2}{3}

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

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Step 1.1

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

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

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

Step 1.2

Add

1

$1$ and

\frac{2}{3}

$\frac{2}{3}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

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

Step 1.2.3

Add

3

$3$ and

2

$2$ .

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

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

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

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

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

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

Step 2

To write

- \frac{5}{3}

$- \frac{5}{3}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 3

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 3.1

Multiply

\frac{5}{3}

$\frac{5}{3}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 3.2

Multiply

3

$3$ by

2

$2$ .

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

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

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

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

Step 4

Combine the numerators over the common denominator.

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

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply

- 5

$- 5$ by

2

$2$ .

\frac{1 - 10}{6}

$\frac{1 - 10}{6}$

Step 5.2

Subtract

10

$10$ from

1

$1$ .

\frac{- 9}{6}

$\frac{- 9}{6}$

\frac{- 9}{6}

$\frac{- 9}{6}$

Step 6

Cancel the common factor of

- 9

$- 9$ and

6

$6$ .

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Step 6.1

Factor

3

$3$ out of

- 9

$- 9$ .

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

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor

3

$3$ out of

6

$6$ .

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

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\frac{- 3}{2}$

Step 7

Move the negative in front of the fraction.

$- \frac{3}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{2}$

Decimal Form:

$- 1.5$

Mixed Number Form:

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