Basic Math Examples

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

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

Step 1

Convert

3 \frac{1}{6}

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

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Step 1.1

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

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

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

Step 1.2

Add

3

$3$ and

\frac{1}{6}

$\frac{1}{6}$ .

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Step 1.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.2.2

Combine

3

$3$ and

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

6

$6$ .

\frac{18 + 1}{6} - 1 \frac{1}{2}

$\frac{18 + 1}{6} - 1 \frac{1}{2}$

Step 1.2.4.2

Add

18

$18$ and

1

$1$ .

\frac{19}{6} - 1 \frac{1}{2}

$\frac{19}{6} - 1 \frac{1}{2}$

\frac{19}{6} - 1 \frac{1}{2}

$\frac{19}{6} - 1 \frac{1}{2}$

\frac{19}{6} - 1 \frac{1}{2}

$\frac{19}{6} - 1 \frac{1}{2}$

\frac{19}{6} - 1 \frac{1}{2}

$\frac{19}{6} - 1 \frac{1}{2}$

Step 2

Convert

1 \frac{1}{2}

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

$\frac{19}{6} - (1 + \frac{1}{2})$

Step 2.2

Add

1

$1$ and

\frac{1}{2}

$\frac{1}{2}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{19}{6} - (\frac{2}{2} + \frac{1}{2})

$\frac{19}{6} - (\frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{19}{6} - \frac{2 + 1}{2}

$\frac{19}{6} - \frac{2 + 1}{2}$

Step 2.2.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

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

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

Step 3

To write

- \frac{3}{2}

$- \frac{3}{2}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

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{3}{2}

$\frac{3}{2}$ by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 4.2

Multiply

2

$2$ by

3

$3$ .

\frac{19}{6} - \frac{3 \cdot 3}{6}

$\frac{19}{6} - \frac{3 \cdot 3}{6}$

\frac{19}{6} - \frac{3 \cdot 3}{6}

$\frac{19}{6} - \frac{3 \cdot 3}{6}$

Step 5

Combine the numerators over the common denominator.

\frac{19 - 3 \cdot 3}{6}

$\frac{19 - 3 \cdot 3}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

- 3

$- 3$ by

3

$3$ .

\frac{19 - 9}{6}

$\frac{19 - 9}{6}$

Step 6.2

Subtract

9

$9$ from

19

$19$ .

\frac{10}{6}

$\frac{10}{6}$

\frac{10}{6}

$\frac{10}{6}$

Step 7

Cancel the common factor of

10

$10$ and

6

$6$ .

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Step 7.1

Factor

2

$2$ out of

10

$10$ .

\frac{2 (5)}{6}

$\frac{2 (5)}{6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor

2

$2$ out of

6

$6$ .

\frac{2 \cdot 5}{2 \cdot 3}

$\frac{2 \cdot 5}{2 \cdot 3}$

Step 7.2.2

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 3}$

Step 7.2.3

Rewrite the expression.

$\frac{5}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$