Basic Math Examples

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

$4 \frac{1}{6} - 3 \frac{5}{6}$

Step 1

Convert

$4 \frac{1}{6}$ to an improper fraction.

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Step 1.1

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

$4 + \frac{1}{6} - 3 \frac{5}{6}$

Step 1.2

Add

$4$ and

$\frac{1}{6}$ .

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Step 1.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{6}{6}$ .

$4 \cdot \frac{6}{6} + \frac{1}{6} - 3 \frac{5}{6}$

Step 1.2.2

Combine

$4$ and

$\frac{6}{6}$ .

$\frac{4 \cdot 6}{6} + \frac{1}{6} - 3 \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 6 + 1}{6} - 3 \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$4$ by

$6$ .

$\frac{24 + 1}{6} - 3 \frac{5}{6}$

Step 1.2.4.2

Add

$24$ and

$1$ .

$\frac{25}{6} - 3 \frac{5}{6}$

Step 2

Convert

$3 \frac{5}{6}$ to an improper fraction.

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Step 2.1

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

$\frac{25}{6} - (3 + \frac{5}{6})$

Step 2.2

Add

$3$ and

$\frac{5}{6}$ .

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Step 2.2.1

To write

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

$\frac{6}{6}$ .

$\frac{25}{6} - (3 \cdot \frac{6}{6} + \frac{5}{6})$

Step 2.2.2

Combine

$3$ and

$\frac{6}{6}$ .

$\frac{25}{6} - (\frac{3 \cdot 6}{6} + \frac{5}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{25}{6} - \frac{3 \cdot 6 + 5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$6$ .

$\frac{25}{6} - \frac{18 + 5}{6}$

Step 2.2.4.2

Add

$18$ and

$5$ .

$\frac{25}{6} - \frac{23}{6}$

Step 3

Combine the numerators over the common denominator.

$\frac{25 - 23}{6}$

Step 4

Subtract

$23$ from

$25$ .

$\frac{2}{6}$

Step 5

Cancel the common factor of

$2$ and

$6$ .

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Step 5.1

Factor

$2$ out of

$2$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor

$2$ out of

$6$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$