Basic Math Examples

$s \div \frac{1}{6} = 22 \frac{2}{3}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $s \div \frac{1}{6}$ .

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Step 1.1.1

To divide by a fraction, multiply by its reciprocal.

$s \cdot 6 = 22 \frac{2}{3}$

Step 1.1.2

Move $6$ to the left of $s$ .

$6 s = 22 \frac{2}{3}$

Step 2

Simplify the right side.

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Step 2.1

Convert $22 \frac{2}{3}$ to an improper fraction.

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Step 2.1.1

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

$6 s = 22 + \frac{2}{3}$

Step 2.1.2

Add $22$ and $\frac{2}{3}$ .

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Step 2.1.2.1

To write $22$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$6 s = 22 \cdot \frac{3}{3} + \frac{2}{3}$

Step 2.1.2.2

Combine $22$ and $\frac{3}{3}$ .

$6 s = \frac{22 \cdot 3}{3} + \frac{2}{3}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$6 s = \frac{22 \cdot 3 + 2}{3}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $22$ by $3$ .

$6 s = \frac{66 + 2}{3}$

Step 2.1.2.4.2

Add $66$ and $2$ .

$6 s = \frac{68}{3}$

Step 3

Divide each term in $6 s = \frac{68}{3}$ by $6$ and simplify.

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Step 3.1

Divide each term in $6 s = \frac{68}{3}$ by $6$ .

$\frac{6 s}{6} = \frac{\frac{68}{3}}{6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6 s}{6} = \frac{\frac{68}{3}}{6}$

Step 3.2.1.2

Divide $s$ by $1$ .

$s = \frac{\frac{68}{3}}{6}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$s = \frac{68}{3} \cdot \frac{1}{6}$

Step 3.3.2

Cancel the common factor of $2$ .

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Step 3.3.2.1

Factor $2$ out of $68$ .

$s = \frac{2 (34)}{3} \cdot \frac{1}{6}$

Step 3.3.2.2

Factor $2$ out of $6$ .

$s = \frac{2 \cdot 34}{3} \cdot \frac{1}{2 \cdot 3}$

Step 3.3.2.3

Cancel the common factor.

$s = \frac{2 \cdot 34}{3} \cdot \frac{1}{2 \cdot 3}$

Step 3.3.2.4

Rewrite the expression.

$s = \frac{34}{3} \cdot \frac{1}{3}$

Step 3.3.3

Multiply $\frac{34}{3}$ by $\frac{1}{3}$ .

$s = \frac{34}{3 \cdot 3}$

Step 3.3.4

Multiply $3$ by $3$ .

$s = \frac{34}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$s = \frac{34}{9}$

Decimal Form:

$s = 3.\overline{7}$

Mixed Number Form:

$s = 3 \frac{7}{9}$