Basic Math Examples

$\frac{1}{6} b = 2 \frac{1}{3}$

Step 1

Simplify the left side.

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Step 1.1

Combine $\frac{1}{6}$ and $b$ .

$\frac{b}{6} = 2 \frac{1}{3}$

Step 2

Simplify the right side.

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Step 2.1

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

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Step 2.1.1

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

$\frac{b}{6} = 2 + \frac{1}{3}$

Step 2.1.2

Add $2$ and $\frac{1}{3}$ .

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Step 2.1.2.1

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

$\frac{b}{6} = 2 \cdot \frac{3}{3} + \frac{1}{3}$

Step 2.1.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{b}{6} = \frac{2 \cdot 3}{3} + \frac{1}{3}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{b}{6} = \frac{2 \cdot 3 + 1}{3}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $3$ .

$\frac{b}{6} = \frac{6 + 1}{3}$

Step 2.1.2.4.2

Add $6$ and $1$ .

$\frac{b}{6} = \frac{7}{3}$

Step 3

Multiply both sides of the equation by $6$ .

$6 \frac{b}{6} = 6 (\frac{7}{3})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $6$ .

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Step 4.1.1.1

Cancel the common factor.

$6 \frac{b}{6} = 6 (\frac{7}{3})$

Step 4.1.1.2

Rewrite the expression.

$b = 6 (\frac{7}{3})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $6 (\frac{7}{3})$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Factor $3$ out of $6$ .

$b = 3 (2) \frac{7}{3}$

Step 4.2.1.1.2

Cancel the common factor.

$b = 3 \cdot 2 \frac{7}{3}$

Step 4.2.1.1.3

Rewrite the expression.

$b = 2 \cdot 7$

Step 4.2.1.2

Multiply $2$ by $7$ .

$b = 14$