Basic Math Examples

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

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

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

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3}{2} (\frac{2}{3} a)$ .

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Step 2.1.1.1

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

$\frac{3}{2} \cdot \frac{2 a}{3} = \frac{3}{2} \cdot \frac{1}{6}$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 a}{3} = \frac{3}{2} \cdot \frac{1}{6}$

Step 2.1.1.2.2

Rewrite the expression.

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

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Factor $2$ out of $2 a$ .

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

Step 2.1.1.3.2

Cancel the common factor.

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

Step 2.1.1.3.3

Rewrite the expression.

$a = \frac{3}{2} \cdot \frac{1}{6}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{2} \cdot \frac{1}{6}$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Factor $3$ out of $6$ .

$a = \frac{3}{2} \cdot \frac{1}{3 (2)}$

Step 2.2.1.1.2

Cancel the common factor.

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

Step 2.2.1.1.3

Rewrite the expression.

$a = \frac{1}{2} \cdot \frac{1}{2}$

Step 2.2.1.2

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

$a = \frac{1}{2 \cdot 2}$

Step 2.2.1.3

Multiply $2$ by $2$ .

$a = \frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$a = \frac{1}{4}$

Decimal Form:

$a = 0.25$