Basic Math Examples

\frac{2}{3} t = 9

$\frac{2}{3} t = 9$

Step 1

Multiply both sides of the equation by

\frac{3}{2}

$\frac{3}{2}$ .

\frac{3}{2} (\frac{2}{3} t) = \frac{3}{2} \cdot 9

$\frac{3}{2} (\frac{2}{3} t) = \frac{3}{2} \cdot 9$

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} t)

$\frac{3}{2} (\frac{2}{3} t)$ .

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Step 2.1.1.1

Combine

\frac{2}{3}

$\frac{2}{3}$ and

t

$t$ .

\frac{3}{2} \cdot \frac{2 t}{3} = \frac{3}{2} \cdot 9

$\frac{3}{2} \cdot \frac{2 t}{3} = \frac{3}{2} \cdot 9$

Step 2.1.1.2

Cancel the common factor of

3

$3$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 t}{3} = \frac{3}{2} \cdot 9$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{1}{2} (2 t) = \frac{3}{2} \cdot 9$

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

$2 t$ .

$\frac{1}{2} (2 (t)) = \frac{3}{2} \cdot 9$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{1}{2} (2 t) = \frac{3}{2} \cdot 9$

Step 2.1.1.3.3

Rewrite the expression.

$t = \frac{3}{2} \cdot 9$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply

$\frac{3}{2} \cdot 9$ .

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Step 2.2.1.1

Combine

$\frac{3}{2}$ and

$9$ .

$t = \frac{3 \cdot 9}{2}$

Step 2.2.1.2

Multiply

$3$ by

$9$ .

$t = \frac{27}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = \frac{27}{2}$

Decimal Form:

$t = 13.5$

Mixed Number Form:

$t = 13 \frac{1}{2}$