Pre-Algebra Examples

6 x = \frac{2}{3}

$6 x = \frac{2}{3}$

Step 1

Divide each term in

6 x = \frac{2}{3}

$6 x = \frac{2}{3}$ by

6

$6$ .

\frac{6 x}{6} = \frac{\frac{2}{3}}{6}

$\frac{6 x}{6} = \frac{\frac{2}{3}}{6}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of

6

$6$ .

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Step 2.1.1

Cancel the common factor.

\frac{6 x}{6} = \frac{\frac{2}{3}}{6}

$\frac{6 x}{6} = \frac{\frac{2}{3}}{6}$

Step 2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{\frac{2}{3}}{6}

$x = \frac{\frac{2}{3}}{6}$

x = \frac{\frac{2}{3}}{6}

$x = \frac{\frac{2}{3}}{6}$

x = \frac{\frac{2}{3}}{6}

$x = \frac{\frac{2}{3}}{6}$

Step 3

Simplify the right side.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

x = \frac{2}{3} \cdot \frac{1}{6}

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

Step 3.2

Cancel the common factor of

2

$2$ .

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Step 3.2.1

Factor

2

$2$ out of

6

$6$ .

x = \frac{2}{3} \cdot \frac{1}{2 (3)}

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

Step 3.2.2

Cancel the common factor.

x = \frac{2}{3} \cdot \frac{1}{2 \cdot 3}

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

Step 3.2.3

Rewrite the expression.

x = \frac{1}{3} \cdot \frac{1}{3}

$x = \frac{1}{3} \cdot \frac{1}{3}$

x = \frac{1}{3} \cdot \frac{1}{3}

$x = \frac{1}{3} \cdot \frac{1}{3}$

Step 3.3

Multiply

\frac{1}{3}

$\frac{1}{3}$ by

\frac{1}{3}

$\frac{1}{3}$ .

x = \frac{1}{3 \cdot 3}

$x = \frac{1}{3 \cdot 3}$

Step 3.4

Multiply

3

$3$ by

3

$3$ .

x = \frac{1}{9}

$x = \frac{1}{9}$

x = \frac{1}{9}

$x = \frac{1}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

x = \frac{1}{9}

$x = \frac{1}{9}$

Decimal Form:

x = 0.\overline{1}

$x = 0.\overline{1}$

6 x = \frac{2}{3}

$6 x = \frac{2}{3}$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$