Basic Math Examples

$\frac{1}{2} = - \frac{2}{3} j + j$

Step 1

Rewrite the equation as $- \frac{2}{3} j + j = \frac{1}{2}$ .

$- \frac{2}{3} j + j = \frac{1}{2}$

Step 2

Simplify $- \frac{2}{3} j + j$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$- \frac{j \cdot 2}{3} + j = \frac{1}{2}$

Step 2.1.2

Move $2$ to the left of $j$ .

$- \frac{2 j}{3} + j = \frac{1}{2}$

Step 2.2

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

$- \frac{2 j}{3} + j \cdot \frac{3}{3} = \frac{1}{2}$

Step 2.3

Simplify terms.

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Step 2.3.1

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

$- \frac{2 j}{3} + \frac{j \cdot 3}{3} = \frac{1}{2}$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{- 2 j + j \cdot 3}{3} = \frac{1}{2}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Move $3$ to the left of $j$ .

$\frac{- 2 j + 3 \cdot j}{3} = \frac{1}{2}$

Step 2.4.2

Add $- 2 j$ and $3 j$ .

$\frac{j}{3} = \frac{1}{2}$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{j}{3} = 3 (\frac{1}{2})$

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 $3$ .

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Step 4.1.1.1

Cancel the common factor.

$3 \frac{j}{3} = 3 (\frac{1}{2})$

Step 4.1.1.2

Rewrite the expression.

$j = 3 (\frac{1}{2})$

Step 4.2

Simplify the right side.

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Step 4.2.1

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

$j = \frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$j = \frac{3}{2}$

Decimal Form:

$j = 1.5$

Mixed Number Form:

$j = 1 \frac{1}{2}$