Basic Math Examples

$\frac{2}{3} + \frac{1}{2} y - 4 = 0$

Step 1

Simplify $\frac{2}{3} + \frac{1}{2} y - 4$ .

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Step 1.1

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

$\frac{2}{3} + \frac{y}{2} - 4 = 0$

Step 1.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{y}{2} + \frac{2}{3} - 4 \cdot \frac{3}{3} = 0$

Step 1.3

Combine $- 4$ and $\frac{3}{3}$ .

$\frac{y}{2} + \frac{2}{3} + \frac{- 4 \cdot 3}{3} = 0$

Step 1.4

Combine the numerators over the common denominator.

$\frac{y}{2} + \frac{2 - 4 \cdot 3}{3} = 0$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 4$ by $3$ .

$\frac{y}{2} + \frac{2 - 12}{3} = 0$

Step 1.5.2

Subtract $12$ from $2$ .

$\frac{y}{2} + \frac{- 10}{3} = 0$

Step 1.6

Move the negative in front of the fraction.

$\frac{y}{2} - \frac{10}{3} = 0$

Step 2

Add $\frac{10}{3}$ to both sides of the equation.

$\frac{y}{2} = \frac{10}{3}$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{y}{2} = 2 (\frac{10}{3})$

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 $2$ .

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Step 4.1.1.1

Cancel the common factor.

$2 \frac{y}{2} = 2 (\frac{10}{3})$

Step 4.1.1.2

Rewrite the expression.

$y = 2 (\frac{10}{3})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $2 (\frac{10}{3})$ .

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Step 4.2.1.1

Combine $2$ and $\frac{10}{3}$ .

$y = \frac{2 \cdot 10}{3}$

Step 4.2.1.2

Multiply $2$ by $10$ .

$y = \frac{20}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{20}{3}$

Decimal Form:

$y = 6.\overline{6}$

Mixed Number Form:

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