Basic Math Examples

$\frac{2}{3} y + \frac{1}{2} = \frac{4}{9} - \frac{1}{3} y + \frac{4}{9}$

Step 1

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

$\frac{2 y}{3} + \frac{1}{2} = \frac{4}{9} - \frac{1}{3} y + \frac{4}{9}$

Step 2

Simplify $\frac{4}{9} - \frac{1}{3} y + \frac{4}{9}$ .

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Step 2.1

Combine the numerators over the common denominator.

$\frac{2 y}{3} + \frac{1}{2} = - \frac{1}{3} y + \frac{4 + 4}{9}$

Step 2.2

Add $4$ and $4$ .

$\frac{2 y}{3} + \frac{1}{2} = - \frac{1}{3} y + \frac{8}{9}$

Step 2.3

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

$\frac{2 y}{3} + \frac{1}{2} = - \frac{y}{3} + \frac{8}{9}$

Step 3

Move all terms containing $y$ to the left side of the equation.

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Step 3.1

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

$\frac{2 y}{3} + \frac{1}{2} + \frac{y}{3} = \frac{8}{9}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 y + y}{3} + \frac{1}{2} = \frac{8}{9}$

Step 3.3

Add $2 y$ and $y$ .

$\frac{3 y}{3} + \frac{1}{2} = \frac{8}{9}$

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Cancel the common factor.

$\frac{3 y}{3} + \frac{1}{2} = \frac{8}{9}$

Step 3.4.2

Divide $y$ by $1$ .

$y + \frac{1}{2} = \frac{8}{9}$

Step 4

Move all terms not containing $y$ to the right side of the equation.

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Step 4.1

Subtract $\frac{1}{2}$ from both sides of the equation.

$y = \frac{8}{9} - \frac{1}{2}$

Step 4.2

To write $\frac{8}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{8}{9} \cdot \frac{2}{2} - \frac{1}{2}$

Step 4.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = \frac{8}{9} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{9}{9}$

Step 4.4

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{8}{9}$ by $\frac{2}{2}$ .

$y = \frac{8 \cdot 2}{9 \cdot 2} - \frac{1}{2} \cdot \frac{9}{9}$

Step 4.4.2

Multiply $9$ by $2$ .

$y = \frac{8 \cdot 2}{18} - \frac{1}{2} \cdot \frac{9}{9}$

Step 4.4.3

Multiply $\frac{1}{2}$ by $\frac{9}{9}$ .

$y = \frac{8 \cdot 2}{18} - \frac{9}{2 \cdot 9}$

Step 4.4.4

Multiply $2$ by $9$ .

$y = \frac{8 \cdot 2}{18} - \frac{9}{18}$

Step 4.5

Combine the numerators over the common denominator.

$y = \frac{8 \cdot 2 - 9}{18}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $8$ by $2$ .

$y = \frac{16 - 9}{18}$

Step 4.6.2

Subtract $9$ from $16$ .

$y = \frac{7}{18}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7}{18}$

Decimal Form:

$y = 0.3\overline{8}$