Basic Math Examples

$- \frac{2}{3} + \frac{5}{3} = \frac{7}{5} y + \frac{2}{5} y$

Step 1

Rewrite the equation as $\frac{7}{5} y + \frac{2}{5} y = - \frac{2}{3} + \frac{5}{3}$ .

$\frac{7}{5} y + \frac{2}{5} y = - \frac{2}{3} + \frac{5}{3}$

Step 2

Simplify $\frac{7}{5} y + \frac{2}{5} y$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $\frac{7}{5}$ and $y$ .

$\frac{7 y}{5} + \frac{2}{5} y = - \frac{2}{3} + \frac{5}{3}$

Step 2.1.2

Combine $\frac{2}{5}$ and $y$ .

$\frac{7 y}{5} + \frac{2 y}{5} = - \frac{2}{3} + \frac{5}{3}$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the numerators over the common denominator.

$\frac{7 y + 2 y}{5} = - \frac{2}{3} + \frac{5}{3}$

Step 2.2.2

Add $7 y$ and $2 y$ .

$\frac{9 y}{5} = - \frac{2}{3} + \frac{5}{3}$

Step 3

Simplify $- \frac{2}{3} + \frac{5}{3}$ .

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Step 3.1

Combine the numerators over the common denominator.

$\frac{9 y}{5} = \frac{- 2 + 5}{3}$

Step 3.2

Simplify the expression.

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Step 3.2.1

Add $- 2$ and $5$ .

$\frac{9 y}{5} = \frac{3}{3}$

Step 3.2.2

Divide $3$ by $3$ .

$\frac{9 y}{5} = 1$

Step 4

Multiply both sides of the equation by $\frac{5}{9}$ .

$\frac{5}{9} \cdot \frac{9 y}{5} = \frac{5}{9} \cdot 1$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{5}{9} \cdot \frac{9 y}{5}$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{9} \cdot \frac{9 y}{5} = \frac{5}{9} \cdot 1$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 y) = \frac{5}{9} \cdot 1$

Step 5.1.1.2

Cancel the common factor of $9$ .

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Step 5.1.1.2.1

Factor $9$ out of $9 y$ .

$\frac{1}{9} (9 (y)) = \frac{5}{9} \cdot 1$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 y) = \frac{5}{9} \cdot 1$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{5}{9} \cdot 1$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{5}{9}$ by $1$ .

$y = \frac{5}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{5}{9}$

Decimal Form:

$y = 0.\overline{5}$