Finite Math Examples

$\frac{32}{15} + \frac{1}{3} y = 2$

Step 1

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

$\frac{32}{15} + \frac{y}{3} = 2$

Step 2

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

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Step 2.1

Subtract $\frac{32}{15}$ from both sides of the equation.

$\frac{y}{3} = 2 - \frac{32}{15}$

Step 2.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{y}{3} = 2 \cdot \frac{15}{15} - \frac{32}{15}$

Step 2.3

Combine $2$ and $\frac{15}{15}$ .

$\frac{y}{3} = \frac{2 \cdot 15}{15} - \frac{32}{15}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{y}{3} = \frac{2 \cdot 15 - 32}{15}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $15$ .

$\frac{y}{3} = \frac{30 - 32}{15}$

Step 2.5.2

Subtract $32$ from $30$ .

$\frac{y}{3} = \frac{- 2}{15}$

Step 2.6

Move the negative in front of the fraction.

$\frac{y}{3} = - \frac{2}{15}$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{y}{3} = 3 (- \frac{2}{15})$

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.

$3 \frac{y}{3} = 3 (- \frac{2}{15})$

Step 4.1.1.2

Rewrite the expression.

$y = 3 (- \frac{2}{15})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $3 (- \frac{2}{15})$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{2}{15}$ into the numerator.

$y = 3 (\frac{- 2}{15})$

Step 4.2.1.1.2

Factor $3$ out of $15$ .

$y = 3 \frac{- 2}{3 (5)}$

Step 4.2.1.1.3

Cancel the common factor.

$y = 3 \frac{- 2}{3 \cdot 5}$

Step 4.2.1.1.4

Rewrite the expression.

$y = \frac{- 2}{5}$

Step 4.2.1.2

Move the negative in front of the fraction.

$y = - \frac{2}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{2}{5}$

Decimal Form:

$y = - 0.4$