Finite Math Examples

$\frac{5}{3} y - y = 20$

Step 1

Simplify $\frac{5}{3} y - y$ .

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Step 1.1

Combine $\frac{5}{3}$ and $y$ .

$\frac{5 y}{3} - y = 20$

Step 1.2

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

$\frac{5 y}{3} - y \cdot \frac{3}{3} = 20$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{5 y}{3} + \frac{- y \cdot 3}{3} = 20$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{5 y - y \cdot 3}{3} = 20$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $y$ out of $5 y - y \cdot 3$ .

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Step 1.4.1.1

Factor $y$ out of $5 y$ .

$\frac{y \cdot 5 - y \cdot 3}{3} = 20$

Step 1.4.1.2

Factor $y$ out of $- y \cdot 3$ .

$\frac{y \cdot 5 + y (- 1 \cdot 3)}{3} = 20$

Step 1.4.1.3

Factor $y$ out of $y \cdot 5 + y (- 1 \cdot 3)$ .

$\frac{y (5 - 1 \cdot 3)}{3} = 20$

Step 1.4.2

Multiply $- 1$ by $3$ .

$\frac{y (5 - 3)}{3} = 20$

Step 1.4.3

Subtract $3$ from $5$ .

$\frac{y \cdot 2}{3} = 20$

Step 1.5

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

$\frac{2 y}{3} = 20$

Step 2

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} \cdot 20$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{3}{2} \cdot \frac{2 y}{3}$ .

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Step 3.1.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} \cdot 20$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 y) = \frac{3}{2} \cdot 20$

Step 3.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.2.1

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) = \frac{3}{2} \cdot 20$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 y) = \frac{3}{2} \cdot 20$

Step 3.1.1.2.3

Rewrite the expression.

$y = \frac{3}{2} \cdot 20$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{3}{2} \cdot 20$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $20$ .

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

Step 3.2.1.1.2

Cancel the common factor.

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

Step 3.2.1.1.3

Rewrite the expression.

$y = 3 \cdot 10$

Step 3.2.1.2

Multiply $3$ by $10$ .

$y = 30$