Basic Math Examples

$\frac{2}{5} y - \frac{1}{3} y = 5$

Step 1

Simplify $\frac{2}{5} y - \frac{1}{3} y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{2 y}{5} - \frac{1}{3} y = 5$

Step 1.1.2

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

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

Step 1.2

To write $\frac{2 y}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.3

To write $- \frac{y}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 1.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{2 y}{5}$ by $\frac{3}{3}$ .

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

Step 1.4.2

Multiply $5$ by $3$ .

$\frac{2 y \cdot 3}{15} - \frac{y}{3} \cdot \frac{5}{5} = 5$

Step 1.4.3

Multiply $\frac{y}{3}$ by $\frac{5}{5}$ .

$\frac{2 y \cdot 3}{15} - \frac{y \cdot 5}{3 \cdot 5} = 5$

Step 1.4.4

Multiply $3$ by $5$ .

$\frac{2 y \cdot 3}{15} - \frac{y \cdot 5}{15} = 5$

Step 1.5

Combine the numerators over the common denominator.

$\frac{2 y \cdot 3 - y \cdot 5}{15} = 5$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $y$ out of $2 y \cdot 3 - y \cdot 5$ .

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Step 1.6.1.1

Factor $y$ out of $2 y \cdot 3$ .

$\frac{y (2 \cdot 3) - y \cdot 5}{15} = 5$

Step 1.6.1.2

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

$\frac{y (2 \cdot 3) + y (- 1 \cdot 5)}{15} = 5$

Step 1.6.1.3

Factor $y$ out of $y (2 \cdot 3) + y (- 1 \cdot 5)$ .

$\frac{y (2 \cdot 3 - 1 \cdot 5)}{15} = 5$

Step 1.6.2

Multiply $2$ by $3$ .

$\frac{y (6 - 1 \cdot 5)}{15} = 5$

Step 1.6.3

Multiply $- 1$ by $5$ .

$\frac{y (6 - 5)}{15} = 5$

Step 1.6.4

Subtract $5$ from $6$ .

$\frac{y \cdot 1}{15} = 5$

Step 1.7

Multiply $y$ by $1$ .

$\frac{y}{15} = 5$

Step 2

Multiply both sides of the equation by $15$ .

$15 \frac{y}{15} = 15 \cdot 5$

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

Cancel the common factor of $15$ .

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Step 3.1.1.1

Cancel the common factor.

$15 \frac{y}{15} = 15 \cdot 5$

Step 3.1.1.2

Rewrite the expression.

$y = 15 \cdot 5$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $15$ by $5$ .

$y = 75$