Pre-Algebra Examples

$\frac{1}{2} - \frac{3}{5} = \frac{x}{10}$

Step 1

Rewrite the equation as $\frac{x}{10} = \frac{1}{2} - \frac{3}{5}$ .

$\frac{x}{10} = \frac{1}{2} - \frac{3}{5}$

Step 2

Multiply both sides of the equation by $10$ .

$10 \frac{x}{10} = 10 (\frac{1}{2} - \frac{3}{5})$

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 $10$ .

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Step 3.1.1.1

Cancel the common factor.

$10 \frac{x}{10} = 10 (\frac{1}{2} - \frac{3}{5})$

Step 3.1.1.2

Rewrite the expression.

$x = 10 (\frac{1}{2} - \frac{3}{5})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $10 (\frac{1}{2} - \frac{3}{5})$ .

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Step 3.2.1.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = 10 (\frac{1}{2} \cdot \frac{5}{5} - \frac{3}{5})$

Step 3.2.1.2

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

$x = 10 (\frac{1}{2} \cdot \frac{5}{5} - \frac{3}{5} \cdot \frac{2}{2})$

Step 3.2.1.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1.3.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$x = 10 (\frac{5}{2 \cdot 5} - \frac{3}{5} \cdot \frac{2}{2})$

Step 3.2.1.3.2

Multiply $2$ by $5$ .

$x = 10 (\frac{5}{10} - \frac{3}{5} \cdot \frac{2}{2})$

Step 3.2.1.3.3

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

$x = 10 (\frac{5}{10} - \frac{3 \cdot 2}{5 \cdot 2})$

Step 3.2.1.3.4

Multiply $5$ by $2$ .

$x = 10 (\frac{5}{10} - \frac{3 \cdot 2}{10})$

Step 3.2.1.4

Combine the numerators over the common denominator.

$x = 10 \frac{5 - 3 \cdot 2}{10}$

Step 3.2.1.5

Simplify the numerator.

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Step 3.2.1.5.1

Multiply $- 3$ by $2$ .

$x = 10 \frac{5 - 6}{10}$

Step 3.2.1.5.2

Subtract $6$ from $5$ .

$x = 10 (\frac{- 1}{10})$

Step 3.2.1.6

Cancel the common factor of $10$ .

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Step 3.2.1.6.1

Cancel the common factor.

$x = 10 (\frac{- 1}{10})$

Step 3.2.1.6.2

Rewrite the expression.

$x = - 1$