Pre-Algebra Examples

$\frac{x}{4} + \frac{x}{5} = 1$

Step 1

Simplify $\frac{x}{4} + \frac{x}{5}$ .

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Step 1.1

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{4} \cdot \frac{5}{5} + \frac{x}{5} = 1$

Step 1.2

To write $\frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{4} \cdot \frac{5}{5} + \frac{x}{5} \cdot \frac{4}{4} = 1$

Step 1.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x}{4}$ by $\frac{5}{5}$ .

$\frac{x \cdot 5}{4 \cdot 5} + \frac{x}{5} \cdot \frac{4}{4} = 1$

Step 1.3.2

Multiply $4$ by $5$ .

$\frac{x \cdot 5}{20} + \frac{x}{5} \cdot \frac{4}{4} = 1$

Step 1.3.3

Multiply $\frac{x}{5}$ by $\frac{4}{4}$ .

$\frac{x \cdot 5}{20} + \frac{x \cdot 4}{5 \cdot 4} = 1$

Step 1.3.4

Multiply $5$ by $4$ .

$\frac{x \cdot 5}{20} + \frac{x \cdot 4}{20} = 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 5 + x \cdot 4}{20} = 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $5$ to the left of $x$ .

$\frac{5 \cdot x + x \cdot 4}{20} = 1$

Step 1.5.2

Move $4$ to the left of $x$ .

$\frac{5 x + 4 \cdot x}{20} = 1$

Step 1.5.3

Add $5 x$ and $4 x$ .

$\frac{9 x}{20} = 1$

Step 2

Multiply both sides of the equation by $\frac{20}{9}$ .

$\frac{20}{9} \cdot \frac{9 x}{20} = \frac{20}{9} \cdot 1$

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 $\frac{20}{9} \cdot \frac{9 x}{20}$ .

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Step 3.1.1.1

Cancel the common factor of $20$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{20}{9} \cdot \frac{9 x}{20} = \frac{20}{9} \cdot 1$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 x) = \frac{20}{9} \cdot 1$

Step 3.1.1.2

Cancel the common factor of $9$ .

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Step 3.1.1.2.1

Factor $9$ out of $9 x$ .

$\frac{1}{9} (9 (x)) = \frac{20}{9} \cdot 1$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 x) = \frac{20}{9} \cdot 1$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{20}{9} \cdot 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{20}{9}$ by $1$ .

$x = \frac{20}{9}$