Pre-Algebra Examples

$\frac{x}{4} + \frac{x}{3} = \frac{7}{12}$

Step 1

Simplify $\frac{x}{4} + \frac{x}{3}$ .

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Step 1.1

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{4} \cdot \frac{3}{3} + \frac{x}{3} = \frac{7}{12}$

Step 1.2

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{4} \cdot \frac{3}{3} + \frac{x}{3} \cdot \frac{4}{4} = \frac{7}{12}$

Step 1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x}{4}$ by $\frac{3}{3}$ .

$\frac{x \cdot 3}{4 \cdot 3} + \frac{x}{3} \cdot \frac{4}{4} = \frac{7}{12}$

Step 1.3.2

Multiply $4$ by $3$ .

$\frac{x \cdot 3}{12} + \frac{x}{3} \cdot \frac{4}{4} = \frac{7}{12}$

Step 1.3.3

Multiply $\frac{x}{3}$ by $\frac{4}{4}$ .

$\frac{x \cdot 3}{12} + \frac{x \cdot 4}{3 \cdot 4} = \frac{7}{12}$

Step 1.3.4

Multiply $3$ by $4$ .

$\frac{x \cdot 3}{12} + \frac{x \cdot 4}{12} = \frac{7}{12}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 3 + x \cdot 4}{12} = \frac{7}{12}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $3$ to the left of $x$ .

$\frac{3 \cdot x + x \cdot 4}{12} = \frac{7}{12}$

Step 1.5.2

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

$\frac{3 x + 4 \cdot x}{12} = \frac{7}{12}$

Step 1.5.3

Add $3 x$ and $4 x$ .

$\frac{7 x}{12} = \frac{7}{12}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$7 x = 7$

Step 3

Divide each term in $7 x = 7$ by $7$ and simplify.

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Step 3.1

Divide each term in $7 x = 7$ by $7$ .

$\frac{7 x}{7} = \frac{7}{7}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{7}{7}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{7}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $7$ by $7$ .

$x = 1$