Algebra Examples

$3 \frac{1}{4} x = \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $3 \frac{1}{4} x$ .

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Step 1.1.1

Convert $3 \frac{1}{4}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$(3 + \frac{1}{4}) x = \frac{1}{2}$

Step 1.1.1.2

Add $3$ and $\frac{1}{4}$ .

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Step 1.1.1.2.1

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

$(3 \cdot \frac{4}{4} + \frac{1}{4}) x = \frac{1}{2}$

Step 1.1.1.2.2

Combine $3$ and $\frac{4}{4}$ .

$(\frac{3 \cdot 4}{4} + \frac{1}{4}) x = \frac{1}{2}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 + 1}{4} x = \frac{1}{2}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $4$ .

$\frac{12 + 1}{4} x = \frac{1}{2}$

Step 1.1.1.2.4.2

Add $12$ and $1$ .

$\frac{13}{4} x = \frac{1}{2}$

Step 1.1.2

Combine $\frac{13}{4}$ and $x$ .

$\frac{13 x}{4} = \frac{1}{2}$

Step 2

Multiply both sides of the equation by $\frac{4}{13}$ .

$\frac{4}{13} \cdot \frac{13 x}{4} = \frac{4}{13} \cdot \frac{1}{2}$

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 $\frac{4}{13} \cdot \frac{13 x}{4}$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{4}{13} \cdot \frac{13 x}{4} = \frac{4}{13} \cdot \frac{1}{2}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{13} (13 x) = \frac{4}{13} \cdot \frac{1}{2}$

Step 3.1.1.2

Cancel the common factor of $13$ .

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Step 3.1.1.2.1

Factor $13$ out of $13 x$ .

$\frac{1}{13} (13 (x)) = \frac{4}{13} \cdot \frac{1}{2}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{13} (13 x) = \frac{4}{13} \cdot \frac{1}{2}$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{4}{13} \cdot \frac{1}{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Factor $2$ out of $4$ .

$x = \frac{2 (2)}{13} \cdot \frac{1}{2}$

Step 3.2.1.2

Cancel the common factor.

$x = \frac{2 \cdot 2}{13} \cdot \frac{1}{2}$

Step 3.2.1.3

Rewrite the expression.

$x = \frac{2}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{13}$

Decimal Form:

$x = 0.\overline{153846}$