Basic Math Examples

$x - 2 \frac{1}{4} = 5$

Step 1

Simplify the left side.

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Step 1.1

Convert $2 \frac{1}{4}$ to an improper fraction.

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Step 1.1.1

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

$x - (2 + \frac{1}{4}) = 5$

Step 1.1.2

Add $2$ and $\frac{1}{4}$ .

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Step 1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x - (2 \cdot \frac{4}{4} + \frac{1}{4}) = 5$

Step 1.1.2.2

Combine $2$ and $\frac{4}{4}$ .

$x - (\frac{2 \cdot 4}{4} + \frac{1}{4}) = 5$

Step 1.1.2.3

Combine the numerators over the common denominator.

$x - \frac{2 \cdot 4 + 1}{4} = 5$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $4$ .

$x - \frac{8 + 1}{4} = 5$

Step 1.1.2.4.2

Add $8$ and $1$ .

$x - \frac{9}{4} = 5$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $\frac{9}{4}$ to both sides of the equation.

$x = 5 + \frac{9}{4}$

Step 2.2

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

$x = 5 \cdot \frac{4}{4} + \frac{9}{4}$

Step 2.3

Combine $5$ and $\frac{4}{4}$ .

$x = \frac{5 \cdot 4}{4} + \frac{9}{4}$

Step 2.4

Combine the numerators over the common denominator.

$x = \frac{5 \cdot 4 + 9}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $5$ by $4$ .

$x = \frac{20 + 9}{4}$

Step 2.5.2

Add $20$ and $9$ .

$x = \frac{29}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{29}{4}$

Decimal Form:

$x = 7.25$

Mixed Number Form:

$x = 7 \frac{1}{4}$