Pre-Algebra Examples

$2 \frac{5}{2} - 2 \frac{3}{2}$

Step 1

Convert $2 \frac{5}{2}$ to an improper fraction.

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Step 1.1

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

$2 + \frac{5}{2} - 2 \frac{3}{2}$

Step 1.2

Add $2$ and $\frac{5}{2}$ .

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Step 1.2.1

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

$2 \cdot \frac{2}{2} + \frac{5}{2} - 2 \frac{3}{2}$

Step 1.2.2

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

$\frac{2 \cdot 2}{2} + \frac{5}{2} - 2 \frac{3}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 5}{2} - 2 \frac{3}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $2$ .

$\frac{4 + 5}{2} - 2 \frac{3}{2}$

Step 1.2.4.2

Add $4$ and $5$ .

$\frac{9}{2} - 2 \frac{3}{2}$

Step 2

Convert $2 \frac{3}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{9}{2} - (2 + \frac{3}{2})$

Step 2.2

Add $2$ and $\frac{3}{2}$ .

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Step 2.2.1

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

$\frac{9}{2} - (2 \cdot \frac{2}{2} + \frac{3}{2})$

Step 2.2.2

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

$\frac{9}{2} - (\frac{2 \cdot 2}{2} + \frac{3}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{9}{2} - \frac{2 \cdot 2 + 3}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $2$ .

$\frac{9}{2} - \frac{4 + 3}{2}$

Step 2.2.4.2

Add $4$ and $3$ .

$\frac{9}{2} - \frac{7}{2}$

Step 3

Combine the numerators over the common denominator.

$\frac{9 - 7}{2}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $7$ from $9$ .

$\frac{2}{2}$

Step 4.2

Divide $2$ by $2$ .

$1$