Pre-Algebra Examples

$1 + \frac{25}{4} \div 1 - \frac{5}{2}$

Step 1

Find the common denominator.

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Step 1.1

Write $1$ as a fraction with denominator $1$ .

$\frac{1}{1} + \frac{25}{4} \div 1 - \frac{5}{2}$

Step 1.2

Multiply $\frac{1}{1}$ by $\frac{2}{2}$ .

$\frac{1}{1} \cdot \frac{2}{2} + \frac{25}{4} \div 1 - \frac{5}{2}$

Step 1.3

Multiply $\frac{1}{1}$ by $\frac{2}{2}$ .

$\frac{2}{2} + \frac{25}{4} \div 1 - \frac{5}{2}$

Step 1.4

Multiply $\frac{25}{4} \div 1$ by $\frac{2}{2}$ .

$\frac{2}{2} + \frac{25}{4} \div 1 \cdot \frac{2}{2} - \frac{5}{2}$

Step 1.5

Multiply $\frac{25}{4} \div 1$ by $\frac{2}{2}$ .

$\frac{2}{2} + \frac{\frac{25}{4} \cdot 2}{2} - \frac{5}{2}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 + \frac{25}{4} \cdot 2 - 5}{2}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $4$ .

$\frac{2 + \frac{25}{2 (2)} \cdot 2 - 5}{2}$

Step 3.2

Cancel the common factor.

$\frac{2 + \frac{25}{2 \cdot 2} \cdot 2 - 5}{2}$

Step 3.3

Rewrite the expression.

$\frac{2 + \frac{25}{2} - 5}{2}$

Step 4

Find the common denominator.

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Step 4.1

Write $2$ as a fraction with denominator $1$ .

$\frac{\frac{2}{1} + \frac{25}{2} - 5}{2}$

Step 4.2

Multiply $\frac{2}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{2}{1} \cdot \frac{2}{2} + \frac{25}{2} - 5}{2}$

Step 4.3

Multiply $\frac{2}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{2 \cdot 2}{2} + \frac{25}{2} - 5}{2}$

Step 4.4

Write $- 5$ as a fraction with denominator $1$ .

$\frac{\frac{2 \cdot 2}{2} + \frac{25}{2} + \frac{- 5}{1}}{2}$

Step 4.5

Multiply $\frac{- 5}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{2 \cdot 2}{2} + \frac{25}{2} + \frac{- 5}{1} \cdot \frac{2}{2}}{2}$

Step 4.6

Multiply $\frac{- 5}{1}$ by $\frac{2}{2}$ .

$\frac{\frac{2 \cdot 2}{2} + \frac{25}{2} + \frac{- 5 \cdot 2}{2}}{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 2 + 25 - 5 \cdot 2}{2}}{2}$

Step 6

Simplify each term.

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Step 6.1

Multiply $2$ by $2$ .

$\frac{\frac{4 + 25 - 5 \cdot 2}{2}}{2}$

Step 6.2

Multiply $- 5$ by $2$ .

$\frac{\frac{4 + 25 - 10}{2}}{2}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Add $4$ and $25$ .

$\frac{\frac{29 - 10}{2}}{2}$

Step 7.2

Subtract $10$ from $29$ .

$\frac{\frac{19}{2}}{2}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{19}{2} \cdot \frac{1}{2}$

Step 9

Multiply $\frac{19}{2} \cdot \frac{1}{2}$ .

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Step 9.1

Multiply $\frac{19}{2}$ by $\frac{1}{2}$ .

$\frac{19}{2 \cdot 2}$

Step 9.2

Multiply $2$ by $2$ .

$\frac{19}{4}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{4}$

Decimal Form:

$4.75$

Mixed Number Form:

$4 \frac{3}{4}$