Pre-Algebra Examples

$\frac{6 - \frac{5}{4}}{9 + \frac{1}{2}}$

Step 1

Multiply the numerator and denominator of the fraction by $4$ .

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Step 1.1

Multiply $\frac{6 - \frac{5}{4}}{9 + \frac{1}{2}}$ by $\frac{4}{4}$ .

$\frac{4}{4} \cdot \frac{6 - \frac{5}{4}}{9 + \frac{1}{2}}$

Step 1.2

Combine.

$\frac{4 (6 - \frac{5}{4})}{4 (9 + \frac{1}{2})}$

Step 2

Apply the distributive property.

$\frac{4 \cdot 6 + 4 (- \frac{5}{4})}{4 \cdot 9 + 4 (\frac{1}{2})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$\frac{4 \cdot 6 + 4 (\frac{- 5}{4})}{4 \cdot 9 + 4 (\frac{1}{2})}$

Step 3.1.2

Cancel the common factor.

$\frac{4 \cdot 6 + 4 (\frac{- 5}{4})}{4 \cdot 9 + 4 (\frac{1}{2})}$

Step 3.1.3

Rewrite the expression.

$\frac{4 \cdot 6 - 5}{4 \cdot 9 + 4 (\frac{1}{2})}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $4$ .

$\frac{4 \cdot 6 - 5}{4 \cdot 9 + 2 (2) \frac{1}{2}}$

Step 3.2.2

Cancel the common factor.

$\frac{4 \cdot 6 - 5}{4 \cdot 9 + 2 \cdot 2 \frac{1}{2}}$

Step 3.2.3

Rewrite the expression.

$\frac{4 \cdot 6 - 5}{4 \cdot 9 + 2}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $4$ by $6$ .

$\frac{24 - 5}{4 \cdot 9 + 2}$

Step 4.2

Subtract $5$ from $24$ .

$\frac{19}{4 \cdot 9 + 2}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $4$ by $9$ .

$\frac{19}{36 + 2}$

Step 5.2

Add $36$ and $2$ .

$\frac{19}{38}$

Step 6

Cancel the common factor of $19$ and $38$ .

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Step 6.1

Factor $19$ out of $19$ .

$\frac{19 (1)}{38}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $19$ out of $38$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$