Basic Math Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $20$ .

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Step 1.1

Multiply $\frac{2 - \frac{4}{5}}{\frac{1}{2} - \frac{1}{4}}$ by $\frac{20}{20}$ .

$\frac{20}{20} \cdot \frac{2 - \frac{4}{5}}{\frac{1}{2} - \frac{1}{4}}$

Step 1.2

Combine.

$\frac{20 (2 - \frac{4}{5})}{20 (\frac{1}{2} - \frac{1}{4})}$

Step 2

Apply the distributive property.

$\frac{20 \cdot 2 + 20 (- \frac{4}{5})}{20 (\frac{1}{2}) + 20 (- \frac{1}{4})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $5$ .

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Step 3.1.1

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

$\frac{20 \cdot 2 + 20 (\frac{- 4}{5})}{20 (\frac{1}{2}) + 20 (- \frac{1}{4})}$

Step 3.1.2

Factor $5$ out of $20$ .

$\frac{20 \cdot 2 + 5 (4) \frac{- 4}{5}}{20 (\frac{1}{2}) + 20 (- \frac{1}{4})}$

Step 3.1.3

Cancel the common factor.

$\frac{20 \cdot 2 + 5 \cdot 4 \frac{- 4}{5}}{20 (\frac{1}{2}) + 20 (- \frac{1}{4})}$

Step 3.1.4

Rewrite the expression.

$\frac{20 \cdot 2 + 4 \cdot - 4}{20 (\frac{1}{2}) + 20 (- \frac{1}{4})}$

Step 3.2

Multiply $4$ by $- 4$ .

$\frac{20 \cdot 2 - 16}{20 (\frac{1}{2}) + 20 (- \frac{1}{4})}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Factor $2$ out of $20$ .

$\frac{20 \cdot 2 - 16}{2 (10) \frac{1}{2} + 20 (- \frac{1}{4})}$

Step 3.3.2

Cancel the common factor.

$\frac{20 \cdot 2 - 16}{2 \cdot 10 \frac{1}{2} + 20 (- \frac{1}{4})}$

Step 3.3.3

Rewrite the expression.

$\frac{20 \cdot 2 - 16}{10 + 20 (- \frac{1}{4})}$

Step 3.4

Cancel the common factor of $4$ .

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Step 3.4.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{20 \cdot 2 - 16}{10 + 20 (\frac{- 1}{4})}$

Step 3.4.2

Factor $4$ out of $20$ .

$\frac{20 \cdot 2 - 16}{10 + 4 (5) \frac{- 1}{4}}$

Step 3.4.3

Cancel the common factor.

$\frac{20 \cdot 2 - 16}{10 + 4 \cdot 5 \frac{- 1}{4}}$

Step 3.4.4

Rewrite the expression.

$\frac{20 \cdot 2 - 16}{10 + 5 \cdot - 1}$

Step 3.5

Multiply $5$ by $- 1$ .

$\frac{20 \cdot 2 - 16}{10 - 5}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $20$ by $2$ .

$\frac{40 - 16}{10 - 5}$

Step 4.2

Subtract $16$ from $40$ .

$\frac{24}{10 - 5}$

Step 5

Subtract $5$ from $10$ .

$\frac{24}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{24}{5}$

Decimal Form:

$4.8$

Mixed Number Form:

$4 \frac{4}{5}$