Basic Math Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $60$ .

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Step 1.1

Multiply $\frac{1 - \frac{1}{4}}{- \frac{1}{5} + \frac{1}{6}}$ by $\frac{60}{60}$ .

$\frac{60}{60} \cdot \frac{1 - \frac{1}{4}}{- \frac{1}{5} + \frac{1}{6}}$

Step 1.2

Combine.

$\frac{60 (1 - \frac{1}{4})}{60 (- \frac{1}{5} + \frac{1}{6})}$

Step 2

Apply the distributive property.

$\frac{60 \cdot 1 + 60 (- \frac{1}{4})}{60 (- \frac{1}{5}) + 60 (\frac{1}{6})}$

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 $- \frac{1}{4}$ into the numerator.

$\frac{60 \cdot 1 + 60 (\frac{- 1}{4})}{60 (- \frac{1}{5}) + 60 (\frac{1}{6})}$

Step 3.1.2

Factor $4$ out of $60$ .

$\frac{60 \cdot 1 + 4 (15) \frac{- 1}{4}}{60 (- \frac{1}{5}) + 60 (\frac{1}{6})}$

Step 3.1.3

Cancel the common factor.

$\frac{60 \cdot 1 + 4 \cdot 15 \frac{- 1}{4}}{60 (- \frac{1}{5}) + 60 (\frac{1}{6})}$

Step 3.1.4

Rewrite the expression.

$\frac{60 \cdot 1 + 15 \cdot - 1}{60 (- \frac{1}{5}) + 60 (\frac{1}{6})}$

Step 3.2

Multiply $15$ by $- 1$ .

$\frac{60 \cdot 1 - 15}{60 (- \frac{1}{5}) + 60 (\frac{1}{6})}$

Step 3.3

Cancel the common factor of $5$ .

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Step 3.3.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$\frac{60 \cdot 1 - 15}{60 (\frac{- 1}{5}) + 60 (\frac{1}{6})}$

Step 3.3.2

Factor $5$ out of $60$ .

$\frac{60 \cdot 1 - 15}{5 (12) \frac{- 1}{5} + 60 (\frac{1}{6})}$

Step 3.3.3

Cancel the common factor.

$\frac{60 \cdot 1 - 15}{5 \cdot 12 \frac{- 1}{5} + 60 (\frac{1}{6})}$

Step 3.3.4

Rewrite the expression.

$\frac{60 \cdot 1 - 15}{12 \cdot - 1 + 60 (\frac{1}{6})}$

Step 3.4

Multiply $12$ by $- 1$ .

$\frac{60 \cdot 1 - 15}{- 12 + 60 (\frac{1}{6})}$

Step 3.5

Cancel the common factor of $6$ .

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Step 3.5.1

Factor $6$ out of $60$ .

$\frac{60 \cdot 1 - 15}{- 12 + 6 (10) \frac{1}{6}}$

Step 3.5.2

Cancel the common factor.

$\frac{60 \cdot 1 - 15}{- 12 + 6 \cdot 10 \frac{1}{6}}$

Step 3.5.3

Rewrite the expression.

$\frac{60 \cdot 1 - 15}{- 12 + 10}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $60$ by $1$ .

$\frac{60 - 15}{- 12 + 10}$

Step 4.2

Subtract $15$ from $60$ .

$\frac{45}{- 12 + 10}$

Step 5

Simplify the expression.

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Step 5.1

Add $- 12$ and $10$ .

$\frac{45}{- 2}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{45}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{45}{2}$

Decimal Form:

$- 22.5$

Mixed Number Form:

$- 22 \frac{1}{2}$