Basic Math Examples

$\frac{\frac{1}{4} - \frac{1}{2}}{\frac{1}{5} - \frac{1}{3}}$

Step 1

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

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Step 1.1

Multiply $\frac{\frac{1}{4} - \frac{1}{2}}{\frac{1}{5} - \frac{1}{3}}$ by $\frac{60}{60}$ .

$\frac{60}{60} \cdot \frac{\frac{1}{4} - \frac{1}{2}}{\frac{1}{5} - \frac{1}{3}}$

Step 1.2

Combine.

$\frac{60 (\frac{1}{4} - \frac{1}{2})}{60 (\frac{1}{5} - \frac{1}{3})}$

Step 2

Apply the distributive property.

$\frac{60 (\frac{1}{4}) + 60 (- \frac{1}{2})}{60 (\frac{1}{5}) + 60 (- \frac{1}{3})}$

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

Factor $4$ out of $60$ .

$\frac{4 (15) \frac{1}{4} + 60 (- \frac{1}{2})}{60 (\frac{1}{5}) + 60 (- \frac{1}{3})}$

Step 3.1.2

Cancel the common factor.

$\frac{4 \cdot 15 \frac{1}{4} + 60 (- \frac{1}{2})}{60 (\frac{1}{5}) + 60 (- \frac{1}{3})}$

Step 3.1.3

Rewrite the expression.

$\frac{15 + 60 (- \frac{1}{2})}{60 (\frac{1}{5}) + 60 (- \frac{1}{3})}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{15 + 60 (\frac{- 1}{2})}{60 (\frac{1}{5}) + 60 (- \frac{1}{3})}$

Step 3.2.2

Factor $2$ out of $60$ .

$\frac{15 + 2 (30) \frac{- 1}{2}}{60 (\frac{1}{5}) + 60 (- \frac{1}{3})}$

Step 3.2.3

Cancel the common factor.

$\frac{15 + 2 \cdot 30 \frac{- 1}{2}}{60 (\frac{1}{5}) + 60 (- \frac{1}{3})}$

Step 3.2.4

Rewrite the expression.

$\frac{15 + 30 \cdot - 1}{60 (\frac{1}{5}) + 60 (- \frac{1}{3})}$

Step 3.3

Multiply $30$ by $- 1$ .

$\frac{15 - 30}{60 (\frac{1}{5}) + 60 (- \frac{1}{3})}$

Step 3.4

Cancel the common factor of $5$ .

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Step 3.4.1

Factor $5$ out of $60$ .

$\frac{15 - 30}{5 (12) \frac{1}{5} + 60 (- \frac{1}{3})}$

Step 3.4.2

Cancel the common factor.

$\frac{15 - 30}{5 \cdot 12 \frac{1}{5} + 60 (- \frac{1}{3})}$

Step 3.4.3

Rewrite the expression.

$\frac{15 - 30}{12 + 60 (- \frac{1}{3})}$

Step 3.5

Cancel the common factor of $3$ .

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Step 3.5.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{15 - 30}{12 + 60 (\frac{- 1}{3})}$

Step 3.5.2

Factor $3$ out of $60$ .

$\frac{15 - 30}{12 + 3 (20) \frac{- 1}{3}}$

Step 3.5.3

Cancel the common factor.

$\frac{15 - 30}{12 + 3 \cdot 20 \frac{- 1}{3}}$

Step 3.5.4

Rewrite the expression.

$\frac{15 - 30}{12 + 20 \cdot - 1}$

Step 3.6

Multiply $20$ by $- 1$ .

$\frac{15 - 30}{12 - 20}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $30$ from $15$ .

$\frac{- 15}{12 - 20}$

Step 4.2

Subtract $20$ from $12$ .

$\frac{- 15}{- 8}$

Step 4.3

Dividing two negative values results in a positive value.

$\frac{15}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{8}$

Decimal Form:

$1.875$

Mixed Number Form:

$1 \frac{7}{8}$