Pre-Algebra Examples

$\frac{\frac{6}{5} - \frac{5}{3}}{\frac{1}{2} - \frac{5}{4}}$

Step 1

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

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Step 1.1

Multiply $\frac{\frac{6}{5} - \frac{5}{3}}{\frac{1}{2} - \frac{5}{4}}$ by $\frac{60}{60}$ .

$\frac{60}{60} \cdot \frac{\frac{6}{5} - \frac{5}{3}}{\frac{1}{2} - \frac{5}{4}}$

Step 1.2

Combine.

$\frac{60 (\frac{6}{5} - \frac{5}{3})}{60 (\frac{1}{2} - \frac{5}{4})}$

Step 2

Apply the distributive property.

$\frac{60 (\frac{6}{5}) + 60 (- \frac{5}{3})}{60 (\frac{1}{2}) + 60 (- \frac{5}{4})}$

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

Factor $5$ out of $60$ .

$\frac{5 (12) \frac{6}{5} + 60 (- \frac{5}{3})}{60 (\frac{1}{2}) + 60 (- \frac{5}{4})}$

Step 3.1.2

Cancel the common factor.

$\frac{5 \cdot 12 \frac{6}{5} + 60 (- \frac{5}{3})}{60 (\frac{1}{2}) + 60 (- \frac{5}{4})}$

Step 3.1.3

Rewrite the expression.

$\frac{12 \cdot 6 + 60 (- \frac{5}{3})}{60 (\frac{1}{2}) + 60 (- \frac{5}{4})}$

Step 3.2

Multiply $12$ by $6$ .

$\frac{72 + 60 (- \frac{5}{3})}{60 (\frac{1}{2}) + 60 (- \frac{5}{4})}$

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$\frac{72 + 60 (\frac{- 5}{3})}{60 (\frac{1}{2}) + 60 (- \frac{5}{4})}$

Step 3.3.2

Factor $3$ out of $60$ .

$\frac{72 + 3 (20) \frac{- 5}{3}}{60 (\frac{1}{2}) + 60 (- \frac{5}{4})}$

Step 3.3.3

Cancel the common factor.

$\frac{72 + 3 \cdot 20 \frac{- 5}{3}}{60 (\frac{1}{2}) + 60 (- \frac{5}{4})}$

Step 3.3.4

Rewrite the expression.

$\frac{72 + 20 \cdot - 5}{60 (\frac{1}{2}) + 60 (- \frac{5}{4})}$

Step 3.4

Multiply $20$ by $- 5$ .

$\frac{72 - 100}{60 (\frac{1}{2}) + 60 (- \frac{5}{4})}$

Step 3.5

Cancel the common factor of $2$ .

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Step 3.5.1

Factor $2$ out of $60$ .

$\frac{72 - 100}{2 (30) \frac{1}{2} + 60 (- \frac{5}{4})}$

Step 3.5.2

Cancel the common factor.

$\frac{72 - 100}{2 \cdot 30 \frac{1}{2} + 60 (- \frac{5}{4})}$

Step 3.5.3

Rewrite the expression.

$\frac{72 - 100}{30 + 60 (- \frac{5}{4})}$

Step 3.6

Cancel the common factor of $4$ .

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Step 3.6.1

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

$\frac{72 - 100}{30 + 60 (\frac{- 5}{4})}$

Step 3.6.2

Factor $4$ out of $60$ .

$\frac{72 - 100}{30 + 4 (15) \frac{- 5}{4}}$

Step 3.6.3

Cancel the common factor.

$\frac{72 - 100}{30 + 4 \cdot 15 \frac{- 5}{4}}$

Step 3.6.4

Rewrite the expression.

$\frac{72 - 100}{30 + 15 \cdot - 5}$

Step 3.7

Multiply $15$ by $- 5$ .

$\frac{72 - 100}{30 - 75}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $100$ from $72$ .

$\frac{- 28}{30 - 75}$

Step 4.2

Subtract $75$ from $30$ .

$\frac{- 28}{- 45}$

Step 4.3

Dividing two negative values results in a positive value.

$\frac{28}{45}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{28}{45}$

Decimal Form:

$0.6\overline{2}$