Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

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 $60$ .

$\frac{4 (15) \frac{1}{4} + 60 (- \frac{3}{2})}{60 (\frac{6}{5}) + 60 (- \frac{5}{3})}$

Step 3.1.2

Cancel the common factor.

$\frac{4 \cdot 15 \frac{1}{4} + 60 (- \frac{3}{2})}{60 (\frac{6}{5}) + 60 (- \frac{5}{3})}$

Step 3.1.3

Rewrite the expression.

$\frac{15 + 60 (- \frac{3}{2})}{60 (\frac{6}{5}) + 60 (- \frac{5}{3})}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{15 + 60 (\frac{- 3}{2})}{60 (\frac{6}{5}) + 60 (- \frac{5}{3})}$

Step 3.2.2

Factor $2$ out of $60$ .

$\frac{15 + 2 (30) \frac{- 3}{2}}{60 (\frac{6}{5}) + 60 (- \frac{5}{3})}$

Step 3.2.3

Cancel the common factor.

$\frac{15 + 2 \cdot 30 \frac{- 3}{2}}{60 (\frac{6}{5}) + 60 (- \frac{5}{3})}$

Step 3.2.4

Rewrite the expression.

$\frac{15 + 30 \cdot - 3}{60 (\frac{6}{5}) + 60 (- \frac{5}{3})}$

Step 3.3

Multiply $30$ by $- 3$ .

$\frac{15 - 90}{60 (\frac{6}{5}) + 60 (- \frac{5}{3})}$

Step 3.4

Cancel the common factor of $5$ .

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Step 3.4.1

Factor $5$ out of $60$ .

$\frac{15 - 90}{5 (12) \frac{6}{5} + 60 (- \frac{5}{3})}$

Step 3.4.2

Cancel the common factor.

$\frac{15 - 90}{5 \cdot 12 \frac{6}{5} + 60 (- \frac{5}{3})}$

Step 3.4.3

Rewrite the expression.

$\frac{15 - 90}{12 \cdot 6 + 60 (- \frac{5}{3})}$

Step 3.5

Multiply $12$ by $6$ .

$\frac{15 - 90}{72 + 60 (- \frac{5}{3})}$

Step 3.6

Cancel the common factor of $3$ .

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Step 3.6.1

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

$\frac{15 - 90}{72 + 60 (\frac{- 5}{3})}$

Step 3.6.2

Factor $3$ out of $60$ .

$\frac{15 - 90}{72 + 3 (20) \frac{- 5}{3}}$

Step 3.6.3

Cancel the common factor.

$\frac{15 - 90}{72 + 3 \cdot 20 \frac{- 5}{3}}$

Step 3.6.4

Rewrite the expression.

$\frac{15 - 90}{72 + 20 \cdot - 5}$

Step 3.7

Multiply $20$ by $- 5$ .

$\frac{15 - 90}{72 - 100}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $90$ from $15$ .

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

Step 4.2

Subtract $100$ from $72$ .

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

Step 4.3

Dividing two negative values results in a positive value.

$\frac{75}{28}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{75}{28}$

Decimal Form:

$2.67857142 \dots$

Mixed Number Form:

$2 \frac{19}{28}$