Basic Math Examples

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

Step 1

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

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Step 1.1

Multiply $\frac{\frac{3}{4} - \frac{5}{2}}{\frac{1}{4} - \frac{2}{5}}$ by $\frac{20}{20}$ .

$\frac{20}{20} \cdot \frac{\frac{3}{4} - \frac{5}{2}}{\frac{1}{4} - \frac{2}{5}}$

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

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 $20$ .

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

Multiply $5$ by $3$ .

$\frac{15 + 20 (- \frac{5}{2})}{20 (\frac{1}{4}) + 20 (- \frac{2}{5})}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{15 + 20 (\frac{- 5}{2})}{20 (\frac{1}{4}) + 20 (- \frac{2}{5})}$

Step 3.3.2

Factor $2$ out of $20$ .

$\frac{15 + 2 (10) \frac{- 5}{2}}{20 (\frac{1}{4}) + 20 (- \frac{2}{5})}$

Step 3.3.3

Cancel the common factor.

$\frac{15 + 2 \cdot 10 \frac{- 5}{2}}{20 (\frac{1}{4}) + 20 (- \frac{2}{5})}$

Step 3.3.4

Rewrite the expression.

$\frac{15 + 10 \cdot - 5}{20 (\frac{1}{4}) + 20 (- \frac{2}{5})}$

Step 3.4

Multiply $10$ by $- 5$ .

$\frac{15 - 50}{20 (\frac{1}{4}) + 20 (- \frac{2}{5})}$

Step 3.5

Cancel the common factor of $4$ .

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Step 3.5.1

Factor $4$ out of $20$ .

$\frac{15 - 50}{4 (5) \frac{1}{4} + 20 (- \frac{2}{5})}$

Step 3.5.2

Cancel the common factor.

$\frac{15 - 50}{4 \cdot 5 \frac{1}{4} + 20 (- \frac{2}{5})}$

Step 3.5.3

Rewrite the expression.

$\frac{15 - 50}{5 + 20 (- \frac{2}{5})}$

Step 3.6

Cancel the common factor of $5$ .

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Step 3.6.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{15 - 50}{5 + 20 (\frac{- 2}{5})}$

Step 3.6.2

Factor $5$ out of $20$ .

$\frac{15 - 50}{5 + 5 (4) \frac{- 2}{5}}$

Step 3.6.3

Cancel the common factor.

$\frac{15 - 50}{5 + 5 \cdot 4 \frac{- 2}{5}}$

Step 3.6.4

Rewrite the expression.

$\frac{15 - 50}{5 + 4 \cdot - 2}$

Step 3.7

Multiply $4$ by $- 2$ .

$\frac{15 - 50}{5 - 8}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $50$ from $15$ .

$\frac{- 35}{5 - 8}$

Step 4.2

Subtract $8$ from $5$ .

$\frac{- 35}{- 3}$

Step 4.3

Dividing two negative values results in a positive value.

$\frac{35}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{3}$

Decimal Form:

$11.\overline{6}$

Mixed Number Form:

$11 \frac{2}{3}$