Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Factor $3$ out of $60$ .

$\frac{3 (20) \frac{1}{3} + 60 (- \frac{6}{5})}{60 (\frac{3}{2}) + 60 (- \frac{3}{4})}$

Step 3.1.2

Cancel the common factor.

$\frac{3 \cdot 20 \frac{1}{3} + 60 (- \frac{6}{5})}{60 (\frac{3}{2}) + 60 (- \frac{3}{4})}$

Step 3.1.3

Rewrite the expression.

$\frac{20 + 60 (- \frac{6}{5})}{60 (\frac{3}{2}) + 60 (- \frac{3}{4})}$

Step 3.2

Cancel the common factor of $5$ .

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Step 3.2.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{20 + 60 (\frac{- 6}{5})}{60 (\frac{3}{2}) + 60 (- \frac{3}{4})}$

Step 3.2.2

Factor $5$ out of $60$ .

$\frac{20 + 5 (12) \frac{- 6}{5}}{60 (\frac{3}{2}) + 60 (- \frac{3}{4})}$

Step 3.2.3

Cancel the common factor.

$\frac{20 + 5 \cdot 12 \frac{- 6}{5}}{60 (\frac{3}{2}) + 60 (- \frac{3}{4})}$

Step 3.2.4

Rewrite the expression.

$\frac{20 + 12 \cdot - 6}{60 (\frac{3}{2}) + 60 (- \frac{3}{4})}$

Step 3.3

Multiply $12$ by $- 6$ .

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

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Factor $2$ out of $60$ .

$\frac{20 - 72}{2 (30) \frac{3}{2} + 60 (- \frac{3}{4})}$

Step 3.4.2

Cancel the common factor.

$\frac{20 - 72}{2 \cdot 30 \frac{3}{2} + 60 (- \frac{3}{4})}$

Step 3.4.3

Rewrite the expression.

$\frac{20 - 72}{30 \cdot 3 + 60 (- \frac{3}{4})}$

Step 3.5

Multiply $30$ by $3$ .

$\frac{20 - 72}{90 + 60 (- \frac{3}{4})}$

Step 3.6

Cancel the common factor of $4$ .

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Step 3.6.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{20 - 72}{90 + 60 (\frac{- 3}{4})}$

Step 3.6.2

Factor $4$ out of $60$ .

$\frac{20 - 72}{90 + 4 (15) \frac{- 3}{4}}$

Step 3.6.3

Cancel the common factor.

$\frac{20 - 72}{90 + 4 \cdot 15 \frac{- 3}{4}}$

Step 3.6.4

Rewrite the expression.

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

Step 3.7

Multiply $15$ by $- 3$ .

$\frac{20 - 72}{90 - 45}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $72$ from $20$ .

$\frac{- 52}{90 - 45}$

Step 4.2

Subtract $45$ from $90$ .

$\frac{- 52}{45}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{52}{45}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{52}{45}$

Decimal Form:

$- 1.1\overline{5}$

Mixed Number Form:

$- 1 \frac{7}{45}$