Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $60$ .

$\frac{2 (30) \frac{1}{2} + 60 (- \frac{4}{5})}{60 (\frac{3}{4}) + 60 (\frac{2}{3})}$

Step 3.1.2

Cancel the common factor.

$\frac{2 \cdot 30 \frac{1}{2} + 60 (- \frac{4}{5})}{60 (\frac{3}{4}) + 60 (\frac{2}{3})}$

Step 3.1.3

Rewrite the expression.

$\frac{30 + 60 (- \frac{4}{5})}{60 (\frac{3}{4}) + 60 (\frac{2}{3})}$

Step 3.2

Cancel the common factor of $5$ .

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Step 3.2.1

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

$\frac{30 + 60 (\frac{- 4}{5})}{60 (\frac{3}{4}) + 60 (\frac{2}{3})}$

Step 3.2.2

Factor $5$ out of $60$ .

$\frac{30 + 5 (12) \frac{- 4}{5}}{60 (\frac{3}{4}) + 60 (\frac{2}{3})}$

Step 3.2.3

Cancel the common factor.

$\frac{30 + 5 \cdot 12 \frac{- 4}{5}}{60 (\frac{3}{4}) + 60 (\frac{2}{3})}$

Step 3.2.4

Rewrite the expression.

$\frac{30 + 12 \cdot - 4}{60 (\frac{3}{4}) + 60 (\frac{2}{3})}$

Step 3.3

Multiply $12$ by $- 4$ .

$\frac{30 - 48}{60 (\frac{3}{4}) + 60 (\frac{2}{3})}$

Step 3.4

Cancel the common factor of $4$ .

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Step 3.4.1

Factor $4$ out of $60$ .

$\frac{30 - 48}{4 (15) \frac{3}{4} + 60 (\frac{2}{3})}$

Step 3.4.2

Cancel the common factor.

$\frac{30 - 48}{4 \cdot 15 \frac{3}{4} + 60 (\frac{2}{3})}$

Step 3.4.3

Rewrite the expression.

$\frac{30 - 48}{15 \cdot 3 + 60 (\frac{2}{3})}$

Step 3.5

Multiply $15$ by $3$ .

$\frac{30 - 48}{45 + 60 (\frac{2}{3})}$

Step 3.6

Cancel the common factor of $3$ .

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Step 3.6.1

Factor $3$ out of $60$ .

$\frac{30 - 48}{45 + 3 (20) \frac{2}{3}}$

Step 3.6.2

Cancel the common factor.

$\frac{30 - 48}{45 + 3 \cdot 20 \frac{2}{3}}$

Step 3.6.3

Rewrite the expression.

$\frac{30 - 48}{45 + 20 \cdot 2}$

Step 3.7

Multiply $20$ by $2$ .

$\frac{30 - 48}{45 + 40}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $48$ from $30$ .

$\frac{- 18}{45 + 40}$

Step 4.2

Add $45$ and $40$ .

$\frac{- 18}{85}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{18}{85}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{18}{85}$

Decimal Form:

$- 0.21176470 \dots$