Evaluate (4/3-1/2)/(2/5+1/3)

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

Multiply the numerator and denominator of the complex fraction by $30$ .

Multiply $\frac{\frac{4}{3} - \frac{1}{2}}{\frac{2}{5} + \frac{1}{3}}$ by $\frac{30}{30}$ .

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $3$ .

Factor $3$ out of $30$ .

$\frac{3 (10) \frac{4}{3} + 30 (- \frac{1}{2})}{30 (\frac{2}{5}) + 30 (\frac{1}{3})}$

Cancel the common factor.

$\frac{3 \cdot 10 \frac{4}{3} + 30 (- \frac{1}{2})}{30 (\frac{2}{5}) + 30 (\frac{1}{3})}$

Rewrite the expression.

$\frac{10 \cdot 4 + 30 (- \frac{1}{2})}{30 (\frac{2}{5}) + 30 (\frac{1}{3})}$

Multiply $10$ by $4$ .

$\frac{40 + 30 (- \frac{1}{2})}{30 (\frac{2}{5}) + 30 (\frac{1}{3})}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{40 + 30 (\frac{- 1}{2})}{30 (\frac{2}{5}) + 30 (\frac{1}{3})}$

Factor $2$ out of $30$ .

$\frac{40 + 2 (15) \frac{- 1}{2}}{30 (\frac{2}{5}) + 30 (\frac{1}{3})}$

Cancel the common factor.

$\frac{40 + 2 \cdot 15 \frac{- 1}{2}}{30 (\frac{2}{5}) + 30 (\frac{1}{3})}$

Rewrite the expression.

$\frac{40 + 15 \cdot - 1}{30 (\frac{2}{5}) + 30 (\frac{1}{3})}$

Multiply $15$ by $- 1$ .

$\frac{40 - 15}{30 (\frac{2}{5}) + 30 (\frac{1}{3})}$

Cancel the common factor of $5$ .

Factor $5$ out of $30$ .

$\frac{40 - 15}{5 (6) \frac{2}{5} + 30 (\frac{1}{3})}$

Cancel the common factor.

$\frac{40 - 15}{5 \cdot 6 \frac{2}{5} + 30 (\frac{1}{3})}$

Rewrite the expression.

$\frac{40 - 15}{6 \cdot 2 + 30 (\frac{1}{3})}$

Multiply $6$ by $2$ .

$\frac{40 - 15}{12 + 30 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $30$ .

$\frac{40 - 15}{12 + 3 (10) \frac{1}{3}}$

Cancel the common factor.

$\frac{40 - 15}{12 + 3 \cdot 10 \frac{1}{3}}$

Rewrite the expression.

$\frac{40 - 15}{12 + 10}$

Simplify by adding and subtracting.

Subtract $15$ from $40$ .

$\frac{25}{12 + 10}$

Add $12$ and $10$ .

$\frac{25}{22}$

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{22}$

Decimal Form:

$1.1\overline{36}$

Mixed Number Form:

$1 \frac{3}{22}$

Evaluate (4/3-1/2)/(2/5+1/3)

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