Solve (-30/16+4/12)div(1/4-1/3)

$$(- \frac{ 30 }{ 16 } + \frac{ 4 }{ 12 } ) \div ( \frac{ 1 }{ 4 } - \frac{ 1 }{ 3 } )$$

Evaluate

$$\frac{37}{2}=18.5$$

Solution Steps

Reduce the fraction \frac{30}{16} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{15}{8}+\frac{4}{12}}{\frac{1}{4}-\frac{1}{3}}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{-\frac{15}{8}+\frac{1}{3}}{\frac{1}{4}-\frac{1}{3}}$$

Least common multiple of 8 and 3 is 24. Convert -\frac{15}{8} and \frac{1}{3} to fractions with denominator 24.

$$\frac{-\frac{45}{24}+\frac{8}{24}}{\frac{1}{4}-\frac{1}{3}}$$

Since -\frac{45}{24} and \frac{8}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-45+8}{24}}{\frac{1}{4}-\frac{1}{3}}$$

Add -45 and 8 to get -37.

$$\frac{-\frac{37}{24}}{\frac{1}{4}-\frac{1}{3}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{-\frac{37}{24}}{\frac{3}{12}-\frac{4}{12}}$$

Since \frac{3}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{37}{24}}{\frac{3-4}{12}}$$

Subtract 4 from 3 to get -1.

$$\frac{-\frac{37}{24}}{-\frac{1}{12}}$$

Divide -\frac{37}{24} by -\frac{1}{12} by multiplying -\frac{37}{24} by the reciprocal of -\frac{1}{12}.

$$-\frac{37}{24}\left(-12\right)$$

Express -\frac{37}{24}\left(-12\right) as a single fraction.

$$\frac{-37\left(-12\right)}{24}$$

Multiply -37 and -12 to get 444.

$$\frac{444}{24}$$

Reduce the fraction \frac{444}{24} to lowest terms by extracting and canceling out 12.

$$\frac{37}{2}$$

Factor

$$\frac{37}{2} = 18\frac{1}{2} = 18.5$$