Solve 1div(-4/5--3/4+1/4)

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

Evaluate

$$5$$

Solution Steps

The opposite of -\frac{3}{4} is \frac{3}{4}.

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

Least common multiple of 5 and 4 is 20. Convert -\frac{4}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{1}{-\frac{16}{20}+\frac{15}{20}+\frac{1}{4}}$$

Since -\frac{16}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{-16+15}{20}+\frac{1}{4}}$$

Add -16 and 15 to get -1.

$$\frac{1}{-\frac{1}{20}+\frac{1}{4}}$$

Least common multiple of 20 and 4 is 20. Convert -\frac{1}{20} and \frac{1}{4} to fractions with denominator 20.

$$\frac{1}{-\frac{1}{20}+\frac{5}{20}}$$

Since -\frac{1}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{-1+5}{20}}$$

Add -1 and 5 to get 4.

$$\frac{1}{\frac{4}{20}}$$

Reduce the fraction \frac{4}{20} to lowest terms by extracting and canceling out 4.

$$\frac{1}{\frac{1}{5}}$$

Divide 1 by \frac{1}{5} by multiplying 1 by the reciprocal of \frac{1}{5}.

$$1\times 5$$

Multiply 1 and 5 to get 5.

$$5$$

Factor

$$5$$