Solve 1/4-1/-5=4-(-1/5)=41/5

$$\frac { 1 } { 4 } - \frac { 1 } { - 5 } = 4 - ( - \frac { 1 } { 5 } ) = 4 \frac { 1 } { 5 }$$

Verify

Solution Steps

Fraction \frac{1}{-5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$\frac{1}{4}-\left(-\frac{1}{5}\right)=4-\left(-\frac{1}{5}\right)\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

The opposite of -\frac{1}{5} is \frac{1}{5}.

$$\frac{1}{4}+\frac{1}{5}=4-\left(-\frac{1}{5}\right)\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{5}{20}+\frac{4}{20}=4-\left(-\frac{1}{5}\right)\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{5+4}{20}=4-\left(-\frac{1}{5}\right)\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

Add 5 and 4 to get 9.

$$\frac{9}{20}=4-\left(-\frac{1}{5}\right)\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

The opposite of -\frac{1}{5} is \frac{1}{5}.

$$\frac{9}{20}=4+\frac{1}{5}\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

Convert 4 to fraction \frac{20}{5}.

$$\frac{9}{20}=\frac{20}{5}+\frac{1}{5}\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

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

$$\frac{9}{20}=\frac{20+1}{5}\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

Add 20 and 1 to get 21.

$$\frac{9}{20}=\frac{21}{5}\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

Least common multiple of 20 and 5 is 20. Convert \frac{9}{20} and \frac{21}{5} to fractions with denominator 20.

$$\frac{9}{20}=\frac{84}{20}\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

Compare \frac{9}{20} and \frac{84}{20}.

$$\text{false}\text{ and }4-\left(-\frac{1}{5}\right)=\frac{4\times 5+1}{5}$$

The opposite of -\frac{1}{5} is \frac{1}{5}.

$$\text{false}\text{ and }4+\frac{1}{5}=\frac{4\times 5+1}{5}$$

Convert 4 to fraction \frac{20}{5}.

$$\text{false}\text{ and }\frac{20}{5}+\frac{1}{5}=\frac{4\times 5+1}{5}$$

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

$$\text{false}\text{ and }\frac{20+1}{5}=\frac{4\times 5+1}{5}$$

Add 20 and 1 to get 21.

$$\text{false}\text{ and }\frac{21}{5}=\frac{4\times 5+1}{5}$$

Multiply 4 and 5 to get 20.

$$\text{false}\text{ and }\frac{21}{5}=\frac{20+1}{5}$$

Add 20 and 1 to get 21.

$$\text{false}\text{ and }\frac{21}{5}=\frac{21}{5}$$

Compare \frac{21}{5} and \frac{21}{5}.

$$\text{false}\text{ and }\text{true}$$

The conjunction of \text{false} and \text{true} is \text{false}.

$$\text{false}$$