Solve 5/12-2/13=-5*2/2*6*13=-5/78frac{}{}

$$\frac{ 5 }{ 12 } - \frac{ 2 }{ 13 } = - \frac{ 5 \cdot 2 }{ 2 \cdot 6 \cdot 13 } = - \frac{ 5 }{ 78 } \frac { } { }$$

Verify

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{5}{12}-\frac{2}{13}=-\frac{5\times 2}{2\times 6\times 13}\text{ and }-\frac{5\times 2}{2\times 6\times 13}=-\frac{5}{78}$$

Least common multiple of 12 and 13 is 156. Convert \frac{5}{12} and \frac{2}{13} to fractions with denominator 156.

$$\frac{65}{156}-\frac{24}{156}=-\frac{5\times 2}{2\times 6\times 13}\text{ and }-\frac{5\times 2}{2\times 6\times 13}=-\frac{5}{78}$$

Since \frac{65}{156} and \frac{24}{156} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-24}{156}=-\frac{5\times 2}{2\times 6\times 13}\text{ and }-\frac{5\times 2}{2\times 6\times 13}=-\frac{5}{78}$$

Subtract 24 from 65 to get 41.

$$\frac{41}{156}=-\frac{5\times 2}{2\times 6\times 13}\text{ and }-\frac{5\times 2}{2\times 6\times 13}=-\frac{5}{78}$$

Cancel out 2 in both numerator and denominator.

$$\frac{41}{156}=-\frac{5}{6\times 13}\text{ and }-\frac{5\times 2}{2\times 6\times 13}=-\frac{5}{78}$$

Multiply 6 and 13 to get 78.

$$\frac{41}{156}=-\frac{5}{78}\text{ and }-\frac{5\times 2}{2\times 6\times 13}=-\frac{5}{78}$$

Least common multiple of 156 and 78 is 156. Convert \frac{41}{156} and -\frac{5}{78} to fractions with denominator 156.

$$\frac{41}{156}=-\frac{10}{156}\text{ and }-\frac{5\times 2}{2\times 6\times 13}=-\frac{5}{78}$$

Compare \frac{41}{156} and -\frac{10}{156}.

$$\text{false}\text{ and }-\frac{5\times 2}{2\times 6\times 13}=-\frac{5}{78}$$

Cancel out 2 in both numerator and denominator.

$$\text{false}\text{ and }-\frac{5}{6\times 13}=-\frac{5}{78}$$

Multiply 6 and 13 to get 78.

$$\text{false}\text{ and }-\frac{5}{78}=-\frac{5}{78}$$

Compare -\frac{5}{78} and -\frac{5}{78}.

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

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

$$\text{false}$$