Solve 1/99-1/99*98-1/98*97

$$\frac { 1 } { 99 } - \frac { 1 } { 99 \times 98 } - \frac { 1 } { 98 \times 97 }$$

Evaluate

$$\frac{95}{9603}\approx 0.009892742$$

Solution Steps

Multiply 99 and 98 to get 9702.

$$\frac{1}{99}-\frac{1}{9702}-\frac{1}{98\times 97}$$

Least common multiple of 99 and 9702 is 9702. Convert \frac{1}{99} and \frac{1}{9702} to fractions with denominator 9702.

$$\frac{98}{9702}-\frac{1}{9702}-\frac{1}{98\times 97}$$

Since \frac{98}{9702} and \frac{1}{9702} have the same denominator, subtract them by subtracting their numerators.

$$\frac{98-1}{9702}-\frac{1}{98\times 97}$$

Subtract 1 from 98 to get 97.

$$\frac{97}{9702}-\frac{1}{98\times 97}$$

Multiply 98 and 97 to get 9506.

$$\frac{97}{9702}-\frac{1}{9506}$$

Least common multiple of 9702 and 9506 is 941094. Convert \frac{97}{9702} and \frac{1}{9506} to fractions with denominator 941094.

$$\frac{9409}{941094}-\frac{99}{941094}$$

Since \frac{9409}{941094} and \frac{99}{941094} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9409-99}{941094}$$

Subtract 99 from 9409 to get 9310.

$$\frac{9310}{941094}$$

Reduce the fraction \frac{9310}{941094} to lowest terms by extracting and canceling out 98.

$$\frac{95}{9603}$$

Factor

$$\frac{5 \cdot 19}{3 ^ {2} \cdot 11 \cdot 97} = 0.009892741851504738$$