Solve +1/3+1/4-1/59-1/100-frac{1}{101}-frac{1}{102})

$$+ \frac { 1 } { 3 } + \frac { 1 } { 4 } - \frac { 1 } { 59 } - \frac { 1 } { 100 } - \frac { 1 } { 101 } - \frac { 1 } { 102 } )$$

Evaluate

$$\frac{2718361}{5065150}\approx 0.536679269$$

Solution Steps

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

$$\frac{4}{12}+\frac{3}{12}-\frac{1}{59}-\frac{1}{100}-\frac{1}{101}-\frac{1}{102}$$

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

$$\frac{4+3}{12}-\frac{1}{59}-\frac{1}{100}-\frac{1}{101}-\frac{1}{102}$$

Add 4 and 3 to get 7.

$$\frac{7}{12}-\frac{1}{59}-\frac{1}{100}-\frac{1}{101}-\frac{1}{102}$$

Least common multiple of 12 and 59 is 708. Convert \frac{7}{12} and \frac{1}{59} to fractions with denominator 708.

$$\frac{413}{708}-\frac{12}{708}-\frac{1}{100}-\frac{1}{101}-\frac{1}{102}$$

Since \frac{413}{708} and \frac{12}{708} have the same denominator, subtract them by subtracting their numerators.

$$\frac{413-12}{708}-\frac{1}{100}-\frac{1}{101}-\frac{1}{102}$$

Subtract 12 from 413 to get 401.

$$\frac{401}{708}-\frac{1}{100}-\frac{1}{101}-\frac{1}{102}$$

Least common multiple of 708 and 100 is 17700. Convert \frac{401}{708} and \frac{1}{100} to fractions with denominator 17700.

$$\frac{10025}{17700}-\frac{177}{17700}-\frac{1}{101}-\frac{1}{102}$$

Since \frac{10025}{17700} and \frac{177}{17700} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10025-177}{17700}-\frac{1}{101}-\frac{1}{102}$$

Subtract 177 from 10025 to get 9848.

$$\frac{9848}{17700}-\frac{1}{101}-\frac{1}{102}$$

Reduce the fraction \frac{9848}{17700} to lowest terms by extracting and canceling out 4.

$$\frac{2462}{4425}-\frac{1}{101}-\frac{1}{102}$$

Least common multiple of 4425 and 101 is 446925. Convert \frac{2462}{4425} and \frac{1}{101} to fractions with denominator 446925.

$$\frac{248662}{446925}-\frac{4425}{446925}-\frac{1}{102}$$

Since \frac{248662}{446925} and \frac{4425}{446925} have the same denominator, subtract them by subtracting their numerators.

$$\frac{248662-4425}{446925}-\frac{1}{102}$$

Subtract 4425 from 248662 to get 244237.

$$\frac{244237}{446925}-\frac{1}{102}$$

Least common multiple of 446925 and 102 is 15195450. Convert \frac{244237}{446925} and \frac{1}{102} to fractions with denominator 15195450.

$$\frac{8304058}{15195450}-\frac{148975}{15195450}$$

Since \frac{8304058}{15195450} and \frac{148975}{15195450} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8304058-148975}{15195450}$$

Subtract 148975 from 8304058 to get 8155083.

$$\frac{8155083}{15195450}$$

Reduce the fraction \frac{8155083}{15195450} to lowest terms by extracting and canceling out 3.

$$\frac{2718361}{5065150}$$

Factor

$$\frac{349 \cdot 7789}{2 \cdot 5 ^ {2} \cdot 17 \cdot 59 \cdot 101} = 0.5366792691233231$$