Solve 12/13+3/5+7/16-25/26-frac{17}{20}=

$$\frac { 12 } { 13 } + \frac { 3 } { 5 } + \frac { 7 } { 16 } - \frac { 25 } { 26 } - \frac { 17 } { 20 } =$$

Evaluate

$$\frac{31}{208}\approx 0.149038462$$

Solution Steps

Least common multiple of 13 and 5 is 65. Convert \frac{12}{13} and \frac{3}{5} to fractions with denominator 65.

$$\frac{60}{65}+\frac{39}{65}+\frac{7}{16}-\frac{25}{26}-\frac{17}{20}$$

Since \frac{60}{65} and \frac{39}{65} have the same denominator, add them by adding their numerators.

$$\frac{60+39}{65}+\frac{7}{16}-\frac{25}{26}-\frac{17}{20}$$

Add 60 and 39 to get 99.

$$\frac{99}{65}+\frac{7}{16}-\frac{25}{26}-\frac{17}{20}$$

Least common multiple of 65 and 16 is 1040. Convert \frac{99}{65} and \frac{7}{16} to fractions with denominator 1040.

$$\frac{1584}{1040}+\frac{455}{1040}-\frac{25}{26}-\frac{17}{20}$$

Since \frac{1584}{1040} and \frac{455}{1040} have the same denominator, add them by adding their numerators.

$$\frac{1584+455}{1040}-\frac{25}{26}-\frac{17}{20}$$

Add 1584 and 455 to get 2039.

$$\frac{2039}{1040}-\frac{25}{26}-\frac{17}{20}$$

Least common multiple of 1040 and 26 is 1040. Convert \frac{2039}{1040} and \frac{25}{26} to fractions with denominator 1040.

$$\frac{2039}{1040}-\frac{1000}{1040}-\frac{17}{20}$$

Since \frac{2039}{1040} and \frac{1000}{1040} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2039-1000}{1040}-\frac{17}{20}$$

Subtract 1000 from 2039 to get 1039.

$$\frac{1039}{1040}-\frac{17}{20}$$

Least common multiple of 1040 and 20 is 1040. Convert \frac{1039}{1040} and \frac{17}{20} to fractions with denominator 1040.

$$\frac{1039}{1040}-\frac{884}{1040}$$

Since \frac{1039}{1040} and \frac{884}{1040} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1039-884}{1040}$$

Subtract 884 from 1039 to get 155.

$$\frac{155}{1040}$$

Reduce the fraction \frac{155}{1040} to lowest terms by extracting and canceling out 5.

$$\frac{31}{208}$$

Factor

$$\frac{31}{2 ^ {4} \cdot 13} = 0.14903846153846154$$