Solve 1-5/6+7/2+9/20+11/50+frac{13}{42}

$$1 - \frac { 5 } { 6 } + \frac { 7 } { 2 } + \frac { 9 } { 20 } + \frac { 11 } { 50 } + \frac { 13 } { 42 }$$

Evaluate

$$\frac{9757}{2100}\approx 4.646190476$$

Solution Steps

Convert 1 to fraction \frac{6}{6}.

$$\frac{6}{6}-\frac{5}{6}+\frac{7}{2}+\frac{9}{20}+\frac{11}{50}+\frac{13}{42}$$

Since \frac{6}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-5}{6}+\frac{7}{2}+\frac{9}{20}+\frac{11}{50}+\frac{13}{42}$$

Subtract 5 from 6 to get 1.

$$\frac{1}{6}+\frac{7}{2}+\frac{9}{20}+\frac{11}{50}+\frac{13}{42}$$

Least common multiple of 6 and 2 is 6. Convert \frac{1}{6} and \frac{7}{2} to fractions with denominator 6.

$$\frac{1}{6}+\frac{21}{6}+\frac{9}{20}+\frac{11}{50}+\frac{13}{42}$$

Since \frac{1}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+21}{6}+\frac{9}{20}+\frac{11}{50}+\frac{13}{42}$$

Add 1 and 21 to get 22.

$$\frac{22}{6}+\frac{9}{20}+\frac{11}{50}+\frac{13}{42}$$

Reduce the fraction \frac{22}{6} to lowest terms by extracting and canceling out 2.

$$\frac{11}{3}+\frac{9}{20}+\frac{11}{50}+\frac{13}{42}$$

Least common multiple of 3 and 20 is 60. Convert \frac{11}{3} and \frac{9}{20} to fractions with denominator 60.

$$\frac{220}{60}+\frac{27}{60}+\frac{11}{50}+\frac{13}{42}$$

Since \frac{220}{60} and \frac{27}{60} have the same denominator, add them by adding their numerators.

$$\frac{220+27}{60}+\frac{11}{50}+\frac{13}{42}$$

Add 220 and 27 to get 247.

$$\frac{247}{60}+\frac{11}{50}+\frac{13}{42}$$

Least common multiple of 60 and 50 is 300. Convert \frac{247}{60} and \frac{11}{50} to fractions with denominator 300.

$$\frac{1235}{300}+\frac{66}{300}+\frac{13}{42}$$

Since \frac{1235}{300} and \frac{66}{300} have the same denominator, add them by adding their numerators.

$$\frac{1235+66}{300}+\frac{13}{42}$$

Add 1235 and 66 to get 1301.

$$\frac{1301}{300}+\frac{13}{42}$$

Least common multiple of 300 and 42 is 2100. Convert \frac{1301}{300} and \frac{13}{42} to fractions with denominator 2100.

$$\frac{9107}{2100}+\frac{650}{2100}$$

Since \frac{9107}{2100} and \frac{650}{2100} have the same denominator, add them by adding their numerators.

$$\frac{9107+650}{2100}$$

Add 9107 and 650 to get 9757.

$$\frac{9757}{2100}$$

Factor

$$\frac{11 \cdot 887}{2 ^ {2} \cdot 3 \cdot 5 ^ {2} \cdot 7} = 4\frac{1357}{2100} = 4.646190476190476$$