Solve 11/42+11/56+11/72+11/100

$$\frac{ 11 }{ 42 } + \frac{ 11 }{ 56 } + \frac{ 11 }{ 72 } + \frac{ 11 }{ 100 }$$

Evaluate

$$\frac{649}{900}\approx 0.721111111$$

Solution Steps

Least common multiple of 42 and 56 is 168. Convert \frac{11}{42} and \frac{11}{56} to fractions with denominator 168.

$$\frac{44}{168}+\frac{33}{168}+\frac{11}{72}+\frac{11}{100}$$

Since \frac{44}{168} and \frac{33}{168} have the same denominator, add them by adding their numerators.

$$\frac{44+33}{168}+\frac{11}{72}+\frac{11}{100}$$

Add 44 and 33 to get 77.

$$\frac{77}{168}+\frac{11}{72}+\frac{11}{100}$$

Reduce the fraction \frac{77}{168} to lowest terms by extracting and canceling out 7.

$$\frac{11}{24}+\frac{11}{72}+\frac{11}{100}$$

Least common multiple of 24 and 72 is 72. Convert \frac{11}{24} and \frac{11}{72} to fractions with denominator 72.

$$\frac{33}{72}+\frac{11}{72}+\frac{11}{100}$$

Since \frac{33}{72} and \frac{11}{72} have the same denominator, add them by adding their numerators.

$$\frac{33+11}{72}+\frac{11}{100}$$

Add 33 and 11 to get 44.

$$\frac{44}{72}+\frac{11}{100}$$

Reduce the fraction \frac{44}{72} to lowest terms by extracting and canceling out 4.

$$\frac{11}{18}+\frac{11}{100}$$

Least common multiple of 18 and 100 is 900. Convert \frac{11}{18} and \frac{11}{100} to fractions with denominator 900.

$$\frac{550}{900}+\frac{99}{900}$$

Since \frac{550}{900} and \frac{99}{900} have the same denominator, add them by adding their numerators.

$$\frac{550+99}{900}$$

Add 550 and 99 to get 649.

$$\frac{649}{900}$$

Factor

$$\frac{11 \cdot 59}{2 ^ {2} \cdot 3 ^ {2} \cdot 5 ^ {2}} = 0.7211111111111111$$