Solve (10/17+25/13)-55/21

$$( \frac{ 10 }{ 17 } +2 \frac{ 5 }{ 13 } )-5 \frac{ 5 }{ 21 }$$

Evaluate

$$-\frac{10513}{4641}\approx -2.265244559$$

Solution Steps

Multiply 2 and 13 to get 26.

$$\frac{10}{17}+\frac{26+5}{13}-\frac{5\times 21+5}{21}$$

Add 26 and 5 to get 31.

$$\frac{10}{17}+\frac{31}{13}-\frac{5\times 21+5}{21}$$

Least common multiple of 17 and 13 is 221. Convert \frac{10}{17} and \frac{31}{13} to fractions with denominator 221.

$$\frac{130}{221}+\frac{527}{221}-\frac{5\times 21+5}{21}$$

Since \frac{130}{221} and \frac{527}{221} have the same denominator, add them by adding their numerators.

$$\frac{130+527}{221}-\frac{5\times 21+5}{21}$$

Add 130 and 527 to get 657.

$$\frac{657}{221}-\frac{5\times 21+5}{21}$$

Multiply 5 and 21 to get 105.

$$\frac{657}{221}-\frac{105+5}{21}$$

Add 105 and 5 to get 110.

$$\frac{657}{221}-\frac{110}{21}$$

Least common multiple of 221 and 21 is 4641. Convert \frac{657}{221} and \frac{110}{21} to fractions with denominator 4641.

$$\frac{13797}{4641}-\frac{24310}{4641}$$

Since \frac{13797}{4641} and \frac{24310}{4641} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13797-24310}{4641}$$

Subtract 24310 from 13797 to get -10513.

$$-\frac{10513}{4641}$$

Factor

$$-\frac{10513}{4641} = -2\frac{1231}{4641} = -2.2652445593622064$$