Solve 5+6/5*6-6+7/6+7+7+8/7*8-8+9/8*9+frac{9+10}{9*10}=

$$\frac { 5 + 6 } { 5 \times 6 } - \frac { 6 + 7 } { 6 + 7 } + \frac { 7 + 8 } { 7 \times 8 } - \frac { 8 + 9 } { 8 \times 9 } + \frac { 9 + 10 } { 9 \times 10 } =$$

Evaluate

$$-\frac{41}{105}\approx -0.39047619$$

Solution Steps

Divide 6+7 by 6+7 to get 1.

$$\frac{5+6}{5\times 6}-1+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Add 5 and 6 to get 11.

$$\frac{11}{5\times 6}-1+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Multiply 5 and 6 to get 30.

$$\frac{11}{30}-1+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Convert 1 to fraction \frac{30}{30}.

$$\frac{11}{30}-\frac{30}{30}+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Since \frac{11}{30} and \frac{30}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-30}{30}+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Subtract 30 from 11 to get -19.

$$-\frac{19}{30}+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Add 7 and 8 to get 15.

$$-\frac{19}{30}+\frac{15}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Multiply 7 and 8 to get 56.

$$-\frac{19}{30}+\frac{15}{56}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Least common multiple of 30 and 56 is 840. Convert -\frac{19}{30} and \frac{15}{56} to fractions with denominator 840.

$$-\frac{532}{840}+\frac{225}{840}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Since -\frac{532}{840} and \frac{225}{840} have the same denominator, add them by adding their numerators.

$$\frac{-532+225}{840}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Add -532 and 225 to get -307.

$$-\frac{307}{840}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Add 8 and 9 to get 17.

$$-\frac{307}{840}-\frac{17}{8\times 9}+\frac{9+10}{9\times 10}$$

Multiply 8 and 9 to get 72.

$$-\frac{307}{840}-\frac{17}{72}+\frac{9+10}{9\times 10}$$

Least common multiple of 840 and 72 is 2520. Convert -\frac{307}{840} and \frac{17}{72} to fractions with denominator 2520.

$$-\frac{921}{2520}-\frac{595}{2520}+\frac{9+10}{9\times 10}$$

Since -\frac{921}{2520} and \frac{595}{2520} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-921-595}{2520}+\frac{9+10}{9\times 10}$$

Subtract 595 from -921 to get -1516.

$$\frac{-1516}{2520}+\frac{9+10}{9\times 10}$$

Reduce the fraction \frac{-1516}{2520} to lowest terms by extracting and canceling out 4.

$$-\frac{379}{630}+\frac{9+10}{9\times 10}$$

Add 9 and 10 to get 19.

$$-\frac{379}{630}+\frac{19}{9\times 10}$$

Multiply 9 and 10 to get 90.

$$-\frac{379}{630}+\frac{19}{90}$$

Least common multiple of 630 and 90 is 630. Convert -\frac{379}{630} and \frac{19}{90} to fractions with denominator 630.

$$-\frac{379}{630}+\frac{133}{630}$$

Since -\frac{379}{630} and \frac{133}{630} have the same denominator, add them by adding their numerators.

$$\frac{-379+133}{630}$$

Add -379 and 133 to get -246.

$$\frac{-246}{630}$$

Reduce the fraction \frac{-246}{630} to lowest terms by extracting and canceling out 6.

$$-\frac{41}{105}$$

Factor

$$-\frac{41}{105} = -0.3904761904761905$$