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

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

Evaluate

$$\frac{3}{10}=0.3$$

Solution Steps

Add 5 and 6 to get 11.

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

Multiply 5 and 6 to get 30.

$$\frac{11}{30}-\frac{6+7}{6\times 7}+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Add 6 and 7 to get 13.

$$\frac{11}{30}-\frac{13}{6\times 7}+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Multiply 6 and 7 to get 42.

$$\frac{11}{30}-\frac{13}{42}+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Least common multiple of 30 and 42 is 210. Convert \frac{11}{30} and \frac{13}{42} to fractions with denominator 210.

$$\frac{77}{210}-\frac{65}{210}+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Since \frac{77}{210} and \frac{65}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{77-65}{210}+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Subtract 65 from 77 to get 12.

$$\frac{12}{210}+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Reduce the fraction \frac{12}{210} to lowest terms by extracting and canceling out 6.

$$\frac{2}{35}+\frac{7+8}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Add 7 and 8 to get 15.

$$\frac{2}{35}+\frac{15}{7\times 8}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Multiply 7 and 8 to get 56.

$$\frac{2}{35}+\frac{15}{56}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Least common multiple of 35 and 56 is 280. Convert \frac{2}{35} and \frac{15}{56} to fractions with denominator 280.

$$\frac{16}{280}+\frac{75}{280}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Since \frac{16}{280} and \frac{75}{280} have the same denominator, add them by adding their numerators.

$$\frac{16+75}{280}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Add 16 and 75 to get 91.

$$\frac{91}{280}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Reduce the fraction \frac{91}{280} to lowest terms by extracting and canceling out 7.

$$\frac{13}{40}-\frac{8+9}{8\times 9}+\frac{9+10}{9\times 10}$$

Add 8 and 9 to get 17.

$$\frac{13}{40}-\frac{17}{8\times 9}+\frac{9+10}{9\times 10}$$

Multiply 8 and 9 to get 72.

$$\frac{13}{40}-\frac{17}{72}+\frac{9+10}{9\times 10}$$

Least common multiple of 40 and 72 is 360. Convert \frac{13}{40} and \frac{17}{72} to fractions with denominator 360.

$$\frac{117}{360}-\frac{85}{360}+\frac{9+10}{9\times 10}$$

Since \frac{117}{360} and \frac{85}{360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{117-85}{360}+\frac{9+10}{9\times 10}$$

Subtract 85 from 117 to get 32.

$$\frac{32}{360}+\frac{9+10}{9\times 10}$$

Reduce the fraction \frac{32}{360} to lowest terms by extracting and canceling out 8.

$$\frac{4}{45}+\frac{9+10}{9\times 10}$$

Add 9 and 10 to get 19.

$$\frac{4}{45}+\frac{19}{9\times 10}$$

Multiply 9 and 10 to get 90.

$$\frac{4}{45}+\frac{19}{90}$$

Least common multiple of 45 and 90 is 90. Convert \frac{4}{45} and \frac{19}{90} to fractions with denominator 90.

$$\frac{8}{90}+\frac{19}{90}$$

Since \frac{8}{90} and \frac{19}{90} have the same denominator, add them by adding their numerators.

$$\frac{8+19}{90}$$

Add 8 and 19 to get 27.

$$\frac{27}{90}$$

Reduce the fraction \frac{27}{90} to lowest terms by extracting and canceling out 9.

$$\frac{3}{10}$$

Factor

$$\frac{3}{2 \cdot 5} = 0.3$$