Solve 9/4*5-11/5*6+13/6*7-15/7*8+frac{17}{8*9}

$$\frac { 9 } { 4 \times 5 } - \frac { 11 } { 5 \times 6 } + \frac { 13 } { 6 \times 7 } - \frac { 15 } { 7 \times 8 } + \frac { 17 } { 8 \times 9 }$$

Evaluate

$$\frac{13}{36}\approx 0.361111111$$

Solution Steps

Multiply 4 and 5 to get 20.

$$\frac{9}{20}-\frac{11}{5\times 6}+\frac{13}{6\times 7}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Multiply 5 and 6 to get 30.

$$\frac{9}{20}-\frac{11}{30}+\frac{13}{6\times 7}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Least common multiple of 20 and 30 is 60. Convert \frac{9}{20} and \frac{11}{30} to fractions with denominator 60.

$$\frac{27}{60}-\frac{22}{60}+\frac{13}{6\times 7}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Since \frac{27}{60} and \frac{22}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-22}{60}+\frac{13}{6\times 7}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Subtract 22 from 27 to get 5.

$$\frac{5}{60}+\frac{13}{6\times 7}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Reduce the fraction \frac{5}{60} to lowest terms by extracting and canceling out 5.

$$\frac{1}{12}+\frac{13}{6\times 7}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Multiply 6 and 7 to get 42.

$$\frac{1}{12}+\frac{13}{42}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Least common multiple of 12 and 42 is 84. Convert \frac{1}{12} and \frac{13}{42} to fractions with denominator 84.

$$\frac{7}{84}+\frac{26}{84}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Since \frac{7}{84} and \frac{26}{84} have the same denominator, add them by adding their numerators.

$$\frac{7+26}{84}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Add 7 and 26 to get 33.

$$\frac{33}{84}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Reduce the fraction \frac{33}{84} to lowest terms by extracting and canceling out 3.

$$\frac{11}{28}-\frac{15}{7\times 8}+\frac{17}{8\times 9}$$

Multiply 7 and 8 to get 56.

$$\frac{11}{28}-\frac{15}{56}+\frac{17}{8\times 9}$$

Least common multiple of 28 and 56 is 56. Convert \frac{11}{28} and \frac{15}{56} to fractions with denominator 56.

$$\frac{22}{56}-\frac{15}{56}+\frac{17}{8\times 9}$$

Since \frac{22}{56} and \frac{15}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-15}{56}+\frac{17}{8\times 9}$$

Subtract 15 from 22 to get 7.

$$\frac{7}{56}+\frac{17}{8\times 9}$$

Reduce the fraction \frac{7}{56} to lowest terms by extracting and canceling out 7.

$$\frac{1}{8}+\frac{17}{8\times 9}$$

Multiply 8 and 9 to get 72.

$$\frac{1}{8}+\frac{17}{72}$$

Least common multiple of 8 and 72 is 72. Convert \frac{1}{8} and \frac{17}{72} to fractions with denominator 72.

$$\frac{9}{72}+\frac{17}{72}$$

Since \frac{9}{72} and \frac{17}{72} have the same denominator, add them by adding their numerators.

$$\frac{9+17}{72}$$

Add 9 and 17 to get 26.

$$\frac{26}{72}$$

Reduce the fraction \frac{26}{72} to lowest terms by extracting and canceling out 2.

$$\frac{13}{36}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 3 ^ {2}} = 0.3611111111111111$$