Solve 3/1*2-6/2*4+11/4*7-18/7*11+frac{27}{11*16}-frac{38}{16*22}

$$\frac { 3 } { 1 \times 2 } - \frac { 6 } { 2 \times 4 } + \frac { 11 } { 4 \times 7 } - \frac { 18 } { 7 \times 11 } + \frac { 27 } { 11 \times 16 } - \frac { 38 } { 16 \times 22 }$$

Evaluate

$$\frac{21}{22}\approx 0.954545455$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{3}{2}-\frac{6}{2\times 4}+\frac{11}{4\times 7}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Multiply 2 and 4 to get 8.

$$\frac{3}{2}-\frac{6}{8}+\frac{11}{4\times 7}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}-\frac{3}{4}+\frac{11}{4\times 7}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{6}{4}-\frac{3}{4}+\frac{11}{4\times 7}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Since \frac{6}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-3}{4}+\frac{11}{4\times 7}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Subtract 3 from 6 to get 3.

$$\frac{3}{4}+\frac{11}{4\times 7}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Multiply 4 and 7 to get 28.

$$\frac{3}{4}+\frac{11}{28}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Least common multiple of 4 and 28 is 28. Convert \frac{3}{4} and \frac{11}{28} to fractions with denominator 28.

$$\frac{21}{28}+\frac{11}{28}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Since \frac{21}{28} and \frac{11}{28} have the same denominator, add them by adding their numerators.

$$\frac{21+11}{28}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Add 21 and 11 to get 32.

$$\frac{32}{28}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Reduce the fraction \frac{32}{28} to lowest terms by extracting and canceling out 4.

$$\frac{8}{7}-\frac{18}{7\times 11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Multiply 7 and 11 to get 77.

$$\frac{8}{7}-\frac{18}{77}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Least common multiple of 7 and 77 is 77. Convert \frac{8}{7} and \frac{18}{77} to fractions with denominator 77.

$$\frac{88}{77}-\frac{18}{77}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Since \frac{88}{77} and \frac{18}{77} have the same denominator, subtract them by subtracting their numerators.

$$\frac{88-18}{77}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Subtract 18 from 88 to get 70.

$$\frac{70}{77}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Reduce the fraction \frac{70}{77} to lowest terms by extracting and canceling out 7.

$$\frac{10}{11}+\frac{27}{11\times 16}-\frac{38}{16\times 22}$$

Multiply 11 and 16 to get 176.

$$\frac{10}{11}+\frac{27}{176}-\frac{38}{16\times 22}$$

Least common multiple of 11 and 176 is 176. Convert \frac{10}{11} and \frac{27}{176} to fractions with denominator 176.

$$\frac{160}{176}+\frac{27}{176}-\frac{38}{16\times 22}$$

Since \frac{160}{176} and \frac{27}{176} have the same denominator, add them by adding their numerators.

$$\frac{160+27}{176}-\frac{38}{16\times 22}$$

Add 160 and 27 to get 187.

$$\frac{187}{176}-\frac{38}{16\times 22}$$

Reduce the fraction \frac{187}{176} to lowest terms by extracting and canceling out 11.

$$\frac{17}{16}-\frac{38}{16\times 22}$$

Multiply 16 and 22 to get 352.

$$\frac{17}{16}-\frac{38}{352}$$

Reduce the fraction \frac{38}{352} to lowest terms by extracting and canceling out 2.

$$\frac{17}{16}-\frac{19}{176}$$

Least common multiple of 16 and 176 is 176. Convert \frac{17}{16} and \frac{19}{176} to fractions with denominator 176.

$$\frac{187}{176}-\frac{19}{176}$$

Since \frac{187}{176} and \frac{19}{176} have the same denominator, subtract them by subtracting their numerators.

$$\frac{187-19}{176}$$

Subtract 19 from 187 to get 168.

$$\frac{168}{176}$$

Reduce the fraction \frac{168}{176} to lowest terms by extracting and canceling out 8.

$$\frac{21}{22}$$

Factor

$$\frac{3 \cdot 7}{2 \cdot 11} = 0.9545454545454546$$