Solve (mixed_frac{1*(4)+(1)}{4})+19/20+11/30-13/42+15/56-frac{17}{72}+frac{18}{90}

$$(\mixed_frac { 1 * ( 4) + ( 1) } { 4 } ) + \frac { 19 } { 20 } + \frac { 11 } { 30 } - \frac { 13 } { 42 } + \frac { 15 } { 56 } - \frac { 17 } { 72 } + \frac { 18 } { 90 }$$

Evaluate

$$\frac{112}{45}\approx 2.488888889$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{4+1}{4}+\frac{19}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Add 4 and 1 to get 5.

$$\frac{5}{4}+\frac{19}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Least common multiple of 4 and 20 is 20. Convert \frac{5}{4} and \frac{19}{20} to fractions with denominator 20.

$$\frac{25}{20}+\frac{19}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Since \frac{25}{20} and \frac{19}{20} have the same denominator, add them by adding their numerators.

$$\frac{25+19}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Add 25 and 19 to get 44.

$$\frac{44}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Reduce the fraction \frac{44}{20} to lowest terms by extracting and canceling out 4.

$$\frac{11}{5}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Least common multiple of 5 and 30 is 30. Convert \frac{11}{5} and \frac{11}{30} to fractions with denominator 30.

$$\frac{66}{30}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Since \frac{66}{30} and \frac{11}{30} have the same denominator, add them by adding their numerators.

$$\frac{66+11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Add 66 and 11 to get 77.

$$\frac{77}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Least common multiple of 30 and 42 is 210. Convert \frac{77}{30} and \frac{13}{42} to fractions with denominator 210.

$$\frac{539}{210}-\frac{65}{210}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Since \frac{539}{210} and \frac{65}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{539-65}{210}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Subtract 65 from 539 to get 474.

$$\frac{474}{210}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Reduce the fraction \frac{474}{210} to lowest terms by extracting and canceling out 6.

$$\frac{79}{35}+\frac{15}{56}-\frac{17}{72}+\frac{18}{90}$$

Least common multiple of 35 and 56 is 280. Convert \frac{79}{35} and \frac{15}{56} to fractions with denominator 280.

$$\frac{632}{280}+\frac{75}{280}-\frac{17}{72}+\frac{18}{90}$$

Since \frac{632}{280} and \frac{75}{280} have the same denominator, add them by adding their numerators.

$$\frac{632+75}{280}-\frac{17}{72}+\frac{18}{90}$$

Add 632 and 75 to get 707.

$$\frac{707}{280}-\frac{17}{72}+\frac{18}{90}$$

Reduce the fraction \frac{707}{280} to lowest terms by extracting and canceling out 7.

$$\frac{101}{40}-\frac{17}{72}+\frac{18}{90}$$

Least common multiple of 40 and 72 is 360. Convert \frac{101}{40} and \frac{17}{72} to fractions with denominator 360.

$$\frac{909}{360}-\frac{85}{360}+\frac{18}{90}$$

Since \frac{909}{360} and \frac{85}{360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{909-85}{360}+\frac{18}{90}$$

Subtract 85 from 909 to get 824.

$$\frac{824}{360}+\frac{18}{90}$$

Reduce the fraction \frac{824}{360} to lowest terms by extracting and canceling out 8.

$$\frac{103}{45}+\frac{18}{90}$$

Reduce the fraction \frac{18}{90} to lowest terms by extracting and canceling out 18.

$$\frac{103}{45}+\frac{1}{5}$$

Least common multiple of 45 and 5 is 45. Convert \frac{103}{45} and \frac{1}{5} to fractions with denominator 45.

$$\frac{103}{45}+\frac{9}{45}$$

Since \frac{103}{45} and \frac{9}{45} have the same denominator, add them by adding their numerators.

$$\frac{103+9}{45}$$

Add 103 and 9 to get 112.

$$\frac{112}{45}$$

Factor

$$\frac{2 ^ {4} \cdot 7}{3 ^ {2} \cdot 5} = 2\frac{22}{45} = 2.488888888888889$$