Solve (73/5+41/12+11/24)+(6+1/18)

$$( 7 \frac { 3 } { 5 } + 4 \frac { 1 } { 12 } + 1 \frac { 1 } { 24 } ) + ( 6 + \frac { 1 } { 18 } )$$

Evaluate

$$\frac{6761}{360}\approx 18.780555556$$

Solution Steps

Multiply 7 and 5 to get 35.

$$\frac{35+3}{5}+\frac{4\times 12+1}{12}+\frac{1\times 24+1}{24}+6+\frac{1}{18}$$

Add 35 and 3 to get 38.

$$\frac{38}{5}+\frac{4\times 12+1}{12}+\frac{1\times 24+1}{24}+6+\frac{1}{18}$$

Multiply 4 and 12 to get 48.

$$\frac{38}{5}+\frac{48+1}{12}+\frac{1\times 24+1}{24}+6+\frac{1}{18}$$

Add 48 and 1 to get 49.

$$\frac{38}{5}+\frac{49}{12}+\frac{1\times 24+1}{24}+6+\frac{1}{18}$$

Least common multiple of 5 and 12 is 60. Convert \frac{38}{5} and \frac{49}{12} to fractions with denominator 60.

$$\frac{456}{60}+\frac{245}{60}+\frac{1\times 24+1}{24}+6+\frac{1}{18}$$

Since \frac{456}{60} and \frac{245}{60} have the same denominator, add them by adding their numerators.

$$\frac{456+245}{60}+\frac{1\times 24+1}{24}+6+\frac{1}{18}$$

Add 456 and 245 to get 701.

$$\frac{701}{60}+\frac{1\times 24+1}{24}+6+\frac{1}{18}$$

Multiply 1 and 24 to get 24.

$$\frac{701}{60}+\frac{24+1}{24}+6+\frac{1}{18}$$

Add 24 and 1 to get 25.

$$\frac{701}{60}+\frac{25}{24}+6+\frac{1}{18}$$

Least common multiple of 60 and 24 is 120. Convert \frac{701}{60} and \frac{25}{24} to fractions with denominator 120.

$$\frac{1402}{120}+\frac{125}{120}+6+\frac{1}{18}$$

Since \frac{1402}{120} and \frac{125}{120} have the same denominator, add them by adding their numerators.

$$\frac{1402+125}{120}+6+\frac{1}{18}$$

Add 1402 and 125 to get 1527.

$$\frac{1527}{120}+6+\frac{1}{18}$$

Reduce the fraction \frac{1527}{120} to lowest terms by extracting and canceling out 3.

$$\frac{509}{40}+6+\frac{1}{18}$$

Convert 6 to fraction \frac{240}{40}.

$$\frac{509}{40}+\frac{240}{40}+\frac{1}{18}$$

Since \frac{509}{40} and \frac{240}{40} have the same denominator, add them by adding their numerators.

$$\frac{509+240}{40}+\frac{1}{18}$$

Add 509 and 240 to get 749.

$$\frac{749}{40}+\frac{1}{18}$$

Least common multiple of 40 and 18 is 360. Convert \frac{749}{40} and \frac{1}{18} to fractions with denominator 360.

$$\frac{6741}{360}+\frac{20}{360}$$

Since \frac{6741}{360} and \frac{20}{360} have the same denominator, add them by adding their numerators.

$$\frac{6741+20}{360}$$

Add 6741 and 20 to get 6761.

$$\frac{6761}{360}$$

Factor

$$\frac{6761}{2 ^ {3} \cdot 3 ^ {2} \cdot 5} = 18\frac{281}{360} = 18.780555555555555$$