Solve 4/1*2*3+5/2*3*4+6/3*4*5+21/18*9*20

$$\frac { 4 } { 1 \times 2 \times 3 } + \frac { 5 } { 2 \times 3 \times 4 } + \frac { 6 } { 3 \times 4 \times 5 } + \frac { 21 } { 18 \times 9 \times 20 }$$

Evaluate

$$\frac{53}{54}\approx 0.981481481$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{4}{2\times 3}+\frac{5}{2\times 3\times 4}+\frac{6}{3\times 4\times 5}+\frac{21}{18\times 9\times 20}$$

Multiply 2 and 3 to get 6.

$$\frac{4}{6}+\frac{5}{2\times 3\times 4}+\frac{6}{3\times 4\times 5}+\frac{21}{18\times 9\times 20}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}+\frac{5}{2\times 3\times 4}+\frac{6}{3\times 4\times 5}+\frac{21}{18\times 9\times 20}$$

Multiply 2 and 3 to get 6.

$$\frac{2}{3}+\frac{5}{6\times 4}+\frac{6}{3\times 4\times 5}+\frac{21}{18\times 9\times 20}$$

Multiply 6 and 4 to get 24.

$$\frac{2}{3}+\frac{5}{24}+\frac{6}{3\times 4\times 5}+\frac{21}{18\times 9\times 20}$$

Least common multiple of 3 and 24 is 24. Convert \frac{2}{3} and \frac{5}{24} to fractions with denominator 24.

$$\frac{16}{24}+\frac{5}{24}+\frac{6}{3\times 4\times 5}+\frac{21}{18\times 9\times 20}$$

Since \frac{16}{24} and \frac{5}{24} have the same denominator, add them by adding their numerators.

$$\frac{16+5}{24}+\frac{6}{3\times 4\times 5}+\frac{21}{18\times 9\times 20}$$

Add 16 and 5 to get 21.

$$\frac{21}{24}+\frac{6}{3\times 4\times 5}+\frac{21}{18\times 9\times 20}$$

Reduce the fraction \frac{21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{7}{8}+\frac{6}{3\times 4\times 5}+\frac{21}{18\times 9\times 20}$$

Multiply 3 and 4 to get 12.

$$\frac{7}{8}+\frac{6}{12\times 5}+\frac{21}{18\times 9\times 20}$$

Multiply 12 and 5 to get 60.

$$\frac{7}{8}+\frac{6}{60}+\frac{21}{18\times 9\times 20}$$

Reduce the fraction \frac{6}{60} to lowest terms by extracting and canceling out 6.

$$\frac{7}{8}+\frac{1}{10}+\frac{21}{18\times 9\times 20}$$

Least common multiple of 8 and 10 is 40. Convert \frac{7}{8} and \frac{1}{10} to fractions with denominator 40.

$$\frac{35}{40}+\frac{4}{40}+\frac{21}{18\times 9\times 20}$$

Since \frac{35}{40} and \frac{4}{40} have the same denominator, add them by adding their numerators.

$$\frac{35+4}{40}+\frac{21}{18\times 9\times 20}$$

Add 35 and 4 to get 39.

$$\frac{39}{40}+\frac{21}{18\times 9\times 20}$$

Multiply 18 and 9 to get 162.

$$\frac{39}{40}+\frac{21}{162\times 20}$$

Multiply 162 and 20 to get 3240.

$$\frac{39}{40}+\frac{21}{3240}$$

Reduce the fraction \frac{21}{3240} to lowest terms by extracting and canceling out 3.

$$\frac{39}{40}+\frac{7}{1080}$$

Least common multiple of 40 and 1080 is 1080. Convert \frac{39}{40} and \frac{7}{1080} to fractions with denominator 1080.

$$\frac{1053}{1080}+\frac{7}{1080}$$

Since \frac{1053}{1080} and \frac{7}{1080} have the same denominator, add them by adding their numerators.

$$\frac{1053+7}{1080}$$

Add 1053 and 7 to get 1060.

$$\frac{1060}{1080}$$

Reduce the fraction \frac{1060}{1080} to lowest terms by extracting and canceling out 20.

$$\frac{53}{54}$$

Factor

$$\frac{53}{2 \cdot 3 ^ {3}} = 0.9814814814814815$$