Solve 1/2*3+1/2*3*4+1/3*4*5+1/4*5*6

$$\frac { 1 } { 2 \cdot 3 } + \frac { 1 } { 2 \cdot 3 \cdot 4 } + \frac { 1 } { 3 \cdot 4 \cdot 5 } + \frac { 1 } { 4 \cdot 5 \cdot 6 }$$

Evaluate

$$\frac{7}{30}\approx 0.233333333$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{1}{6}+\frac{1}{2\times 3\times 4}+\frac{1}{3\times 4\times 5}+\frac{1}{4\times 5\times 6}$$

Multiply 2 and 3 to get 6.

$$\frac{1}{6}+\frac{1}{6\times 4}+\frac{1}{3\times 4\times 5}+\frac{1}{4\times 5\times 6}$$

Multiply 6 and 4 to get 24.

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

Least common multiple of 6 and 24 is 24. Convert \frac{1}{6} and \frac{1}{24} to fractions with denominator 24.

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

Since \frac{4}{24} and \frac{1}{24} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

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

Multiply 3 and 4 to get 12.

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

Multiply 12 and 5 to get 60.

$$\frac{5}{24}+\frac{1}{60}+\frac{1}{4\times 5\times 6}$$

Least common multiple of 24 and 60 is 120. Convert \frac{5}{24} and \frac{1}{60} to fractions with denominator 120.

$$\frac{25}{120}+\frac{2}{120}+\frac{1}{4\times 5\times 6}$$

Since \frac{25}{120} and \frac{2}{120} have the same denominator, add them by adding their numerators.

$$\frac{25+2}{120}+\frac{1}{4\times 5\times 6}$$

Add 25 and 2 to get 27.

$$\frac{27}{120}+\frac{1}{4\times 5\times 6}$$

Reduce the fraction \frac{27}{120} to lowest terms by extracting and canceling out 3.

$$\frac{9}{40}+\frac{1}{4\times 5\times 6}$$

Multiply 4 and 5 to get 20.

$$\frac{9}{40}+\frac{1}{20\times 6}$$

Multiply 20 and 6 to get 120.

$$\frac{9}{40}+\frac{1}{120}$$

Least common multiple of 40 and 120 is 120. Convert \frac{9}{40} and \frac{1}{120} to fractions with denominator 120.

$$\frac{27}{120}+\frac{1}{120}$$

Since \frac{27}{120} and \frac{1}{120} have the same denominator, add them by adding their numerators.

$$\frac{27+1}{120}$$

Add 27 and 1 to get 28.

$$\frac{28}{120}$$

Reduce the fraction \frac{28}{120} to lowest terms by extracting and canceling out 4.

$$\frac{7}{30}$$

Factor

$$\frac{7}{2 \cdot 3 \cdot 5} = 0.23333333333333334$$