Solve 3/1*2*4*5+4/2*3*5*6+5/3*4*6*7+6/4*5*7*8=

$$\frac { 3 } { 1 \times 2 \times 4 \times 5 } + \frac { 4 } { 2 \times 3 \times 5 \times 6 } + \frac { 5 } { 3 \times 4 \times 6 \times 7 } + \frac { 6 } { 4 \times 5 \times 7 \times 8 } =$$

Evaluate

$$\frac{9}{80}=0.1125$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{3}{2\times 4\times 5}+\frac{4}{2\times 3\times 5\times 6}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Multiply 2 and 4 to get 8.

$$\frac{3}{8\times 5}+\frac{4}{2\times 3\times 5\times 6}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Multiply 8 and 5 to get 40.

$$\frac{3}{40}+\frac{4}{2\times 3\times 5\times 6}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Multiply 2 and 3 to get 6.

$$\frac{3}{40}+\frac{4}{6\times 5\times 6}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Multiply 6 and 5 to get 30.

$$\frac{3}{40}+\frac{4}{30\times 6}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Multiply 30 and 6 to get 180.

$$\frac{3}{40}+\frac{4}{180}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Reduce the fraction \frac{4}{180} to lowest terms by extracting and canceling out 4.

$$\frac{3}{40}+\frac{1}{45}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Least common multiple of 40 and 45 is 360. Convert \frac{3}{40} and \frac{1}{45} to fractions with denominator 360.

$$\frac{27}{360}+\frac{8}{360}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Since \frac{27}{360} and \frac{8}{360} have the same denominator, add them by adding their numerators.

$$\frac{27+8}{360}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Add 27 and 8 to get 35.

$$\frac{35}{360}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Reduce the fraction \frac{35}{360} to lowest terms by extracting and canceling out 5.

$$\frac{7}{72}+\frac{5}{3\times 4\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Multiply 3 and 4 to get 12.

$$\frac{7}{72}+\frac{5}{12\times 6\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Multiply 12 and 6 to get 72.

$$\frac{7}{72}+\frac{5}{72\times 7}+\frac{6}{4\times 5\times 7\times 8}$$

Multiply 72 and 7 to get 504.

$$\frac{7}{72}+\frac{5}{504}+\frac{6}{4\times 5\times 7\times 8}$$

Least common multiple of 72 and 504 is 504. Convert \frac{7}{72} and \frac{5}{504} to fractions with denominator 504.

$$\frac{49}{504}+\frac{5}{504}+\frac{6}{4\times 5\times 7\times 8}$$

Since \frac{49}{504} and \frac{5}{504} have the same denominator, add them by adding their numerators.

$$\frac{49+5}{504}+\frac{6}{4\times 5\times 7\times 8}$$

Add 49 and 5 to get 54.

$$\frac{54}{504}+\frac{6}{4\times 5\times 7\times 8}$$

Reduce the fraction \frac{54}{504} to lowest terms by extracting and canceling out 18.

$$\frac{3}{28}+\frac{6}{4\times 5\times 7\times 8}$$

Multiply 4 and 5 to get 20.

$$\frac{3}{28}+\frac{6}{20\times 7\times 8}$$

Multiply 20 and 7 to get 140.

$$\frac{3}{28}+\frac{6}{140\times 8}$$

Multiply 140 and 8 to get 1120.

$$\frac{3}{28}+\frac{6}{1120}$$

Reduce the fraction \frac{6}{1120} to lowest terms by extracting and canceling out 2.

$$\frac{3}{28}+\frac{3}{560}$$

Least common multiple of 28 and 560 is 560. Convert \frac{3}{28} and \frac{3}{560} to fractions with denominator 560.

$$\frac{60}{560}+\frac{3}{560}$$

Since \frac{60}{560} and \frac{3}{560} have the same denominator, add them by adding their numerators.

$$\frac{60+3}{560}$$

Add 60 and 3 to get 63.

$$\frac{63}{560}$$

Reduce the fraction \frac{63}{560} to lowest terms by extracting and canceling out 7.

$$\frac{9}{80}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {4} \cdot 5} = 0.1125$$