Solve 1155*(5/2*3*4+7/3*4*5+1+17/8*9*10+19/9*10*11)=

$$1155 \times ( \frac { 5 } { 2 \times 3 \times 4 } + \frac { 7 } { 3 \times 4 \times 5 } + 1 + \frac { 17 } { 8 \times 9 \times 10 } + \frac { 19 } { 9 \times 10 \times 11 } ) =$$

Evaluate

$$\frac{25277}{16}=1579.8125$$

Solution Steps

Multiply 2 and 3 to get 6.

$$1155\left(\frac{5}{6\times 4}+\frac{7}{3\times 4\times 5}+1+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Multiply 6 and 4 to get 24.

$$1155\left(\frac{5}{24}+\frac{7}{3\times 4\times 5}+1+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Multiply 3 and 4 to get 12.

$$1155\left(\frac{5}{24}+\frac{7}{12\times 5}+1+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Multiply 12 and 5 to get 60.

$$1155\left(\frac{5}{24}+\frac{7}{60}+1+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Least common multiple of 24 and 60 is 120. Convert \frac{5}{24} and \frac{7}{60} to fractions with denominator 120.

$$1155\left(\frac{25}{120}+\frac{14}{120}+1+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Since \frac{25}{120} and \frac{14}{120} have the same denominator, add them by adding their numerators.

$$1155\left(\frac{25+14}{120}+1+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Add 25 and 14 to get 39.

$$1155\left(\frac{39}{120}+1+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Reduce the fraction \frac{39}{120} to lowest terms by extracting and canceling out 3.

$$1155\left(\frac{13}{40}+1+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Convert 1 to fraction \frac{40}{40}.

$$1155\left(\frac{13}{40}+\frac{40}{40}+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Since \frac{13}{40} and \frac{40}{40} have the same denominator, add them by adding their numerators.

$$1155\left(\frac{13+40}{40}+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Add 13 and 40 to get 53.

$$1155\left(\frac{53}{40}+\frac{17}{8\times 9\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Multiply 8 and 9 to get 72.

$$1155\left(\frac{53}{40}+\frac{17}{72\times 10}+\frac{19}{9\times 10\times 11}\right)$$

Multiply 72 and 10 to get 720.

$$1155\left(\frac{53}{40}+\frac{17}{720}+\frac{19}{9\times 10\times 11}\right)$$

Least common multiple of 40 and 720 is 720. Convert \frac{53}{40} and \frac{17}{720} to fractions with denominator 720.

$$1155\left(\frac{954}{720}+\frac{17}{720}+\frac{19}{9\times 10\times 11}\right)$$

Since \frac{954}{720} and \frac{17}{720} have the same denominator, add them by adding their numerators.

$$1155\left(\frac{954+17}{720}+\frac{19}{9\times 10\times 11}\right)$$

Add 954 and 17 to get 971.

$$1155\left(\frac{971}{720}+\frac{19}{9\times 10\times 11}\right)$$

Multiply 9 and 10 to get 90.

$$1155\left(\frac{971}{720}+\frac{19}{90\times 11}\right)$$

Multiply 90 and 11 to get 990.

$$1155\left(\frac{971}{720}+\frac{19}{990}\right)$$

Least common multiple of 720 and 990 is 7920. Convert \frac{971}{720} and \frac{19}{990} to fractions with denominator 7920.

$$1155\left(\frac{10681}{7920}+\frac{152}{7920}\right)$$

Since \frac{10681}{7920} and \frac{152}{7920} have the same denominator, add them by adding their numerators.

$$1155\times \frac{10681+152}{7920}$$

Add 10681 and 152 to get 10833.

$$1155\times \frac{10833}{7920}$$

Reduce the fraction \frac{10833}{7920} to lowest terms by extracting and canceling out 3.

$$1155\times \frac{3611}{2640}$$

Express 1155\times \frac{3611}{2640} as a single fraction.

$$\frac{1155\times 3611}{2640}$$

Multiply 1155 and 3611 to get 4170705.

$$\frac{4170705}{2640}$$

Reduce the fraction \frac{4170705}{2640} to lowest terms by extracting and canceling out 165.

$$\frac{25277}{16}$$

Factor

$$\frac{7 \cdot 23 \cdot 157}{2 ^ {4}} = 1579\frac{13}{16} = 1579.8125$$