Solve 3/2*5+3/5*8+4/8*12+5/12*17+frac{3}{17*20}=

$$\frac { 3 } { 2 \times 5 } + \frac { 3 } { 5 \times 8 } + \frac { 4 } { 8 \times 12 } + \frac { 5 } { 12 \times 17 } + \frac { 3 } { 17 \times 20 } =$$

Evaluate

$$\frac{9}{20}=0.45$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{3}{10}+\frac{3}{5\times 8}+\frac{4}{8\times 12}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Multiply 5 and 8 to get 40.

$$\frac{3}{10}+\frac{3}{40}+\frac{4}{8\times 12}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Least common multiple of 10 and 40 is 40. Convert \frac{3}{10} and \frac{3}{40} to fractions with denominator 40.

$$\frac{12}{40}+\frac{3}{40}+\frac{4}{8\times 12}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Since \frac{12}{40} and \frac{3}{40} have the same denominator, add them by adding their numerators.

$$\frac{12+3}{40}+\frac{4}{8\times 12}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Add 12 and 3 to get 15.

$$\frac{15}{40}+\frac{4}{8\times 12}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Reduce the fraction \frac{15}{40} to lowest terms by extracting and canceling out 5.

$$\frac{3}{8}+\frac{4}{8\times 12}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Multiply 8 and 12 to get 96.

$$\frac{3}{8}+\frac{4}{96}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Reduce the fraction \frac{4}{96} to lowest terms by extracting and canceling out 4.

$$\frac{3}{8}+\frac{1}{24}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Least common multiple of 8 and 24 is 24. Convert \frac{3}{8} and \frac{1}{24} to fractions with denominator 24.

$$\frac{9}{24}+\frac{1}{24}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Since \frac{9}{24} and \frac{1}{24} have the same denominator, add them by adding their numerators.

$$\frac{9+1}{24}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Add 9 and 1 to get 10.

$$\frac{10}{24}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Reduce the fraction \frac{10}{24} to lowest terms by extracting and canceling out 2.

$$\frac{5}{12}+\frac{5}{12\times 17}+\frac{3}{17\times 20}$$

Multiply 12 and 17 to get 204.

$$\frac{5}{12}+\frac{5}{204}+\frac{3}{17\times 20}$$

Least common multiple of 12 and 204 is 204. Convert \frac{5}{12} and \frac{5}{204} to fractions with denominator 204.

$$\frac{85}{204}+\frac{5}{204}+\frac{3}{17\times 20}$$

Since \frac{85}{204} and \frac{5}{204} have the same denominator, add them by adding their numerators.

$$\frac{85+5}{204}+\frac{3}{17\times 20}$$

Add 85 and 5 to get 90.

$$\frac{90}{204}+\frac{3}{17\times 20}$$

Reduce the fraction \frac{90}{204} to lowest terms by extracting and canceling out 6.

$$\frac{15}{34}+\frac{3}{17\times 20}$$

Multiply 17 and 20 to get 340.

$$\frac{15}{34}+\frac{3}{340}$$

Least common multiple of 34 and 340 is 340. Convert \frac{15}{34} and \frac{3}{340} to fractions with denominator 340.

$$\frac{150}{340}+\frac{3}{340}$$

Since \frac{150}{340} and \frac{3}{340} have the same denominator, add them by adding their numerators.

$$\frac{150+3}{340}$$

Add 150 and 3 to get 153.

$$\frac{153}{340}$$

Reduce the fraction \frac{153}{340} to lowest terms by extracting and canceling out 17.

$$\frac{9}{20}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2} \cdot 5} = 0.45$$