Solve 2/12*14+2/14*16+2/16*18,2/18*20,frac{1}{20}

$$\frac { 2 } { 12 \times 14 } + \frac { 2 } { 14 \times 16 } + \frac { 2 } { 16 \times 18 } , \frac { 2 } { 18 \times 20 } , \frac { 1 } { 20 }$$

Sort

$$\frac{1}{180},\frac{1}{36},\frac{1}{20}$$

Solution Steps

Multiply 12 and 14 to get 168.

$$sort(\frac{2}{168}+\frac{2}{14\times 16}+\frac{2}{16\times 18},\frac{2}{18\times 20},\frac{1}{20})$$

Reduce the fraction \frac{2}{168} to lowest terms by extracting and canceling out 2.

$$sort(\frac{1}{84}+\frac{2}{14\times 16}+\frac{2}{16\times 18},\frac{2}{18\times 20},\frac{1}{20})$$

Multiply 14 and 16 to get 224.

$$sort(\frac{1}{84}+\frac{2}{224}+\frac{2}{16\times 18},\frac{2}{18\times 20},\frac{1}{20})$$

Reduce the fraction \frac{2}{224} to lowest terms by extracting and canceling out 2.

$$sort(\frac{1}{84}+\frac{1}{112}+\frac{2}{16\times 18},\frac{2}{18\times 20},\frac{1}{20})$$

Least common multiple of 84 and 112 is 336. Convert \frac{1}{84} and \frac{1}{112} to fractions with denominator 336.

$$sort(\frac{4}{336}+\frac{3}{336}+\frac{2}{16\times 18},\frac{2}{18\times 20},\frac{1}{20})$$

Since \frac{4}{336} and \frac{3}{336} have the same denominator, add them by adding their numerators.

$$sort(\frac{4+3}{336}+\frac{2}{16\times 18},\frac{2}{18\times 20},\frac{1}{20})$$

Add 4 and 3 to get 7.

$$sort(\frac{7}{336}+\frac{2}{16\times 18},\frac{2}{18\times 20},\frac{1}{20})$$

Reduce the fraction \frac{7}{336} to lowest terms by extracting and canceling out 7.

$$sort(\frac{1}{48}+\frac{2}{16\times 18},\frac{2}{18\times 20},\frac{1}{20})$$

Multiply 16 and 18 to get 288.

$$sort(\frac{1}{48}+\frac{2}{288},\frac{2}{18\times 20},\frac{1}{20})$$

Reduce the fraction \frac{2}{288} to lowest terms by extracting and canceling out 2.

$$sort(\frac{1}{48}+\frac{1}{144},\frac{2}{18\times 20},\frac{1}{20})$$

Least common multiple of 48 and 144 is 144. Convert \frac{1}{48} and \frac{1}{144} to fractions with denominator 144.

$$sort(\frac{3}{144}+\frac{1}{144},\frac{2}{18\times 20},\frac{1}{20})$$

Since \frac{3}{144} and \frac{1}{144} have the same denominator, add them by adding their numerators.

$$sort(\frac{3+1}{144},\frac{2}{18\times 20},\frac{1}{20})$$

Add 3 and 1 to get 4.

$$sort(\frac{4}{144},\frac{2}{18\times 20},\frac{1}{20})$$

Reduce the fraction \frac{4}{144} to lowest terms by extracting and canceling out 4.

$$sort(\frac{1}{36},\frac{2}{18\times 20},\frac{1}{20})$$

Multiply 18 and 20 to get 360.

$$sort(\frac{1}{36},\frac{2}{360},\frac{1}{20})$$

Reduce the fraction \frac{2}{360} to lowest terms by extracting and canceling out 2.

$$sort(\frac{1}{36},\frac{1}{180},\frac{1}{20})$$

Least common denominator of the numbers in the list \frac{1}{36},\frac{1}{180},\frac{1}{20} is 180. Convert numbers in the list to fractions with denominator 180.

$$\frac{5}{180},\frac{1}{180},\frac{9}{180}$$

To sort the list, start from a single element \frac{5}{180}.

$$\frac{5}{180}$$

Insert \frac{1}{180} to the appropriate location in the new list.

$$\frac{1}{180},\frac{5}{180}$$

Insert \frac{9}{180} to the appropriate location in the new list.

$$\frac{1}{180},\frac{5}{180},\frac{9}{180}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{180},\frac{1}{36},\frac{1}{20}$$

Evaluate

$$\frac{1}{36},\frac{1}{180},\frac{1}{20}$$