Solve [2/3-2/5-2/7(2/5-frac{3}{4})]+frac{1}{21}}:(-frac{3}{4}+frac{1}{2}-frac{5}{12})

$$[ \frac { 2 } { 3 } - \frac { 2 } { 5 } - \frac { 2 } { 7 } ( \frac { 2 } { 5 } - \frac { 3 } { 4 } ) ] + \frac { 1 } { 21 } \} : ( - \frac { 3 } { 4 } + \frac { 1 } { 2 } - \frac { 5 } { 12 } )$$

Evaluate

$$\frac{29}{70}\approx 0.414285714$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{10}{15}-\frac{6}{15}-\frac{2}{7}\left(\frac{2}{5}-\frac{3}{4}\right)+\frac{1}{21}$$

Since \frac{10}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-6}{15}-\frac{2}{7}\left(\frac{2}{5}-\frac{3}{4}\right)+\frac{1}{21}$$

Subtract 6 from 10 to get 4.

$$\frac{4}{15}-\frac{2}{7}\left(\frac{2}{5}-\frac{3}{4}\right)+\frac{1}{21}$$

Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{4}{15}-\frac{2}{7}\left(\frac{8}{20}-\frac{15}{20}\right)+\frac{1}{21}$$

Since \frac{8}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{15}-\frac{2}{7}\times \frac{8-15}{20}+\frac{1}{21}$$

Subtract 15 from 8 to get -7.

$$\frac{4}{15}-\frac{2}{7}\left(-\frac{7}{20}\right)+\frac{1}{21}$$

Multiply \frac{2}{7} times -\frac{7}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{15}-\frac{2\left(-7\right)}{7\times 20}+\frac{1}{21}$$

Do the multiplications in the fraction \frac{2\left(-7\right)}{7\times 20}.

$$\frac{4}{15}-\frac{-14}{140}+\frac{1}{21}$$

Reduce the fraction \frac{-14}{140} to lowest terms by extracting and canceling out 14.

$$\frac{4}{15}-\left(-\frac{1}{10}\right)+\frac{1}{21}$$

The opposite of -\frac{1}{10} is \frac{1}{10}.

$$\frac{4}{15}+\frac{1}{10}+\frac{1}{21}$$

Least common multiple of 15 and 10 is 30. Convert \frac{4}{15} and \frac{1}{10} to fractions with denominator 30.

$$\frac{8}{30}+\frac{3}{30}+\frac{1}{21}$$

Since \frac{8}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{8+3}{30}+\frac{1}{21}$$

Add 8 and 3 to get 11.

$$\frac{11}{30}+\frac{1}{21}$$

Least common multiple of 30 and 21 is 210. Convert \frac{11}{30} and \frac{1}{21} to fractions with denominator 210.

$$\frac{77}{210}+\frac{10}{210}$$

Since \frac{77}{210} and \frac{10}{210} have the same denominator, add them by adding their numerators.

$$\frac{77+10}{210}$$

Add 77 and 10 to get 87.

$$\frac{87}{210}$$

Reduce the fraction \frac{87}{210} to lowest terms by extracting and canceling out 3.

$$\frac{29}{70}$$

Factor

$$\frac{29}{2 \cdot 5 \cdot 7} = 0.4142857142857143$$