Solve {8/35+[(3/2-33/35)+(3/14-frac{2}{35})-(2-frac{12}{7}+frac{5}{14})]}*3frac{1}{3}

$$\{ \frac { 8 } { 35 } + [ ( \frac { 3 } { 2 } - \frac { 33 } { 35 } ) + ( \frac { 3 } { 14 } - \frac { 2 } { 35 } ) - ( 2 - \frac { 12 } { 7 } + \frac { 5 } { 14 } ) ] \} \cdot 3 \frac { 1 } { 3 }$$

Evaluate

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Solution Steps

Least common multiple of 2 and 35 is 70. Convert \frac{3}{2} and \frac{33}{35} to fractions with denominator 70.

$$\left(\frac{8}{35}+\frac{105}{70}-\frac{66}{70}+\frac{3}{14}-\frac{2}{35}-\left(2-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Since \frac{105}{70} and \frac{66}{70} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{8}{35}+\frac{105-66}{70}+\frac{3}{14}-\frac{2}{35}-\left(2-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Subtract 66 from 105 to get 39.

$$\left(\frac{8}{35}+\frac{39}{70}+\frac{3}{14}-\frac{2}{35}-\left(2-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Least common multiple of 70 and 14 is 70. Convert \frac{39}{70} and \frac{3}{14} to fractions with denominator 70.

$$\left(\frac{8}{35}+\frac{39}{70}+\frac{15}{70}-\frac{2}{35}-\left(2-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Since \frac{39}{70} and \frac{15}{70} have the same denominator, add them by adding their numerators.

$$\left(\frac{8}{35}+\frac{39+15}{70}-\frac{2}{35}-\left(2-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Add 39 and 15 to get 54.

$$\left(\frac{8}{35}+\frac{54}{70}-\frac{2}{35}-\left(2-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Reduce the fraction \frac{54}{70} to lowest terms by extracting and canceling out 2.

$$\left(\frac{8}{35}+\frac{27}{35}-\frac{2}{35}-\left(2-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Since \frac{27}{35} and \frac{2}{35} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{8}{35}+\frac{27-2}{35}-\left(2-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Subtract 2 from 27 to get 25.

$$\left(\frac{8}{35}+\frac{25}{35}-\left(2-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Reduce the fraction \frac{25}{35} to lowest terms by extracting and canceling out 5.

$$\left(\frac{8}{35}+\frac{5}{7}-\left(2-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Convert 2 to fraction \frac{14}{7}.

$$\left(\frac{8}{35}+\frac{5}{7}-\left(\frac{14}{7}-\frac{12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Since \frac{14}{7} and \frac{12}{7} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{8}{35}+\frac{5}{7}-\left(\frac{14-12}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Subtract 12 from 14 to get 2.

$$\left(\frac{8}{35}+\frac{5}{7}-\left(\frac{2}{7}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Least common multiple of 7 and 14 is 14. Convert \frac{2}{7} and \frac{5}{14} to fractions with denominator 14.

$$\left(\frac{8}{35}+\frac{5}{7}-\left(\frac{4}{14}+\frac{5}{14}\right)\right)\times \frac{3\times 3+1}{3}$$

Since \frac{4}{14} and \frac{5}{14} have the same denominator, add them by adding their numerators.

$$\left(\frac{8}{35}+\frac{5}{7}-\frac{4+5}{14}\right)\times \frac{3\times 3+1}{3}$$

Add 4 and 5 to get 9.

$$\left(\frac{8}{35}+\frac{5}{7}-\frac{9}{14}\right)\times \frac{3\times 3+1}{3}$$

Least common multiple of 7 and 14 is 14. Convert \frac{5}{7} and \frac{9}{14} to fractions with denominator 14.

$$\left(\frac{8}{35}+\frac{10}{14}-\frac{9}{14}\right)\times \frac{3\times 3+1}{3}$$

Since \frac{10}{14} and \frac{9}{14} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{8}{35}+\frac{10-9}{14}\right)\times \frac{3\times 3+1}{3}$$

Subtract 9 from 10 to get 1.

$$\left(\frac{8}{35}+\frac{1}{14}\right)\times \frac{3\times 3+1}{3}$$

Least common multiple of 35 and 14 is 70. Convert \frac{8}{35} and \frac{1}{14} to fractions with denominator 70.

$$\left(\frac{16}{70}+\frac{5}{70}\right)\times \frac{3\times 3+1}{3}$$

Since \frac{16}{70} and \frac{5}{70} have the same denominator, add them by adding their numerators.

$$\frac{16+5}{70}\times \frac{3\times 3+1}{3}$$

Add 16 and 5 to get 21.

$$\frac{21}{70}\times \frac{3\times 3+1}{3}$$

Reduce the fraction \frac{21}{70} to lowest terms by extracting and canceling out 7.

$$\frac{3}{10}\times \frac{3\times 3+1}{3}$$

Multiply 3 and 3 to get 9.

$$\frac{3}{10}\times \frac{9+1}{3}$$

Add 9 and 1 to get 10.

$$\frac{3}{10}\times \frac{10}{3}$$

Cancel out \frac{3}{10} and its reciprocal \frac{10}{3}.

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Factor

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