Solve {2-3/2+[(1/5+4/3-5/2)-frac{3}{7}+frac{5}{4}]-frac{1}{4}}*frac{35}{11}=

$$\{ 2 - \frac { 3 } { 2 } + [ ( \frac { 1 } { 5 } + \frac { 4 } { 3 } - \frac { 5 } { 2 } ) - \frac { 3 } { 7 } + \frac { 5 } { 4 } ] - \frac { 1 } { 4 } \} \cdot \frac { 35 } { 11 } =$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

$$\left(\frac{4}{2}-\frac{3}{2}+\frac{1}{5}+\frac{4}{3}-\frac{5}{2}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Since \frac{4}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{4-3}{2}+\frac{1}{5}+\frac{4}{3}-\frac{5}{2}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Subtract 3 from 4 to get 1.

$$\left(\frac{1}{2}+\frac{1}{5}+\frac{4}{3}-\frac{5}{2}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{1}{5} to fractions with denominator 10.

$$\left(\frac{5}{10}+\frac{2}{10}+\frac{4}{3}-\frac{5}{2}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Since \frac{5}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$\left(\frac{5+2}{10}+\frac{4}{3}-\frac{5}{2}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Add 5 and 2 to get 7.

$$\left(\frac{7}{10}+\frac{4}{3}-\frac{5}{2}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Least common multiple of 10 and 3 is 30. Convert \frac{7}{10} and \frac{4}{3} to fractions with denominator 30.

$$\left(\frac{21}{30}+\frac{40}{30}-\frac{5}{2}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Since \frac{21}{30} and \frac{40}{30} have the same denominator, add them by adding their numerators.

$$\left(\frac{21+40}{30}-\frac{5}{2}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Add 21 and 40 to get 61.

$$\left(\frac{61}{30}-\frac{5}{2}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Least common multiple of 30 and 2 is 30. Convert \frac{61}{30} and \frac{5}{2} to fractions with denominator 30.

$$\left(\frac{61}{30}-\frac{75}{30}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Since \frac{61}{30} and \frac{75}{30} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{61-75}{30}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Subtract 75 from 61 to get -14.

$$\left(\frac{-14}{30}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Reduce the fraction \frac{-14}{30} to lowest terms by extracting and canceling out 2.

$$\left(-\frac{7}{15}-\frac{3}{7}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Least common multiple of 15 and 7 is 105. Convert -\frac{7}{15} and \frac{3}{7} to fractions with denominator 105.

$$\left(-\frac{49}{105}-\frac{45}{105}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Since -\frac{49}{105} and \frac{45}{105} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{-49-45}{105}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Subtract 45 from -49 to get -94.

$$\left(-\frac{94}{105}+\frac{5}{4}-\frac{1}{4}\right)\times \frac{35}{11}$$

Least common multiple of 105 and 4 is 420. Convert -\frac{94}{105} and \frac{5}{4} to fractions with denominator 420.

$$\left(-\frac{376}{420}+\frac{525}{420}-\frac{1}{4}\right)\times \frac{35}{11}$$

Since -\frac{376}{420} and \frac{525}{420} have the same denominator, add them by adding their numerators.

$$\left(\frac{-376+525}{420}-\frac{1}{4}\right)\times \frac{35}{11}$$

Add -376 and 525 to get 149.

$$\left(\frac{149}{420}-\frac{1}{4}\right)\times \frac{35}{11}$$

Least common multiple of 420 and 4 is 420. Convert \frac{149}{420} and \frac{1}{4} to fractions with denominator 420.

$$\left(\frac{149}{420}-\frac{105}{420}\right)\times \frac{35}{11}$$

Since \frac{149}{420} and \frac{105}{420} have the same denominator, subtract them by subtracting their numerators.

$$\frac{149-105}{420}\times \frac{35}{11}$$

Subtract 105 from 149 to get 44.

$$\frac{44}{420}\times \frac{35}{11}$$

Reduce the fraction \frac{44}{420} to lowest terms by extracting and canceling out 4.

$$\frac{11}{105}\times \frac{35}{11}$$

Multiply \frac{11}{105} times \frac{35}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 35}{105\times 11}$$

Cancel out 11 in both numerator and denominator.

$$\frac{35}{105}$$

Reduce the fraction \frac{35}{105} to lowest terms by extracting and canceling out 35.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$