Solve (3/10+7/15+4/45):11/30+(frac{7}{12}-frac{1}{4})-(frac{31}{35}-frac{5}{42}):frac{23}{15}-frac{1}{6}=

$$( \frac { 3 } { 10 } + \frac { 7 } { 15 } + \frac { 4 } { 45 } ) : \frac { 11 } { 30 } + ( \frac { 7 } { 12 } - \frac { 1 } { 4 } ) - ( \frac { 31 } { 35 } - \frac { 5 } { 42 } ) : \frac { 23 } { 15 } - \frac { 1 } { 6 } =$$

Evaluate

$$2$$

Solution Steps

Least common multiple of 10 and 15 is 30. Convert \frac{3}{10} and \frac{7}{15} to fractions with denominator 30.

$$\frac{\frac{9}{30}+\frac{14}{30}+\frac{4}{45}}{\frac{11}{30}}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Since \frac{9}{30} and \frac{14}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+14}{30}+\frac{4}{45}}{\frac{11}{30}}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Add 9 and 14 to get 23.

$$\frac{\frac{23}{30}+\frac{4}{45}}{\frac{11}{30}}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Least common multiple of 30 and 45 is 90. Convert \frac{23}{30} and \frac{4}{45} to fractions with denominator 90.

$$\frac{\frac{69}{90}+\frac{8}{90}}{\frac{11}{30}}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Since \frac{69}{90} and \frac{8}{90} have the same denominator, add them by adding their numerators.

$$\frac{\frac{69+8}{90}}{\frac{11}{30}}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Add 69 and 8 to get 77.

$$\frac{\frac{77}{90}}{\frac{11}{30}}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Divide \frac{77}{90} by \frac{11}{30} by multiplying \frac{77}{90} by the reciprocal of \frac{11}{30}.

$$\frac{77}{90}\times \frac{30}{11}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Multiply \frac{77}{90} times \frac{30}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{77\times 30}{90\times 11}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Do the multiplications in the fraction \frac{77\times 30}{90\times 11}.

$$\frac{2310}{990}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Reduce the fraction \frac{2310}{990} to lowest terms by extracting and canceling out 330.

$$\frac{7}{3}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Least common multiple of 3 and 12 is 12. Convert \frac{7}{3} and \frac{7}{12} to fractions with denominator 12.

$$\frac{28}{12}+\frac{7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Since \frac{28}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$\frac{28+7}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Add 28 and 7 to get 35.

$$\frac{35}{12}-\frac{1}{4}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Least common multiple of 12 and 4 is 12. Convert \frac{35}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{35}{12}-\frac{3}{12}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Since \frac{35}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-3}{12}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Subtract 3 from 35 to get 32.

$$\frac{32}{12}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Reduce the fraction \frac{32}{12} to lowest terms by extracting and canceling out 4.

$$\frac{8}{3}-\frac{\frac{31}{35}-\frac{5}{42}}{\frac{23}{15}}-\frac{1}{6}$$

Least common multiple of 35 and 42 is 210. Convert \frac{31}{35} and \frac{5}{42} to fractions with denominator 210.

$$\frac{8}{3}-\frac{\frac{186}{210}-\frac{25}{210}}{\frac{23}{15}}-\frac{1}{6}$$

Since \frac{186}{210} and \frac{25}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{3}-\frac{\frac{186-25}{210}}{\frac{23}{15}}-\frac{1}{6}$$

Subtract 25 from 186 to get 161.

$$\frac{8}{3}-\frac{\frac{161}{210}}{\frac{23}{15}}-\frac{1}{6}$$

Reduce the fraction \frac{161}{210} to lowest terms by extracting and canceling out 7.

$$\frac{8}{3}-\frac{\frac{23}{30}}{\frac{23}{15}}-\frac{1}{6}$$

Divide \frac{23}{30} by \frac{23}{15} by multiplying \frac{23}{30} by the reciprocal of \frac{23}{15}.

$$\frac{8}{3}-\frac{23}{30}\times \frac{15}{23}-\frac{1}{6}$$

Multiply \frac{23}{30} times \frac{15}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{3}-\frac{23\times 15}{30\times 23}-\frac{1}{6}$$

Cancel out 23 in both numerator and denominator.

$$\frac{8}{3}-\frac{15}{30}-\frac{1}{6}$$

Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.

$$\frac{8}{3}-\frac{1}{2}-\frac{1}{6}$$

Least common multiple of 3 and 2 is 6. Convert \frac{8}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{16}{6}-\frac{3}{6}-\frac{1}{6}$$

Since \frac{16}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-3}{6}-\frac{1}{6}$$

Subtract 3 from 16 to get 13.

$$\frac{13}{6}-\frac{1}{6}$$

Since \frac{13}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-1}{6}$$

Subtract 1 from 13 to get 12.

$$\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$2$$

Factor

$$2$$