Solve [(6/7+4/21)*21/11+3/2:(frac{5}{4}-frac{1}{2})]

$$[ ( \frac { 6 } { 7 } + \frac { 4 } { 21 } ) \cdot \frac { 21 } { 11 } + \frac { 3 } { 2 } : ( \frac { 5 } { 4 } - \frac { 1 } { 2 } ) ]$$

Evaluate

$$4$$

Solution Steps

Least common multiple of 7 and 21 is 21. Convert \frac{6}{7} and \frac{4}{21} to fractions with denominator 21.

$$\left(\frac{18}{21}+\frac{4}{21}\right)\times \frac{21}{11}+\frac{\frac{3}{2}}{\frac{5}{4}-\frac{1}{2}}$$

Since \frac{18}{21} and \frac{4}{21} have the same denominator, add them by adding their numerators.

$$\frac{18+4}{21}\times \frac{21}{11}+\frac{\frac{3}{2}}{\frac{5}{4}-\frac{1}{2}}$$

Add 18 and 4 to get 22.

$$\frac{22}{21}\times \frac{21}{11}+\frac{\frac{3}{2}}{\frac{5}{4}-\frac{1}{2}}$$

Multiply \frac{22}{21} times \frac{21}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 21}{21\times 11}+\frac{\frac{3}{2}}{\frac{5}{4}-\frac{1}{2}}$$

Cancel out 21 in both numerator and denominator.

$$\frac{22}{11}+\frac{\frac{3}{2}}{\frac{5}{4}-\frac{1}{2}}$$

Divide 22 by 11 to get 2.

$$2+\frac{\frac{3}{2}}{\frac{5}{4}-\frac{1}{2}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{1}{2} to fractions with denominator 4.

$$2+\frac{\frac{3}{2}}{\frac{5}{4}-\frac{2}{4}}$$

Since \frac{5}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$2+\frac{\frac{3}{2}}{\frac{5-2}{4}}$$

Subtract 2 from 5 to get 3.

$$2+\frac{\frac{3}{2}}{\frac{3}{4}}$$

Divide \frac{3}{2} by \frac{3}{4} by multiplying \frac{3}{2} by the reciprocal of \frac{3}{4}.

$$2+\frac{3}{2}\times \frac{4}{3}$$

Multiply \frac{3}{2} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$2+\frac{3\times 4}{2\times 3}$$

Cancel out 3 in both numerator and denominator.

$$2+\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$2+2$$

Add 2 and 2 to get 4.

$$4$$

Factor

$$2^{2}$$