Solve [(3/5-1/2)+(1/4+1/3)]*frac{2}{55}:(frac{3}{5}+frac{1}{10})

$$[ ( \frac { 3 } { 5 } - \frac { 1 } { 2 } ) + ( \frac { 1 } { 4 } + \frac { 1 } { 3 } ) ] \cdot \frac { 2 } { 55 } : ( \frac { 3 } { 5 } + \frac { 1 } { 10 } )$$

Evaluate

$$\frac{41}{1155}\approx 0.035497835$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{\left(\frac{6}{10}-\frac{5}{10}+\frac{1}{4}+\frac{1}{3}\right)\times \frac{2}{55}}{\frac{3}{5}+\frac{1}{10}}$$

Since \frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{6-5}{10}+\frac{1}{4}+\frac{1}{3}\right)\times \frac{2}{55}}{\frac{3}{5}+\frac{1}{10}}$$

Subtract 5 from 6 to get 1.

$$\frac{\left(\frac{1}{10}+\frac{1}{4}+\frac{1}{3}\right)\times \frac{2}{55}}{\frac{3}{5}+\frac{1}{10}}$$

Least common multiple of 10 and 4 is 20. Convert \frac{1}{10} and \frac{1}{4} to fractions with denominator 20.

$$\frac{\left(\frac{2}{20}+\frac{5}{20}+\frac{1}{3}\right)\times \frac{2}{55}}{\frac{3}{5}+\frac{1}{10}}$$

Since \frac{2}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{2+5}{20}+\frac{1}{3}\right)\times \frac{2}{55}}{\frac{3}{5}+\frac{1}{10}}$$

Add 2 and 5 to get 7.

$$\frac{\left(\frac{7}{20}+\frac{1}{3}\right)\times \frac{2}{55}}{\frac{3}{5}+\frac{1}{10}}$$

Least common multiple of 20 and 3 is 60. Convert \frac{7}{20} and \frac{1}{3} to fractions with denominator 60.

$$\frac{\left(\frac{21}{60}+\frac{20}{60}\right)\times \frac{2}{55}}{\frac{3}{5}+\frac{1}{10}}$$

Since \frac{21}{60} and \frac{20}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{21+20}{60}\times \frac{2}{55}}{\frac{3}{5}+\frac{1}{10}}$$

Add 21 and 20 to get 41.

$$\frac{\frac{41}{60}\times \frac{2}{55}}{\frac{3}{5}+\frac{1}{10}}$$

Multiply \frac{41}{60} times \frac{2}{55} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{41\times 2}{60\times 55}}{\frac{3}{5}+\frac{1}{10}}$$

Do the multiplications in the fraction \frac{41\times 2}{60\times 55}.

$$\frac{\frac{82}{3300}}{\frac{3}{5}+\frac{1}{10}}$$

Reduce the fraction \frac{82}{3300} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{41}{1650}}{\frac{3}{5}+\frac{1}{10}}$$

Least common multiple of 5 and 10 is 10. Convert \frac{3}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{\frac{41}{1650}}{\frac{6}{10}+\frac{1}{10}}$$

Since \frac{6}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{41}{1650}}{\frac{6+1}{10}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{41}{1650}}{\frac{7}{10}}$$

Divide \frac{41}{1650} by \frac{7}{10} by multiplying \frac{41}{1650} by the reciprocal of \frac{7}{10}.

$$\frac{41}{1650}\times \frac{10}{7}$$

Multiply \frac{41}{1650} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41\times 10}{1650\times 7}$$

Do the multiplications in the fraction \frac{41\times 10}{1650\times 7}.

$$\frac{410}{11550}$$

Reduce the fraction \frac{410}{11550} to lowest terms by extracting and canceling out 10.

$$\frac{41}{1155}$$

Factor

$$\frac{41}{3 \cdot 5 \cdot 7 \cdot 11} = 0.0354978354978355$$