Solve (37/3+37/5+37/7)div(11/3+frac{11}{5}+frac{11}{7})

$$( \frac { 37 } { 3 } + \frac { 37 } { 5 } + \frac { 37 } { 7 } ) \div ( \frac { 11 } { 3 } + \frac { 11 } { 5 } + \frac { 11 } { 7 } )$$

Evaluate

$$\frac{37}{11}\approx 3.363636364$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{37}{3} and \frac{37}{5} to fractions with denominator 15.

$$\frac{\frac{185}{15}+\frac{111}{15}+\frac{37}{7}}{\frac{11}{3}+\frac{11}{5}+\frac{11}{7}}$$

Since \frac{185}{15} and \frac{111}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{185+111}{15}+\frac{37}{7}}{\frac{11}{3}+\frac{11}{5}+\frac{11}{7}}$$

Add 185 and 111 to get 296.

$$\frac{\frac{296}{15}+\frac{37}{7}}{\frac{11}{3}+\frac{11}{5}+\frac{11}{7}}$$

Least common multiple of 15 and 7 is 105. Convert \frac{296}{15} and \frac{37}{7} to fractions with denominator 105.

$$\frac{\frac{2072}{105}+\frac{555}{105}}{\frac{11}{3}+\frac{11}{5}+\frac{11}{7}}$$

Since \frac{2072}{105} and \frac{555}{105} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2072+555}{105}}{\frac{11}{3}+\frac{11}{5}+\frac{11}{7}}$$

Add 2072 and 555 to get 2627.

$$\frac{\frac{2627}{105}}{\frac{11}{3}+\frac{11}{5}+\frac{11}{7}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{11}{3} and \frac{11}{5} to fractions with denominator 15.

$$\frac{\frac{2627}{105}}{\frac{55}{15}+\frac{33}{15}+\frac{11}{7}}$$

Since \frac{55}{15} and \frac{33}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2627}{105}}{\frac{55+33}{15}+\frac{11}{7}}$$

Add 55 and 33 to get 88.

$$\frac{\frac{2627}{105}}{\frac{88}{15}+\frac{11}{7}}$$

Least common multiple of 15 and 7 is 105. Convert \frac{88}{15} and \frac{11}{7} to fractions with denominator 105.

$$\frac{\frac{2627}{105}}{\frac{616}{105}+\frac{165}{105}}$$

Since \frac{616}{105} and \frac{165}{105} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2627}{105}}{\frac{616+165}{105}}$$

Add 616 and 165 to get 781.

$$\frac{\frac{2627}{105}}{\frac{781}{105}}$$

Divide \frac{2627}{105} by \frac{781}{105} by multiplying \frac{2627}{105} by the reciprocal of \frac{781}{105}.

$$\frac{2627}{105}\times \frac{105}{781}$$

Multiply \frac{2627}{105} times \frac{105}{781} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2627\times 105}{105\times 781}$$

Cancel out 105 in both numerator and denominator.

$$\frac{2627}{781}$$

Reduce the fraction \frac{2627}{781} to lowest terms by extracting and canceling out 71.

$$\frac{37}{11}$$

Factor

$$\frac{37}{11} = 3\frac{4}{11} = 3.3636363636363638$$