Solve (2890+5/6+7/8+7/10)div(5/6+frac{7}{8}+frac{7}{10})

$$( 2890 + \frac { 5 } { 6 } + \frac { 7 } { 8 } + \frac { 7 } { 10 } ) \div ( \frac { 5 } { 6 } + \frac { 7 } { 8 } + \frac { 7 } { 10 } )$$

Evaluate

$$1201$$

Solution Steps

Convert 2890 to fraction \frac{17340}{6}.

$$\frac{\frac{17340}{6}+\frac{5}{6}+\frac{7}{8}+\frac{7}{10}}{\frac{5}{6}+\frac{7}{8}+\frac{7}{10}}$$

Since \frac{17340}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{17340+5}{6}+\frac{7}{8}+\frac{7}{10}}{\frac{5}{6}+\frac{7}{8}+\frac{7}{10}}$$

Add 17340 and 5 to get 17345.

$$\frac{\frac{17345}{6}+\frac{7}{8}+\frac{7}{10}}{\frac{5}{6}+\frac{7}{8}+\frac{7}{10}}$$

Least common multiple of 6 and 8 is 24. Convert \frac{17345}{6} and \frac{7}{8} to fractions with denominator 24.

$$\frac{\frac{69380}{24}+\frac{21}{24}+\frac{7}{10}}{\frac{5}{6}+\frac{7}{8}+\frac{7}{10}}$$

Since \frac{69380}{24} and \frac{21}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{69380+21}{24}+\frac{7}{10}}{\frac{5}{6}+\frac{7}{8}+\frac{7}{10}}$$

Add 69380 and 21 to get 69401.

$$\frac{\frac{69401}{24}+\frac{7}{10}}{\frac{5}{6}+\frac{7}{8}+\frac{7}{10}}$$

Least common multiple of 24 and 10 is 120. Convert \frac{69401}{24} and \frac{7}{10} to fractions with denominator 120.

$$\frac{\frac{347005}{120}+\frac{84}{120}}{\frac{5}{6}+\frac{7}{8}+\frac{7}{10}}$$

Since \frac{347005}{120} and \frac{84}{120} have the same denominator, add them by adding their numerators.

$$\frac{\frac{347005+84}{120}}{\frac{5}{6}+\frac{7}{8}+\frac{7}{10}}$$

Add 347005 and 84 to get 347089.

$$\frac{\frac{347089}{120}}{\frac{5}{6}+\frac{7}{8}+\frac{7}{10}}$$

Least common multiple of 6 and 8 is 24. Convert \frac{5}{6} and \frac{7}{8} to fractions with denominator 24.

$$\frac{\frac{347089}{120}}{\frac{20}{24}+\frac{21}{24}+\frac{7}{10}}$$

Since \frac{20}{24} and \frac{21}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{347089}{120}}{\frac{20+21}{24}+\frac{7}{10}}$$

Add 20 and 21 to get 41.

$$\frac{\frac{347089}{120}}{\frac{41}{24}+\frac{7}{10}}$$

Least common multiple of 24 and 10 is 120. Convert \frac{41}{24} and \frac{7}{10} to fractions with denominator 120.

$$\frac{\frac{347089}{120}}{\frac{205}{120}+\frac{84}{120}}$$

Since \frac{205}{120} and \frac{84}{120} have the same denominator, add them by adding their numerators.

$$\frac{\frac{347089}{120}}{\frac{205+84}{120}}$$

Add 205 and 84 to get 289.

$$\frac{\frac{347089}{120}}{\frac{289}{120}}$$

Divide \frac{347089}{120} by \frac{289}{120} by multiplying \frac{347089}{120} by the reciprocal of \frac{289}{120}.

$$\frac{347089}{120}\times \frac{120}{289}$$

Multiply \frac{347089}{120} times \frac{120}{289} by multiplying numerator times numerator and denominator times denominator.

$$\frac{347089\times 120}{120\times 289}$$

Cancel out 120 in both numerator and denominator.

$$\frac{347089}{289}$$

Divide 347089 by 289 to get 1201.

$$1201$$

Factor

$$1201$$