Solve (36/5+44/7+52/9)div(11/7+frac{13}{9}+frac{9}{5})

$$( \frac { 36 } { 5 } + \frac { 44 } { 7 } + \frac { 52 } { 9 } ) \div ( \frac { 11 } { 7 } + \frac { 13 } { 9 } + \frac { 9 } { 5 } )$$

Evaluate

$$4$$

Solution Steps

Least common multiple of 5 and 7 is 35. Convert \frac{36}{5} and \frac{44}{7} to fractions with denominator 35.

$$\frac{\frac{252}{35}+\frac{220}{35}+\frac{52}{9}}{\frac{11}{7}+\frac{13}{9}+\frac{9}{5}}$$

Since \frac{252}{35} and \frac{220}{35} have the same denominator, add them by adding their numerators.

$$\frac{\frac{252+220}{35}+\frac{52}{9}}{\frac{11}{7}+\frac{13}{9}+\frac{9}{5}}$$

Add 252 and 220 to get 472.

$$\frac{\frac{472}{35}+\frac{52}{9}}{\frac{11}{7}+\frac{13}{9}+\frac{9}{5}}$$

Least common multiple of 35 and 9 is 315. Convert \frac{472}{35} and \frac{52}{9} to fractions with denominator 315.

$$\frac{\frac{4248}{315}+\frac{1820}{315}}{\frac{11}{7}+\frac{13}{9}+\frac{9}{5}}$$

Since \frac{4248}{315} and \frac{1820}{315} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4248+1820}{315}}{\frac{11}{7}+\frac{13}{9}+\frac{9}{5}}$$

Add 4248 and 1820 to get 6068.

$$\frac{\frac{6068}{315}}{\frac{11}{7}+\frac{13}{9}+\frac{9}{5}}$$

Least common multiple of 7 and 9 is 63. Convert \frac{11}{7} and \frac{13}{9} to fractions with denominator 63.

$$\frac{\frac{6068}{315}}{\frac{99}{63}+\frac{91}{63}+\frac{9}{5}}$$

Since \frac{99}{63} and \frac{91}{63} have the same denominator, add them by adding their numerators.

$$\frac{\frac{6068}{315}}{\frac{99+91}{63}+\frac{9}{5}}$$

Add 99 and 91 to get 190.

$$\frac{\frac{6068}{315}}{\frac{190}{63}+\frac{9}{5}}$$

Least common multiple of 63 and 5 is 315. Convert \frac{190}{63} and \frac{9}{5} to fractions with denominator 315.

$$\frac{\frac{6068}{315}}{\frac{950}{315}+\frac{567}{315}}$$

Since \frac{950}{315} and \frac{567}{315} have the same denominator, add them by adding their numerators.

$$\frac{\frac{6068}{315}}{\frac{950+567}{315}}$$

Add 950 and 567 to get 1517.

$$\frac{\frac{6068}{315}}{\frac{1517}{315}}$$

Divide \frac{6068}{315} by \frac{1517}{315} by multiplying \frac{6068}{315} by the reciprocal of \frac{1517}{315}.

$$\frac{6068}{315}\times \frac{315}{1517}$$

Multiply \frac{6068}{315} times \frac{315}{1517} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6068\times 315}{315\times 1517}$$

Cancel out 315 in both numerator and denominator.

$$\frac{6068}{1517}$$

Divide 6068 by 1517 to get 4.

$$4$$

Factor

$$2^{2}$$