Solve 5/5+5/3/frac{1{3}+1/9}

$$\frac { \frac { 5 } { 5 } + \frac { 5 } { 3 } } { \frac { 1 } { 3 } + \frac { 1 } { 9 } }$$

Evaluate

$$6$$

Solution Steps

Divide 5 by 5 to get 1.

$$\frac{1+\frac{5}{3}}{\frac{1}{3}+\frac{1}{9}}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{3}{3}+\frac{5}{3}}{\frac{1}{3}+\frac{1}{9}}$$

Since \frac{3}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+5}{3}}{\frac{1}{3}+\frac{1}{9}}$$

Add 3 and 5 to get 8.

$$\frac{\frac{8}{3}}{\frac{1}{3}+\frac{1}{9}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{1}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{\frac{8}{3}}{\frac{3}{9}+\frac{1}{9}}$$

Since \frac{3}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8}{3}}{\frac{3+1}{9}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{8}{3}}{\frac{4}{9}}$$

Divide \frac{8}{3} by \frac{4}{9} by multiplying \frac{8}{3} by the reciprocal of \frac{4}{9}.

$$\frac{8}{3}\times \frac{9}{4}$$

Multiply \frac{8}{3} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 9}{3\times 4}$$

Do the multiplications in the fraction \frac{8\times 9}{3\times 4}.

$$\frac{72}{12}$$

Divide 72 by 12 to get 6.

$$6$$

Factor

$$2\times 3$$