Solve 8/9+1/5/frac{5{6}+1/2}

$$\frac { \frac { 8 } { 9 } + \frac { 1 } { 5 } } { \frac { 5 } { 6 } + \frac { 1 } { 2 } }$$

Evaluate

$$\frac{49}{60}\approx 0.816666667$$

Solution Steps

Least common multiple of 9 and 5 is 45. Convert \frac{8}{9} and \frac{1}{5} to fractions with denominator 45.

$$\frac{\frac{40}{45}+\frac{9}{45}}{\frac{5}{6}+\frac{1}{2}}$$

Since \frac{40}{45} and \frac{9}{45} have the same denominator, add them by adding their numerators.

$$\frac{\frac{40+9}{45}}{\frac{5}{6}+\frac{1}{2}}$$

Add 40 and 9 to get 49.

$$\frac{\frac{49}{45}}{\frac{5}{6}+\frac{1}{2}}$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{49}{45}}{\frac{5}{6}+\frac{3}{6}}$$

Since \frac{5}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{49}{45}}{\frac{5+3}{6}}$$

Add 5 and 3 to get 8.

$$\frac{\frac{49}{45}}{\frac{8}{6}}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{49}{45}}{\frac{4}{3}}$$

Divide \frac{49}{45} by \frac{4}{3} by multiplying \frac{49}{45} by the reciprocal of \frac{4}{3}.

$$\frac{49}{45}\times \frac{3}{4}$$

Multiply \frac{49}{45} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 3}{45\times 4}$$

Do the multiplications in the fraction \frac{49\times 3}{45\times 4}.

$$\frac{147}{180}$$

Reduce the fraction \frac{147}{180} to lowest terms by extracting and canceling out 3.

$$\frac{49}{60}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {2} \cdot 3 \cdot 5} = 0.8166666666666667$$