Solve 1/3+4/5*1/4*5/9+frac{1}{2}

$$\frac { 1 } { 3 } + \frac { 4 } { 5 } \times \frac { 1 } { 4 } \times \frac { 5 } { 9 } + \frac { 1 } { 2 }$$

Evaluate

$$\frac{17}{18}\approx 0.944444444$$

Solution Steps

Multiply \frac{4}{5} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}+\frac{4\times 1}{5\times 4}\times \frac{5}{9}+\frac{1}{2}$$

Cancel out 4 in both numerator and denominator.

$$\frac{1}{3}+\frac{1}{5}\times \frac{5}{9}+\frac{1}{2}$$

Multiply \frac{1}{5} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{3}+\frac{1\times 5}{5\times 9}+\frac{1}{2}$$

Cancel out 5 in both numerator and denominator.

$$\frac{1}{3}+\frac{1}{9}+\frac{1}{2}$$

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

$$\frac{3}{9}+\frac{1}{9}+\frac{1}{2}$$

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

$$\frac{3+1}{9}+\frac{1}{2}$$

Add 3 and 1 to get 4.

$$\frac{4}{9}+\frac{1}{2}$$

Least common multiple of 9 and 2 is 18. Convert \frac{4}{9} and \frac{1}{2} to fractions with denominator 18.

$$\frac{8}{18}+\frac{9}{18}$$

Since \frac{8}{18} and \frac{9}{18} have the same denominator, add them by adding their numerators.

$$\frac{8+9}{18}$$

Add 8 and 9 to get 17.

$$\frac{17}{18}$$

Factor

$$\frac{17}{2 \cdot 3 ^ {2}} = 0.9444444444444444$$