Solve 1/5*5/9+2/3*1/4+frac{2}{3}*frac{1}{12}

$$\frac { 1 } { 5 } \times \frac { 5 } { 9 } + \frac { 2 } { 3 } \times \frac { 1 } { 4 } + \frac { 2 } { 3 } \times \frac { 1 } { 12 }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

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

$$\frac{1\times 5}{5\times 9}+\frac{2}{3}\times \frac{1}{4}+\frac{2}{3}\times \frac{1}{12}$$

Cancel out 5 in both numerator and denominator.

$$\frac{1}{9}+\frac{2}{3}\times \frac{1}{4}+\frac{2}{3}\times \frac{1}{12}$$

Multiply \frac{2}{3} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{9}+\frac{2\times 1}{3\times 4}+\frac{2}{3}\times \frac{1}{12}$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 4}.

$$\frac{1}{9}+\frac{2}{12}+\frac{2}{3}\times \frac{1}{12}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\frac{1}{9}+\frac{1}{6}+\frac{2}{3}\times \frac{1}{12}$$

Least common multiple of 9 and 6 is 18. Convert \frac{1}{9} and \frac{1}{6} to fractions with denominator 18.

$$\frac{2}{18}+\frac{3}{18}+\frac{2}{3}\times \frac{1}{12}$$

Since \frac{2}{18} and \frac{3}{18} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{18}+\frac{2}{3}\times \frac{1}{12}$$

Add 2 and 3 to get 5.

$$\frac{5}{18}+\frac{2}{3}\times \frac{1}{12}$$

Multiply \frac{2}{3} times \frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{18}+\frac{2\times 1}{3\times 12}$$

Do the multiplications in the fraction \frac{2\times 1}{3\times 12}.

$$\frac{5}{18}+\frac{2}{36}$$

Reduce the fraction \frac{2}{36} to lowest terms by extracting and canceling out 2.

$$\frac{5}{18}+\frac{1}{18}$$

Since \frac{5}{18} and \frac{1}{18} have the same denominator, add them by adding their numerators.

$$\frac{5+1}{18}$$

Add 5 and 1 to get 6.

$$\frac{6}{18}$$

Reduce the fraction \frac{6}{18} to lowest terms by extracting and canceling out 6.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$