Solve 14/21div11/14+1/3

$$1 \frac { 4 } { 21 } \div 1 \frac { 1 } { 14 } + \frac { 1 } { 3 }$$

Evaluate

$$\frac{13}{9}\approx 1.444444444$$

Solution Steps

Divide \frac{1\times 21+4}{21} by \frac{1\times 14+1}{14} by multiplying \frac{1\times 21+4}{21} by the reciprocal of \frac{1\times 14+1}{14}.

$$\frac{\left(1\times 21+4\right)\times 14}{21\left(1\times 14+1\right)}+\frac{1}{3}$$

Cancel out 7 in both numerator and denominator.

$$\frac{2\left(4+21\right)}{3\left(1+14\right)}+\frac{1}{3}$$

Add 4 and 21 to get 25.

$$\frac{2\times 25}{3\left(1+14\right)}+\frac{1}{3}$$

Multiply 2 and 25 to get 50.

$$\frac{50}{3\left(1+14\right)}+\frac{1}{3}$$

Add 1 and 14 to get 15.

$$\frac{50}{3\times 15}+\frac{1}{3}$$

Multiply 3 and 15 to get 45.

$$\frac{50}{45}+\frac{1}{3}$$

Reduce the fraction \frac{50}{45} to lowest terms by extracting and canceling out 5.

$$\frac{10}{9}+\frac{1}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{10}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{10}{9}+\frac{3}{9}$$

Since \frac{10}{9} and \frac{3}{9} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{9}$$

Add 10 and 3 to get 13.

$$\frac{13}{9}$$

Factor

$$\frac{13}{3 ^ {2}} = 1\frac{4}{9} = 1.4444444444444444$$