Solve 1/3-5/21+2/1*2/7

$$\frac{ 1 }{ 3 } - \frac{ 5 }{ 21 } + \frac{ 2 }{ 1 } \times \frac{ 2 }{ 7 }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Least common multiple of 3 and 21 is 21. Convert \frac{1}{3} and \frac{5}{21} to fractions with denominator 21.

$$\frac{7}{21}-\frac{5}{21}+\frac{2}{1}\times \frac{2}{7}$$

Since \frac{7}{21} and \frac{5}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-5}{21}+\frac{2}{1}\times \frac{2}{7}$$

Subtract 5 from 7 to get 2.

$$\frac{2}{21}+\frac{2}{1}\times \frac{2}{7}$$

Anything divided by one gives itself.

$$\frac{2}{21}+2\times \frac{2}{7}$$

Express 2\times \frac{2}{7} as a single fraction.

$$\frac{2}{21}+\frac{2\times 2}{7}$$

Multiply 2 and 2 to get 4.

$$\frac{2}{21}+\frac{4}{7}$$

Least common multiple of 21 and 7 is 21. Convert \frac{2}{21} and \frac{4}{7} to fractions with denominator 21.

$$\frac{2}{21}+\frac{12}{21}$$

Since \frac{2}{21} and \frac{12}{21} have the same denominator, add them by adding their numerators.

$$\frac{2+12}{21}$$

Add 2 and 12 to get 14.

$$\frac{14}{21}$$

Reduce the fraction \frac{14}{21} to lowest terms by extracting and canceling out 7.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$