Solve 21*(3/7+1/2)*1/21

$$21 \times ( \frac{ 3 }{ 7 } + \frac{ 1 }{ 2 } ) \times \frac{ 1 }{ 21 }$$

Evaluate

$$\frac{13}{14}\approx 0.928571429$$

Solution Steps

Least common multiple of 7 and 2 is 14. Convert \frac{3}{7} and \frac{1}{2} to fractions with denominator 14.

$$21\left(\frac{6}{14}+\frac{7}{14}\right)\times \frac{1}{21}$$

Since \frac{6}{14} and \frac{7}{14} have the same denominator, add them by adding their numerators.

$$21\times \frac{6+7}{14}\times \frac{1}{21}$$

Add 6 and 7 to get 13.

$$21\times \frac{13}{14}\times \frac{1}{21}$$

Express 21\times \frac{13}{14} as a single fraction.

$$\frac{21\times 13}{14}\times \frac{1}{21}$$

Multiply 21 and 13 to get 273.

$$\frac{273}{14}\times \frac{1}{21}$$

Reduce the fraction \frac{273}{14} to lowest terms by extracting and canceling out 7.

$$\frac{39}{2}\times \frac{1}{21}$$

Multiply \frac{39}{2} times \frac{1}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39\times 1}{2\times 21}$$

Do the multiplications in the fraction \frac{39\times 1}{2\times 21}.

$$\frac{39}{42}$$

Reduce the fraction \frac{39}{42} to lowest terms by extracting and canceling out 3.

$$\frac{13}{14}$$

Factor

$$\frac{13}{2 \cdot 7} = 0.9285714285714286$$