Solve 21/7+113/14+35/21

$$2 \frac { 1 } { 7 } + 1 \frac { 13 } { 14 } + 3 \frac { 5 } { 21 }$$

Evaluate

$$\frac{307}{42}\approx 7.30952381$$

Solution Steps

Multiply 2 and 7 to get 14.

$$\frac{14+1}{7}+\frac{1\times 14+13}{14}+\frac{3\times 21+5}{21}$$

Add 14 and 1 to get 15.

$$\frac{15}{7}+\frac{1\times 14+13}{14}+\frac{3\times 21+5}{21}$$

Multiply 1 and 14 to get 14.

$$\frac{15}{7}+\frac{14+13}{14}+\frac{3\times 21+5}{21}$$

Add 14 and 13 to get 27.

$$\frac{15}{7}+\frac{27}{14}+\frac{3\times 21+5}{21}$$

Least common multiple of 7 and 14 is 14. Convert \frac{15}{7} and \frac{27}{14} to fractions with denominator 14.

$$\frac{30}{14}+\frac{27}{14}+\frac{3\times 21+5}{21}$$

Since \frac{30}{14} and \frac{27}{14} have the same denominator, add them by adding their numerators.

$$\frac{30+27}{14}+\frac{3\times 21+5}{21}$$

Add 30 and 27 to get 57.

$$\frac{57}{14}+\frac{3\times 21+5}{21}$$

Multiply 3 and 21 to get 63.

$$\frac{57}{14}+\frac{63+5}{21}$$

Add 63 and 5 to get 68.

$$\frac{57}{14}+\frac{68}{21}$$

Least common multiple of 14 and 21 is 42. Convert \frac{57}{14} and \frac{68}{21} to fractions with denominator 42.

$$\frac{171}{42}+\frac{136}{42}$$

Since \frac{171}{42} and \frac{136}{42} have the same denominator, add them by adding their numerators.

$$\frac{171+136}{42}$$

Add 171 and 136 to get 307.

$$\frac{307}{42}$$

Factor

$$\frac{307}{2 \cdot 3 \cdot 7} = 7\frac{13}{42} = 7.309523809523809$$