Solve 3/7+7/16+9/16+21/14

$$\frac { 3 } { 7 } + \frac { 7 } { 16 } + \frac { 9 } { 16 } + 2 \frac { 1 } { 14 }$$

Evaluate

$$\frac{7}{2}=3.5$$

Solution Steps

Least common multiple of 7 and 16 is 112. Convert \frac{3}{7} and \frac{7}{16} to fractions with denominator 112.

$$\frac{48}{112}+\frac{49}{112}+\frac{9}{16}+\frac{2\times 14+1}{14}$$

Since \frac{48}{112} and \frac{49}{112} have the same denominator, add them by adding their numerators.

$$\frac{48+49}{112}+\frac{9}{16}+\frac{2\times 14+1}{14}$$

Add 48 and 49 to get 97.

$$\frac{97}{112}+\frac{9}{16}+\frac{2\times 14+1}{14}$$

Least common multiple of 112 and 16 is 112. Convert \frac{97}{112} and \frac{9}{16} to fractions with denominator 112.

$$\frac{97}{112}+\frac{63}{112}+\frac{2\times 14+1}{14}$$

Since \frac{97}{112} and \frac{63}{112} have the same denominator, add them by adding their numerators.

$$\frac{97+63}{112}+\frac{2\times 14+1}{14}$$

Add 97 and 63 to get 160.

$$\frac{160}{112}+\frac{2\times 14+1}{14}$$

Reduce the fraction \frac{160}{112} to lowest terms by extracting and canceling out 16.

$$\frac{10}{7}+\frac{2\times 14+1}{14}$$

Multiply 2 and 14 to get 28.

$$\frac{10}{7}+\frac{28+1}{14}$$

Add 28 and 1 to get 29.

$$\frac{10}{7}+\frac{29}{14}$$

Least common multiple of 7 and 14 is 14. Convert \frac{10}{7} and \frac{29}{14} to fractions with denominator 14.

$$\frac{20}{14}+\frac{29}{14}$$

Since \frac{20}{14} and \frac{29}{14} have the same denominator, add them by adding their numerators.

$$\frac{20+29}{14}$$

Add 20 and 29 to get 49.

$$\frac{49}{14}$$

Reduce the fraction \frac{49}{14} to lowest terms by extracting and canceling out 7.

$$\frac{7}{2}$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$