Solve 31/7-14/9+21/14

$$3 \frac { 1 } { 7 } - 1 \frac { 4 } { 9 } + 2 \frac { 1 } { 14 }$$

Evaluate

$$\frac{475}{126}\approx 3.76984127$$

Solution Steps

Multiply 3 and 7 to get 21.

$$\frac{21+1}{7}-\frac{1\times 9+4}{9}+\frac{2\times 14+1}{14}$$

Add 21 and 1 to get 22.

$$\frac{22}{7}-\frac{1\times 9+4}{9}+\frac{2\times 14+1}{14}$$

Multiply 1 and 9 to get 9.

$$\frac{22}{7}-\frac{9+4}{9}+\frac{2\times 14+1}{14}$$

Add 9 and 4 to get 13.

$$\frac{22}{7}-\frac{13}{9}+\frac{2\times 14+1}{14}$$

Least common multiple of 7 and 9 is 63. Convert \frac{22}{7} and \frac{13}{9} to fractions with denominator 63.

$$\frac{198}{63}-\frac{91}{63}+\frac{2\times 14+1}{14}$$

Since \frac{198}{63} and \frac{91}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{198-91}{63}+\frac{2\times 14+1}{14}$$

Subtract 91 from 198 to get 107.

$$\frac{107}{63}+\frac{2\times 14+1}{14}$$

Multiply 2 and 14 to get 28.

$$\frac{107}{63}+\frac{28+1}{14}$$

Add 28 and 1 to get 29.

$$\frac{107}{63}+\frac{29}{14}$$

Least common multiple of 63 and 14 is 126. Convert \frac{107}{63} and \frac{29}{14} to fractions with denominator 126.

$$\frac{214}{126}+\frac{261}{126}$$

Since \frac{214}{126} and \frac{261}{126} have the same denominator, add them by adding their numerators.

$$\frac{214+261}{126}$$

Add 214 and 261 to get 475.

$$\frac{475}{126}$$

Factor

$$\frac{5 ^ {2} \cdot 19}{2 \cdot 3 ^ {2} \cdot 7} = 3\frac{97}{126} = 3.7698412698412698$$