Solve 1/4+1/9+31/7

$$\frac { 1 } { 4 } + \frac { 1 } { 9 } + 3 \frac { 1 } { 7 }$$

Evaluate

$$\frac{883}{252}\approx 3.503968254$$

Solution Steps

Least common multiple of 4 and 9 is 36. Convert \frac{1}{4} and \frac{1}{9} to fractions with denominator 36.

$$\frac{9}{36}+\frac{4}{36}+\frac{3\times 7+1}{7}$$

Since \frac{9}{36} and \frac{4}{36} have the same denominator, add them by adding their numerators.

$$\frac{9+4}{36}+\frac{3\times 7+1}{7}$$

Add 9 and 4 to get 13.

$$\frac{13}{36}+\frac{3\times 7+1}{7}$$

Multiply 3 and 7 to get 21.

$$\frac{13}{36}+\frac{21+1}{7}$$

Add 21 and 1 to get 22.

$$\frac{13}{36}+\frac{22}{7}$$

Least common multiple of 36 and 7 is 252. Convert \frac{13}{36} and \frac{22}{7} to fractions with denominator 252.

$$\frac{91}{252}+\frac{792}{252}$$

Since \frac{91}{252} and \frac{792}{252} have the same denominator, add them by adding their numerators.

$$\frac{91+792}{252}$$

Add 91 and 792 to get 883.

$$\frac{883}{252}$$

Factor

$$\frac{883}{2 ^ {2} \cdot 3 ^ {2} \cdot 7} = 3\frac{127}{252} = 3.503968253968254$$