Solve 1/3*4+1/4+5+1/5+6+1/6+7

$$\frac { 1 } { 3 \times 4 } + \frac { 1 } { 4 + 5 } + \frac { 1 } { 5 + 6 } + \frac { 1 } { 6 + 7 }$$

Evaluate

$$\frac{1865}{5148}\approx 0.362276612$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{1}{12}+\frac{1}{4+5}+\frac{1}{5+6}+\frac{1}{6+7}$$

Add 4 and 5 to get 9.

$$\frac{1}{12}+\frac{1}{9}+\frac{1}{5+6}+\frac{1}{6+7}$$

Least common multiple of 12 and 9 is 36. Convert \frac{1}{12} and \frac{1}{9} to fractions with denominator 36.

$$\frac{3}{36}+\frac{4}{36}+\frac{1}{5+6}+\frac{1}{6+7}$$

Since \frac{3}{36} and \frac{4}{36} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{36}+\frac{1}{5+6}+\frac{1}{6+7}$$

Add 3 and 4 to get 7.

$$\frac{7}{36}+\frac{1}{5+6}+\frac{1}{6+7}$$

Add 5 and 6 to get 11.

$$\frac{7}{36}+\frac{1}{11}+\frac{1}{6+7}$$

Least common multiple of 36 and 11 is 396. Convert \frac{7}{36} and \frac{1}{11} to fractions with denominator 396.

$$\frac{77}{396}+\frac{36}{396}+\frac{1}{6+7}$$

Since \frac{77}{396} and \frac{36}{396} have the same denominator, add them by adding their numerators.

$$\frac{77+36}{396}+\frac{1}{6+7}$$

Add 77 and 36 to get 113.

$$\frac{113}{396}+\frac{1}{6+7}$$

Add 6 and 7 to get 13.

$$\frac{113}{396}+\frac{1}{13}$$

Least common multiple of 396 and 13 is 5148. Convert \frac{113}{396} and \frac{1}{13} to fractions with denominator 5148.

$$\frac{1469}{5148}+\frac{396}{5148}$$

Since \frac{1469}{5148} and \frac{396}{5148} have the same denominator, add them by adding their numerators.

$$\frac{1469+396}{5148}$$

Add 1469 and 396 to get 1865.

$$\frac{1865}{5148}$$

Factor

$$\frac{5 \cdot 373}{2 ^ {2} \cdot 3 ^ {2} \cdot 11 \cdot 13} = 0.3622766122766123$$