To find the answer to this question, it is better to group integers and fractions. Remember that 7 and ^{6}/_{7} is the same as 7+ ^{6}/_{7}, for example.

7 and ^{6}/_{7} + 6 and ^{5}/_{49} + ^{3}/_{98} + 1 and ^{6}/_{7} =

7 + ^{6}/_{7} + 6 + ^{5}/_{49} + ^{3}_{98} + 1 + ^{6}/_{7} =

7 + 6 + 1 + ^{6}/_{7} + ^{5}/_{49} + ^{3}/_{98} + ^{6}/_{7} =

14 + ^{6}/_{7} + ^{6}/_{7} + ^{5}/_{49} + ^{3}/_{98} =

14 + ^{12}/_{7} + ^{5}/_{49} + ^{3}/_{98} =

Note that the LCM (least commom multiple) of all denominators is 98. So, we can rewrite the expression as

14 + ^{(14 x 12)}/_{98} + ^{(2 x 5)}/_{98} + ^{3}_{/98} =

14 + ^{(14 x 12 + 2 x 5 + 3)}/_{98} =

14 + ^{(168 + 10 + 3)}/_{98} =

finally:

7 and ^{6}/_{7} + 6 and ^{5}/_{49} + ^{3}/_{98} + 1 and ^{6}/_{7} = **14 + **^{181}/_{98} (answer)

This last expression can be expressed as a decimal

14 + ^{181}/_{98} = 15,84693877551

Note: The Least Common Multiple (LCM) for 7, 49 and 98, notation LCM(7,49,98), is 98.

Explanation:

- Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, ..., 98
- Multiples of 49: 49, 98
- Multiples of 98: 98

Because 98 is the first number to appear on both lists of multiples, 98 is the LCM of 7, 49 and 98.

Reference: http://coolconversion.com/math/lcm/