7 and 6/7 + 6 and 5/49 + 3/98 + 1 and 6/7 = n?

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 + 398 + 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/