Question

Let m&n = m/n + n/m for all integers m,n ≠ 0. What is the value of 5 & 8?

Answer 1

To find the value of 5 & 8, we substitute m = 5 and n = 8 into the expression m&n = m/n + n/m.

m/n = 5/8
n/m = 8/5

Therefore, 5 & 8 = 5/8 + 8/5.

To add these fractions, we need a common denominator. The common denominator is 5 * 8 = 40.

(5/8)(5/5) = 25/40
(8/5)(8/8) = 64/40

Now we can add the fractions:

25/40 + 64/40 = (25 + 64)/40 = 89/40.

Thus, the value of 5 & 8 is 89/40.