Final answer:
The rational number halfway between ⅛ and ⅝ is ½. This is found by converting both fractions to have the common denominator of 12 and then averaging their numerators.
Step-by-step explanation:
To find the rational number halfway between ⅛ and ⅝, we first need to find a common denominator. The least common denominator of 4 and 6 is 12. Hence, we convert ⅛ to ⅛ × ⅓/⅓ = ⅓/⅗ and ⅝ to ⅝ × ⅒/⅒ = ⅒/⅗.
Next, we find the average of these two new fractions to get the number halfway between them: (⅓/⅗ + ⅒/⅗) / ⅒ = (⅔/⅗) / ⅒ = ⅔/⅚ = ½. Thus, the rational number halfway between ⅛ and ⅝ is ½.
To check, you can ensure that both fractions are indeed the same distance away from ½ by calculating their difference with ½: ⅛ - ½ = ⅓/⅗ - ⅖/⅗ = -¼ and ½ - ⅝ = ⅖/⅗ - ⅒/⅗ = ¼, showing they are both ¼ away from ½.