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Find the rational number halfway between (1)/(4)and (1)/(6) in each pair.

User Vikscool
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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.

User Tvorog
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