Write all proper fractions whose sum of numerator and denominator is 12.

Question

KnowledgeBoat · Accepted Answer

A proper fraction has numerator less than denominator.

We need pairs of (numerator, denominator) such that numerator + denominator = 12 and numerator < denominator.

Numerator + denominator = 12 with numerator < denominator means numerator < 6.

The possible fractions are:

If numerator = 1, denominator = 11 → $\dfrac{1}{11}$ .

If numerator = 2, denominator = 10 → $\dfrac{2}{10}$ .

If numerator = 3, denominator = 9 → $\dfrac{3}{9}$ .

If numerator = 4, denominator = 8 → $\dfrac{4}{8}$ .

If numerator = 5, denominator = 7 → $\dfrac{5}{7}$ .

Hence, the proper fractions are: $\dfrac{1}{11}, \dfrac{2}{10}, \dfrac{3}{9}, \dfrac{4}{8}$ and $\dfrac{5}{7}$ .

Mathematics