Hints:

1. Why can’t 5 be one of the numbers used?

2. Why can’t 7 be one of the numbers used?

3. Try looking for compatible denominators—what values allow the fractions to combine neatly?

Solution:

To narrow down the possibilities, notice a few key constraints:

• Improper fractions can’t be used—so all fractions must be less than 1.

• The fractions must be equal and expressed using single-digit numerators and denominators.

• Denominator 5 cannot be used: any fraction with 5 as a denominator would require another 5 or a 0 to make an equivalent fraction using only single digits, which is not possible.

Strategy:

We’re looking for sets of equal fractions formed by two or more different single-digit fractions. Start by exploring pairs of denominators and checking whether the resulting fractions are equal.

Testing Fraction Pairs (Denominator combinations):

• 4 & 8:

  • 1/4=2/8​ ❌ (but 2 is not equal to 1)

  • 2/4=4/8​ ❌

  • 3/4=6/8=9/12​ ✅

• 2 & 8:

  • 1/2=4/8 ❌ (numerators don’t match)

• 6 & 8:

  • 3/6=4/8​ ❌

• 3 & 6:

  • 1/3=2/6​ ❌

  • 2/3=4/6​ ❌

• 4 & 6:

  • 2/4=3/6=9/18✅

Valid Solutions:

We find two valid sets of equal single-digit fractions:

1. 3/4=6/8=9/12​

2. 2/4=3/6=9/18​

Conclusion:

There are exactly two sets of equal fractions that use only single-digit numerators and denominators:

• 3/4=6/8=9/12​​

• 2/4=3/6=9/18​​

These sets are found by checking pairs with compatible denominators and ensuring all values remain within single-digit limits.