Which is larger: three quarters or five eighths? Looking only at the numerators suggests five, while looking only at the denominators creates another guess. Fractions describe parts of a whole, so the size of those parts matters.
Start with two equal-sized paper strips. Divide one into four equal parts and shade three. Divide the other into eight equal parts and shade five. Keeping the wholes equal is essential; a fraction of a larger object cannot be compared visually with a fraction of a smaller one without accounting for that difference.
Make the pieces comparable
Divide each quarter on the first strip into two equal pieces. The shaded amount has not changed, but it is now six eighths. Six eighths is larger than five eighths because both are measured using the same-sized pieces.
In symbols, 3/4 = 6/8, and 6/8 > 5/8. Multiplying the numerator and denominator by the same nonzero number changes the way the fraction is written, not the quantity it represents.
Try another pair
Compare 2/3 and 3/5 using fifteenths. Two thirds becomes 10/15, while three fifths becomes 9/15. The first fraction is therefore larger. Check the result with a rough visual estimate: both are above one half, and two thirds is a little further above it.
A common denominator does not always have to be the smallest possible one to produce a correct comparison. A convenient shared denominator can work, though unnecessarily large numbers make arithmetic harder.
When a learner gets stuck, ask them to explain what the denominator tells us about the pieces. The aim is more than remembering a procedure. If they can show why the shaded amount stays the same when the pieces are subdivided, they have a reason for trusting the calculation.