Two fractions are equivalent when they describe the same amount, like 1/2 and 3/6 — you get from one to the other by multiplying or dividing the numerator and the denominator by the same number. A fraction is in its simplest form when the two numbers share no common factor other than 1. The same idea lets you rewrite an improper fraction like 17/5 as the mixed number 3 2/5, and back again.
Worked example
Problem Express 18/24 in its simplest form.
Look for the highest common factor of 18 and 24 — it is 6.
Divide the numerator and the denominator by the same number: 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
So 18/24 = 3/4, and 3 and 4 share no common factor, so it is fully simplified.
Tip Dividing by a smaller common factor is not wrong — you just have to keep going until nothing divides both parts.