Expert: Josh - 11/5/2009

Question
By looking at the denominator and the numerator how can you tell if the fraction is greater or less than 1/2?

Answer
Hi Crystal,

There are several ways to answer this question. The best answer for you would depend on your knowledge and maths experience. A particular answer will not work for everyone.

Answer 1: One can tell from experience. As you gain more exposure to simple fractions, e.g., 1/3, 1/4, 2/5 etc., the answer becomes more intuitive. You can visualize in your mind what proportion is represented by a given fraction. For example, if 1/2 is 50%, 1/4 is 25%, then 1/3 is somewhere in between.

Answer 2: A sure way to checking this is by using a calculator, or through long division. But usually, intuition works best. With something like 7/18 for instance, half of 18 is 9. So, the numerator has got to be larger than 9 (at least 10/18) to exceed a half.

Answer 3: A more formal approach is by considering an inequality.
Suppose we want to check whether 3/8 is greater than 1/2.
If TRUE, then we must have 3/8 > 1/2.
Using "cross-multiplication" (do a search on Google if you want to see examples), we get 3 x 2 = 6 on the left hand side and 1 x 8 = 8 on the right hand side. We yield a contradiction, as 6 is clearly NOT greater than 8. So, our original assumption was wrong. 3/8 is NOT greater than 1/2.

Another example: Is 5/8 greater than 1/2?
If TRUE, then we must have 5/8 > 1/2.
Using "cross-multiplication", we get 5 x 2 = 10 on the left hand side and 1 x 8 = 8 on the right hand side. This time, it checks out. So, our original assumption was right. 5/8 is greater than 1/2.