I think a problem for many people with fractions is that there are many different ways to think of them. Numbers, slices of a pie, divisions, ratios, scales, qu

I think a problem for many people with fractions is that there are many different ways to think of them. Numbers, slices of a pie, divisions, ratios, scales, quantities of non-whole units. This is a benefit: you can think of them in the most convenient way for what you are doing at a given moment. But I think it confuses people. I wonder if it would be helpful to ban the division sign ÷. Often when I ask a young person what is 8/4 they will say 2/1 (great, they know how to simply fractions!). But 8 divided by 4 goes exactly, and you can just do that. First present division of natural numbers with natural number answers as e.g. 18/6 = 3. Then present 1/2 ???!!! But wait, one object split equally between two people means each person gets half of the object. So 1/2 is a half.