Multiplying unit fractions and whole numbers

let's think about how or what 1/2 times 5 represents so one way to think about it is that this could be five one halfs added together so you could view this as 1/2 plus 1/2 plus 1/2 plus 1/2 plus 1/2 which is the same thing as 1 plus 1 plus 1 plus 1 plus 1 over 2 which is equal to 5 halves which is equal to 5 halves the other way to think about this is that you start with 5 things you start with 5 things you start with 5 things so let's say that's one thing let me copy and paste that so they all look the same so and then let me paste it so that's two things that's three things that's four things and that's five things so the other way to think about it is you start with five things and you take half of them so what would be half of this well let's see you have five things so you would mate you would get five divided by 2 would be two and a half but so you would get you would get this far let me make it like this so you would get this one you would get this one and you would get this one now is this the same thing as five halves well what happens if we divide each of these wholes in two halves so let's do that so if we just multiplied so we just divide each of these into two so we have instead of having five holes we now have ten halfs we now have 10 asks how many of those halves have we filled in well we have filled in one two three four five so this is also equal to this is also equal to five halves now if you're looking for how we could write now so far we just did it thinking about what multiplication actually means but if you said well you know how did I how did I compute this well the way you could think about it and multiplying fractions is actually straight forward from from that point of view is as long as you can express both of them as fractions and five we already know is the same thing as five ones so this we can just multiply times 5 over 1 5 over 1 so now that I've expressed both of them as fractions I can just multiply the numerator so 1 times 5 1 times 5 over over 2 times 1 over 2 times 1 and what's that going to be equal to well 1 times 5 is 5 2 times 1 is 2 2 times 1 is 2 so once again we get 5 halves