How To Add Fractions And Whole Numbers With Different Denominators

let's think about how orwhat 1/2 times 5 represents. so one way to think about it isthat this could be five 1/2's added together. so you could view thisas 1/2 plus 1/2 plus 1/2 plus 1/2 plus 1/2, which is thesame thing as 1 plus 1 plus 1

How To Add Fractions And Whole Numbers With Different Denominators, plus 1 plus 1, over 2,which is equal to 5/2. the other way tothink about this is that you start with 5 things. so let's say, that's 1 thing.

let me copy and paste thatso they all look the same. so then let me paste it. so that's 2 things. that's 3 things. that's 4 things. and that's 5 things. so the other way to think aboutit is you start with 5 things, and you take 1/2 of them. so what would be 1/2 of this?

well, let's see. you have 5 things, so youwould get-- 5 divided by 2 would be 2 and 1/2. so 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 thesame thing as 5/2?

well, what happens if wedivide each of these wholes into halves? so let's do that. so if we just multiplied-- sowe just divide each of these into 2. so instead of having 5wholes, we now have 10 halves. how many of those halveshave we filled in? well, we have filledin 1, 2, 3, 4, 5. so this is also equal to 5/2.

so far we just did itthinking about what multiplication actually means. but if you said, well,how did i compute this? well, the way youcould think about it, and multiplyingfractions is actually straightforward fromthat point of view, is as long as you can expressboth of them as fractions, and 5 we already know isthe same thing as 5 ones, so this we can justmultiply times 5/1.

so now that i've expressedboth of them as fractions, i can just multiplythe numerator. so 1 times 5 over 2 times 1. and what's thatgoing to be equal to? well, 1 times 5 is 5. 2 times 1 is 2. so once again, we get 5/2.