Fractions with denominators of 10 and 100
- [Instructor] So what we're going to try to do in this video is add 7/10 to 13/100, pause this video and see if you can figure what that is. Alright so despite being a little bit intimidating at first because we're adding tenths here, 7/10 and we're adding hundredths here 13/100, how do I add a certain number of tenths to a certain number of hundredths? The key idea is to re-express 7/10 as a certain number of hundredths, so how do we do that? Well let's just first visualize each of these fractions. So 7/10 if we imagine this square is a whole and that we've divided it into ten equal sections I tried to hand draw it as best as I can, notice I have filled in seven of those ten equal sections that we have split the whole into. So this represents 7/10 and 13/100 you could split the whole into 100 equal sections and I tried to hand draw it, let's assume that these are 100 equal sections. And so notice this is a ten by ten square, it's got 100 of these squares and notice we have ten plus three 13 filled in so we want to add these 7/10 to these 13/100. Now how do we express 7/10 in terms of hundredths? Well visually you could take each of your tenths and split them into ten equal sections, now you have your whole split into hundredths and each of your tenths is now a hundredth so you have ten times as many things in the denominator and you also have ten times as many things in the numerator. Before you had seven of the tenths filled in, now you have 70 of the hundredths filled in. Or another way to think about it, we multiplied the numerator by ten and the we multiplied the denominator by ten. And if you do the same thing to the numerator and the denominator, you multiply or divide it by the same number, you're not changing the value, think about it, ten over ten is the same thing as one, so we're just taking one and multiplying it by 7/10 isn't going to change the value. But this is as we already talked about this is equivalent to 70/100, so this is equal to 70/100 which is this right over here plus 13/100, plus 13/100. Well now we're adding 100s in both cases, if I have 70 of something and I add to that 13 of the same somethings in this case the something is hundredths, I'm going to have 83 of that so this is going to be 70, get the same color, this is going to be equal to 70 plus 13, plus 13/100. 70 plus 13/100 and what's 70 plus 13, well that of course is going to be 83/100. And we are done.