Adding tenths to hundredths

So what we're going to try to do in this video is add 7 tenths to 13 hundredths. Pause this video and see if you can figure what that is.

All right, so this might be a little bit intimidating at first because we're adding tenths here, seven tenths, and we're adding hundredths here, thirteen hundredths. How do I add a certain number of tenths to a certain number of hundredths? The key idea is to re-express seven tenths as a certain number of hundredths.

So how do we do that? Well, let's just first visualize each of these fractions. So seven tenths, 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 seven tenths.

Thirteen hundredths, you could split the whole into a hundred equal sections, and I tried to hand draw it. So assume that these are a hundred equal sections. Notice this is a ten by ten square, and so you're going to have a hundred of these squares. Notice we have ten plus three; that's thirteen filled in.

So we want to add seven tenths to these thirteen hundredths. Now, how do we express seven tenths in terms of hundreds? 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 10 times as many things in the denominator, and you also have 10 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 10 and we multiplied the denominator by 10. If you do the same thing to the numerator and the denominator, if you multiply or divide it by the same number, you're not changing the value. Think about it; 10 over 10 is the same thing as 1.

So we're just taking 1 and multiplying it by 7 tenths isn't going to change the value. But this is, as we've already talked about, equivalent to 70 over 100. So this is equal to 70 hundredths, which is this right over here, plus 13 hundredths.

Plus 13 hundredths. Well, now we're adding hundredths 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 thing.

So this is going to be 70. Let me do that in the same color. This is going to be equal to 70 plus 13 plus 13 hundredths; 70 plus 13 hundredths.

And what's 70 plus 13? Well, that of course is going to be 83 hundredths. And we are done.