Fractions with denominators of 10 and 100
Let's see if we can add 3/10 to 7/100. And I encourage you to try adding these two fractions on your own first before I work through it, and I'll give you one hint. Right now, it's very hard to add these fractions. You're adding 3/10 to 7/100. You're adding two different fractions with two different denominators. So what I would encourage you to do is try to rewrite 3/10 in a way that it has 100 as a denominator, or so it's expressed in terms of hundredths, and then see if you can add them. Well, I'm assuming you've given a go at it. Let's see how we can rewrite 3/10, and I'll try to visualize it. So what I've done here, so this you could consider a whole, and this is a whole as well. And this whole is divided into tenths-- 1,2, 3, 4, 5, 6, 7, 8, 9, 10. So what would 3/10 look like? Well, it would be one, two, and three of the tenths. Now, what would happen if you took each of those tenths and you divided them into 10 more sections? So you're essentially taking each of those tenths and you're dividing them into 10 sections. Well, you have 10 sections and then each of them will have 10 subsections in it. So you're going to have hundredths. Then the sections are going to describe hundredths. So 10-- let me write it this way. 10 times 10. You are then going to have hundredths. And 3/10 would be equivalent to how many of these hundredths? Well, each of these tenths will now become 10. So you're going to have 10, 20, and-- let me color them in better. So that's 10, 20, and then 30 hundredths. So this part right over here. This-- let me get my tool right-- this part right over here, this is going to be 3 times 10, which is going to be equal to 30. 10 times 10 is equal to 100. So this is how we're going to change the denominator. Instead of thinking in terms of tenths, we're going to think in terms of hundredths. And now our numerator, 3/10, is equivalent to 30 hundredths so we can rewrite this fraction. We essentially multiplied the numerator by 10, and we multiplied the denominator by 10, which didn't change the value of the fraction. It still represents the same-- it still represents 3/10 of the whole. So when you do that, you end up-- we can rewrite this thing as 30 over 100. Three tenths is equivalent to 30 over 100. We add that to 7 over 100. Or another way of thinking about it, three tenths is the same thing as 30 hundredths. And we add that to 7 hundredths. Well, now we're going to have 30 plus 7 hundredths. So now, we're going to have 30 plus 7 hundredths. Or we could say that this is now going to be 37 hundredths. So this extra 7 that we're adding here-- maybe I'll do this in-- that's the same color. This extra sevenths-- let me do this in a new color. This 7 hundredths that we're adding, that's going to be one, two-- let me paint that in a little bit clearer. So that's 1, 2, so it gets us all the way to 7. Let's see, 1, 2, 3, so 7 hundredths is right over there. So let me get back to my pen. So that, whoops, this right over here is 7 out of the 100 so 30/100 plus 7/100 is going to get us to 37/100.