Adding fractions (denominators 10 & 100)

let's see if we can add 3/10 to 7 hundredths 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 have your adding 3/10 to 7 hundredths 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 a hundred 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 have done here so this you could consider a hole and this is a hole as well and this whole is divided into tenths 1 2 3 4 5 6 7 8 9 10 so what would three tenths look like well it would be 1 2 & 3 of the tenths 3 of the tents now what would happen if you turn it if you took each of those tenths and you divided them if you took each of those tents and you divided them into 10 more sections so you're essentially taking each of those tents and you're dividing them into ten sections well you have 10 sections and then each of them will have ten subsections in it so you're going to have you're going to have a hundredths then the sections are going to describe hundreds so ten we write it this way ten ten times ten times ten you're then going to have hundreds and 3/10 would be equivalent to how many of these hundredths well each of these tents will now become ten so you're going to have you're going to have ten twenty and we color them in better so that's 10 20 and then 30 hundredths so this part right over here this get my tool right this part right over here this is going to be three times ten three times ten which is going to be equal to thirty ten times ten is equal to 100 so this is how we're going to change the denominator instead of thinking in terms of ten so we're going to think in terms of hundredths and now our numerator the aquit 3/10 is equivalent to 30 hundredths so we can rewrite this fraction we essentially multiplied the numerator by 10 we 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 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 3/10 is equivalent to 30 over 100 we add that to 7 over 100 or another way of thinking about it 3/10 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 30 plus 7 hundredths 30 plus 7 hundredths or we could say that this is now going to be 37 hundredths 37 hundredths so this extra 7 that we're adding here maybe I'll do this in not that's the same color this extra sevenths let me do this in a new color this extra the 700s that we're adding that's going to be 1/2 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 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 hundred so 30 hundredths plus 7 hundredths is going to get us to 37 1 it's