Adding fractions: 7/10+13/100

so we're going to try to do in this video is add 7/10 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 hundreds here 1300s how do I add a certain number of tenths to a certain number of hundreds and the key idea is to reexpress 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 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 hole into so this represents seven tenths and thirteen hundredths you could split the hole into a hundred equal sections and I try to draw and draw it so assume that these are a hundred equal sections and so notice this is a 10 by 10 square and so you're gonna have a hundred of these squares and notice we have 10 plus 3 13 filled in so we want to add these 7 tenths to these 1300s now how do we express 7/10 in terms of hundredths well visually you could take each of your tenths and split them into 10 equal sections now you have your whole split into hundredths and each of your tenths is now a hundredths 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 and if you do the same thing to the numerator and the denominator you multiply it 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 7/10 isn't going to change the value but this is as we've already talked about this is equivalent to 70 over 100 so this is equal to 70 hundredths which is this right over here plus 13 hundredths plus 1300s well now we're adding hundredths in both cases if I have 70 of something and I add to that 13 of the same thumb things in this case the something is hundredths I'm gonna have 83 of that thing so this is going to be 70 let me do that same color this is going to be equal to 70 plus 13 plus 13 hundredths 70 plus 1300s and what's the 70 plus 13 well that of course is going to be 83 hundredths and we are done