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Hi, this is Julie Harland and I'm your math gal.
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Please visit my website at yourmathgal.com where you could search for any of my videos organized by topic.
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On this video we do the following six problems.
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Alright, we're going to learn how to subtract a fraction or a mixed number from a whole number.
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First you have to remember how to change a whole number to a fraction and see my video on that if you're not sure how to do that.
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But here's a quick review. Let's say you've got the number eight and you want to write it as a fraction. There's two ways of doing it.
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One way is to begin by just writing it as eight over one and then multiplying it by something to make an equivalent fraction with the denominator that you want.
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So let's say you wanted a denominator of five. So what would you multiply one times to get five?
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You'd have one times five and whatever you multiply the denominator by, you multiply the numerator by so that you're just taking that number eight and multiplying by one.
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So your new numerator is 40.
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So that's a quick review of how to write the number eight as a fraction with the denominator of five. The other way of doing it is say if I want to write eight with the denominator of five, you have to figure out what goes up in the numerator is just going to be five times eight.
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And then make sure that your answer makes sense is 40 divided by five the same as eight. Yes it is.
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Okay so that's a little quick review of how to write a whole number as a fraction that has a certain denominator.
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All right so now let's take a problem using this idea. Let's take eight minus and let's first just subtract a fraction.
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So let's do eight minus five six. There's a couple of ways of doing this. One way is thinking well eight is really the same thing as seven plus one.
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So I could think of that as seven right eight is the same thing as seven but I could think of it as seven plus one right and seven plus one. Well instead of writing one, how about if I write it with the same denominator as I have for the five six.
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So I want to write the number one as six six. So this becomes seven and six six minus five six. Now look at this carefully. See if that makes sense to you.
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Eight is the same thing as seven and six six because that's the same thing as seven plus one.
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So now how am I going to do this? I got seven and six six minus five six. Well I still have seven.
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And then I just got to go six six minus five six which is one six. So that's one way of doing it.
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Right another way of doing it is just changing the eight to a fraction right off the bat.
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So five six I'm going to leave as is but eight, how can I write that as something over six using this little idea up here?
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I would multiply eight times six, 48.
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So now if you do it this way you might have bigger numbers to subtract but a lot of people find this easier than this kind of borrowing idea rewriting seven.
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I mean rewriting eight is seven and six six. So now what do I have? Well I've got the denominator of six and then 48 minus five is 43.
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And that's the correct answer by the way. Just like this is a correct answer.
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Because one is just written as an improper fraction, 43 over six and the other one's written as a mixed number but they're exactly the same thing.
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So I've taken a whole number eight and subtracted a fraction from it.
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Right let's have you try one. How about six minus three fours.
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Now I've shown you two ways to do it. It really doesn't matter which way you do it but you know usually people find one way easier for them over a different way so that's really up to you.
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So try this on your own by putting the video on pause.
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Okay one method is to just change both of them to just fractions so I'd have to change six to a fraction right.
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So now I'm going to do it as fourths so I have the same denominators I have over here and what would go in the numerator there?
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24 because 24 divided by four is six right.
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So then I have a common denominator and I just have to subtract the numerators. 24 minus three is 21.
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Now you could do this in a vertical fashion by the way. It doesn't really matter. Some people like to subtract going up and down.
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Then you would just change this to 24 fours minus three fours again options.
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So you will say why do you show me more than one way just show me one way and it's like well it's because there isn't one easiest way for everybody.
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Alright now what's the other method we use for six minus three fours? Well I could take six and remember six of the same thing is five plus one.
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So I'm going to write that five and I'm going to write the one as four fours because I want to have the same denominator as I have for the other fraction which is the three fours.
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So I've got five and four fours minus three fours. Okay so I still have five and one fourth.
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This time the answer is coming up as a mix number because of writing this is a mix number still.
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But again the same thing is 21 fourths and also this could have been written in vertical format as well.
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Five and four fours minus three fours and you still would have gotten the five and one fourth for your answer.
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Some people can do this in their head they think well six minus three fours.
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Well one way of thinking about subtraction is what do you add to three fours to get six and if I added one fourth to three fours I would have one.
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So if I add a fourth and then five more get me six. That's okay.
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Hey if you get the right answer and it makes sense to you that works.
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If not go ahead and use the method I just showed you.
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Alright let's try a different one now.
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This time I'm subtracting a mix number from a whole number and I'm doing it in vertical form. It's usually easier for most people.
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Okay so if I could do eight minus two and then zero minus four sevens but there's a problem here.
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Zero minus four sevens you're going to get a negative number.
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So let's not go there although there is a way of doing that as well.
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How about we just change both of these to fractions.
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So this is one method change both of them to fractions having the same denominator.
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Since the two and four sevens is the one with the denominator we'll make that sevens and then we need to also make eight in terms of sevens.
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So what does that give me? Well in the top how do I change the whole number eight to a fraction with seven?
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I got to do seven times eight for my numerator. That's 56.
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Alright two and four sevens how do I change that to an improper fraction?
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Seven times two is 14 plus four is 18.
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And now I could subtract so I'm going to have sevens and I've got to do 56 minus 18.
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So that's 38 sevens.
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Or if you change it to a mixed number that's going to be let's see five and three sevens.
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Alright so that's by just changing each of them to improper fractions.
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Now some people what I just said a minute ago can do this in their head.
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They're going to say well what do I have to add to two and four sevens to get back up to eight?
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Well if I add three sevens that gives me one right?
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Plus I have two more already so if I add all this together so it gives me one plus three more and then five more will get you back up to eight.
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That's kind of a way of doing it in your head reasoning it out a little bit differently.
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Just wanted to show you that that is a perfectly okay way to get the answer.
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Okay now the other way of doing it is with the borrowing technique eight and four eight minus two and four sevens.
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Alright we're going to borrow from the eight and make it one.
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So it's seven plus one think of it seven plus one.
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So now I have seven and I want to write the one is having as a fraction with the same denominator I have down here which will be sevens.
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Oops what happened here.
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Sorry.
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Let's get that back to seven.
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Okay so I'm going to have seven and what seven sevens right?
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So I'm going to have the same denominator minus two and four sevens.
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So right now do the seven minus two which is five and seven sevens minus four sevens is three sevens and we get it again.
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So as you can see there's just different ways to do it but you don't need to know how to do it all of the different ways what you have to do is try at least one problem be able to get it right.
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You know use one method and if you want to stick with that method this first method here where you change both to improper fractions I think more people like doing it that way.
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Okay but you know depends on the person.
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Okay here's one for you to try how about nine minus three and one eighth.
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Try any method you want see if you can get the right answer.
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Okay hopefully you put the video on pause and now you're ready to go.
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All right first of all I'm just going to show you the way of reasoning it out.
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What do I have to add to one eighths to get one?
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I need seven eighths more so that adds up to one so far plus three more is four plus what will give you nine five.
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All right so the answer is going to be five and seven eighths so if you got five and seven eighths using some method that's the correct answer if you'd written a result mix number.
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Okay let's do it by changing each to improper fractions.
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So when you write a whole number as a fraction you're writing it as an improper fraction.
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So what will go up in the numerator here it's going to be eight times nine seventy two and then we have eight times three is twenty four plus one is twenty five.
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And now I could subtract and let's see I think that's forty seven eighths.
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Okay and then the question is are these the same and yes they are.
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If you change five and seven eighths to an improper fraction you would get forty seven eighths and if you change forty seven eighths to a mix number you'd have five and seven eighths.
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So I just showed you two ways to do it.
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And of course you could do the borrowing method just for fun those of you like that way.
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You would borrow an ad one. Now to take less room how about instead of writing one we just write with the improper fractions going to be we could write we want to write it in eights so it'll be eight eighths.
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So that would give you eight minus three is five and eight eighths minus one eighths is seven eighths okay there we go again.
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So sort of showed you a few ways that you might get the answer and all of these are correct it doesn't matter if you write it is five and seven eighths or forty seven eighths it doesn't matter if you reason out the answer if you change to improper fractions and subtract or if you use borrowing get a common denominator.
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We're all ending up at the same place the answer is five and seven eighths.
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Here are three problems for you to try so let's put the video on pause and try these three problems using any method.
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Okay you back. All right so let's just I'm just going to write the answers not show all the work this time because there's of course three or four different ways to do it.
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Seven minus four fifths is six and one fifth if you wrote it as a mixed number or thirty one fifths if you wrote it as an improper fraction nine minus five and two thirds is three and one third if you wrote it as a mixed number or ten thirds if you wrote it as a fraction and improper fraction and six minus one and a half is four and a half.
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Or nine halves the way I did this was just by reasoning it out by the way I just figured out seven minus four fifths I'm going to figure out what I have to add to that to get back up to seven.
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So that's the method I actually use but you can do it by getting the improper you know fractions writing the whole numbers you know as fractions etc.
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you could do the borrowing method or you can reason out the answer and the way to check your answer is if you add the answer back to what you're subtracting you should get back to the original number.
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So for instance if you add four fifths and six and one fifth does that add up to seven well that would be six and five fifths or six plus one with to seven.
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If you add five and two thirds plus three and one third you would get eight and three thirds which is eight plus one adds up to nine and one and a half plus four and a half same reasoning add up to six.
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So that's how you could tell you got the right answer. So it doesn't matter if you write your answer as mixed number or improper fraction but in this case it was easier to check by taking the mixed number.
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Okay keep practicing.
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Please visit my website at yourmathgal.com where you can view all of my videos which are organized by topic.