Video transcript
We're asked to subtract and simplify the answer, and we have 8/18 minus 5/18. So subtracting fractions is very similar to adding fractions. If we have the same denominator, the denominator in the difference is going to be the same as the denominators in the two numbers that we're subtracting, so it's going to be 18. And our numerator is going to be the difference between the numerators. So in this case, it is 8 minus 5, and this will be equal to 3 over 18, which is the answer, but it's not completely simplified, because both 3 and 18 are divisible by 3. So let's divide them both by 3. So you divide 3 by 3, you divide 18 by 3, and you get 3 divided by 3 is 1. 18 divided by 3 is 6, so you get 1/6. And just to see this visually, let me draw 18 parts. Let me draw 18 parts here. So it might be a little bit of a messy drawing. I'll try the best I can. So let me draw six in this direction. So that is three right there. We have another three, so that's six parts. And then let me split this into three columns. So there we go. We have 18 parts. Now 8/18 is equal to one, two, three, four, five, six, seven, eight. That's 8/18. And now we want to subtract five of the eighteenths, so we subtract one, two, three, four, five. Now, what do we have left over? Well, we have three of the eighteenths left over, so you have that right there. You have three of the eighteenths left over. Now, if you turn three of the eighteenths into one piece, how many of those bigger pieces do you have? This is one of those big pieces. Now, where are the other ones? Well, this is another big piece right here. This is another big piece right here, another one, another one, and another one. If you had 18 pieces and you merged three of the pieces into one, then you actually end up with only six pieces. You end up with six pieces. Hopefully, you see that each row is one of the pieces now, and the blue is exactly one of the six, so 3/18 is the same as 1/6.
Video transcript
- [Voiceover] So we have the expression 17 4/9 minus 12 and 2/3. And I encourage to pause the video and see if you can figure out what this is. So now let's work through it. So what I'm going to do is I'm going to rewrite these mixed numbers. So I'm going to write this as 17 and 4/9 minus 12 and 2/3. I'm going to write the 12 right under the 17, and I'm going to write the 2/3 right under the 4/9. Let me make it very clear, we are subtracting 12 and 2/3 from 17 and 4/9. So the first thing that we might want to do is we could look at the fraction parts and we might want to start subtracting until we see, look, we have different denominators here. We have ninths and we have thirds. So the first thing we'd want to do is let's get to a common denominator, and a good common denominator would be the least common multiple of nine and three. Well, what's that going to be? Well to think about that, I like to start with a larger number, nine. And say, well, is that divisible by three? Well, yes, it is divisible by three. It is divisible by the other denominator, so this actually is the least common multiple. If it wasn't, I would keep taking higher and higher multiples of 9. I would go to 18 and then I would go to 27, and I would keep going until I found one that's divisible by three. But I didn't have to do that because nine is divisible by three. So I can rewrite both of these fraction parts in terms of ninths. Now the one on top already is written in terms of ninths, so I can just rewrite that. 17 and 4/9. And the one on the bottom, I can write as 12 and some number of ninths. So 2/3 is how many ninths? Well, to go from thirds to ninths I had to multiply by three, had to multiply by three, so the numerator, I need to multiply by three as well. Two times three is six. 2/3 is the same thing as 6/9. And now I can try to subtract. But even here, when I try to subtract, I have a larger fraction down here that I'm trying to subtract from a smaller one. I have 4/9 minus 6/9. So what can I do? Well, be answer is I can regroup. I can take a whole from the 17. Let me do that. So if I take a whole from the 17, that's going to become 16, and then that whole that I just took from, I guess you could say the whole number place, I can add it to the fraction. Well, a whole is just going to be 9/9. So all I did was I regrouped here. I took 9/9 from 17. 9/9 is one, so I took 9/9 from 17, I'm left with 16, and then I regrouped them and I added them to the fractions place, as one way to think about it. Well, what's 4/9 plus 9/9? Well, that's going to be 13/9. So this right over here is 13/9. 13/9. It's a very strange way to write it, but 17 and 4/9 is the same thing as 16 and 13/9, because notice, this is greater than one. This is the same thing as one and 4/9. One and 4/9 plus 16 is going to be 17 and 4/9. Now why did I do all of this? Well 13/9 is larger than 6/9, so I can subtract. What's 13/9 minus 6/9 going to be? Well, 13 of something, in this case, ninths, minus six of that same something is going to be 7/9. Seven, let me write that in a neutral color. So that's going to be 7/9. 13/9 minus 6/9 is 7/9. And then I can look over in the whole number place. All I have left a 16 here. 16 minus 12 is four, and I'm done. 17 and 4/9 minus 12 and 2/3 is equal to four and 7/9.