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# Fractions in lowest terms

## Video transcript

Simplify 48/64 to lowest terms. Let's see if we can visualize this. So we have 64. I guess 64 would be a whole, so let's draw a whole here. So let's say that's a whole. Maybe we're talking about a candy bar. Let me draw the whole. We're talking about a whole candy bar. That would be 64 fourths. It would be the whole candy bar right there. And 48 of the 64, you could imagine splitting this up into 64 super-small pieces. You wouldn't be able to see what I drew here, but if we had 48 of them, it would get us about that much of them, so that would be the 48 out of the 64. So this whole blue area is 64. The 48 is this purple area right over here. So let me write it over here. 48/64, and we want to write it in lowest terms, and we'll talk more about what lowest terms even means. Now, is there a way to group these 48 or these 64 into groups of numbers that will maybe simplify them a little bit? And to think about that, you'd have to think about what is the largest factor that is common to both 48 and 64? Or you can think of it as what is their greatest common divisor? Well, the largest number that I can think of that goes into 48-- you could do it either by just thinking about it or you could actually write out all of its factors. But if you were to write all the factors for 48 and all the factors for 64, the one that pops out at me as the largest that goes into both is 16. So you could say that 48 is equal to-- well, what is it? It's 3 times 16, and 64 is 4 times 16. Now this is interesting. So this 48 that we drew in magenta right here, we could view this as three groups of 16. So that's one, two-- let me make them a little bit more even. So one, two, three groups of 16, so that's 16, that's 16, and that is 16. That would be 48. I could draw 16 bars here so that we have 16 pieces, but that's a group of 16, a group of 16 and a group of 16. That's what 48 is. Now, 64 is four groups of 16. So we could make, if you look at the 64, that is a 16, that is a 16, that is a 16, and then that is another 16. These should all be the same length. I drew it a little bit off. So what is 48/64 in lowest terms? We want to write this in as simple as possible fraction. Well, if we make each of the pieces equal to 16 of our old pieces, if we make this into one piece, if we turn 16 into one, then we are talking about instead of 48/64, we're talking about three. So this is one piece, two pieces, three pieces of a total of four. So this is going to be equal to 3/4. And hopefully, you see kind of a mathematical way of immediately thinking about it. If you can factor this out and you can actually factor out its greatest common factor, so 48 is 3 times 16, 64 is 4 times 16, and then these cancel each other out. view This is equivalent to 3/4 times 16/16. This is the same thing as that. And 16/16 is 1, and you're just left with 3/4. Now, if you didn't immediately recognize that 16 goes into both 48 and 64, you could do it step by step. So let's say we started off with 48/64. Now, the key thing to remember with any fraction, whatever you do to the numerator, you have to do to the denominator. So let's say we divide the numerator by 2, we also have to divide the denominator by 2, so we could get 2. We know that these are both divisible by 2. They're both even. So that would get us to 24/32. And we'll say, well, look, these two numbers, those are both divisible by 2. Well, see if we can think of a larger number. Well, actually, they're both divisible by 4, so maybe you don't realize that they're also both divisible by 8. So let's say you did it with 4. So now we divide the top by 4. So we're going to divide by 4. We get 6. You have to do the same to the bottom, to the denominator. Divide by 4, you get 8. So 48/64 is the same thing as 24/32, which is the same thing as 6/8. And these are both divisible by 2, so if you divide the numerator by 2, you get 3. You divide that the denominator by 2, you get 4. And so this is the simplest possible terms, because 3 and 4 share no common factors greater than 1, so we're in lowest possible terms. So however you want to do it. The easiest way or the fastest way is to say, hey, 16 is the biggest number that goes into both of these. Divide both by 16. You get 3/4. And really when you're dividing the numerator and denominator by 16, you're turning groups of 16 into one piece or 16 super-small pieces of the pie into one bigger piece of the pie. So this goes from 64 pieces to 4 pieces. This goes from 48 pieces to 3 pieces.