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Example of subtracting fractions with unlike denominators

Addition and subtraction of fractions

Video transcript

Let's figure out 7/12 minus 6/13. And in order to be able to do this, we need to find a common denominator. We notice that they're not common right over here. Here, the denominator is 12. Here, it is 13. And the common denominator is going to be the least common multiple of 12 and 13. And 12 and 13 share no common factors other than 1, so their least common multiple is actually just going to be 12 times 13. Actually, I'm just going to leave it written as 12 times 13. So let's first try to rewrite this right over here. And I'll do the denominator first. So 7/12. Instead of the denominator being 12, I'm going to write it as 12 times 13. Well, if we multiply the denominator by 13 in order to not change the value of the fraction, we need to multiply the numerator times 13. So notice, all I did is I multiplied the numerator and the denominator by the same number that's equivalent to just multiplying it by 13/13, or 1. And so this is still equivalent to 7/12. Similarly-- let me do this one in blue right over here-- the common denominator, we want is 12 times 13. So here in the denominator, we multiply-- let me now write it as 13 times 12. 13 times 12. Well, if we multiply the denominator by 12, we have to multiply the numerator by 12 as well. So I'll write the numerator as 6 times 12. Notice, here we multiplied the numerator and the denominator by 13. Here, we multiplied the numerator and the denominator by 12. How did I know to multiply this by 12? Well, the common denominator is 13 times 12. So here, I multiplied the denominator by 12 so I have do the numerator by 12. The common denominator here is 13 times 12. But here, I had to multiply it by 13 to get it, so I have to multiply the numerator by 13 as well. But now we are ready to subtract. You might say, hey, Sal. Hold on. Wait, what do these actually evaluate to? Well, maybe that's a good idea. Let's figure that out first . So this is equal to 7 times 13. Let's see, 7 times 13 is 70 plus 21. It's 91 over 12 times 13. Let's see, I haven't memorized my 13 times tables. So we know that 12 times 12 is 144. You put on one more 12, you get to 156. 156. So 91/156 is the exact same thing as 7/12. I just multiplied the numerator and denominator by 13. And from that we are going to subtract 6 times 12. 6 times 12 is 72. 72 over. Well, we already figured out what 12 times 13 is or what 13 times 12 is. It is 156. And now that we have a common denominator, we can rewrite this as being equal to 91 minus 72 over 156. I'll just write that in a neutral color, over 156. Let's see, if it was 92 minus 72, it would be 20. That's 1 less, so it's going to be 19/156. So this is going to be equal to 19/156. And as far as I can tell, let's see. 19 does not go into 156. Let me just make sure of that, that somehow, magically, 156 isn't a multiple of 19 so I could simplify this. So let's see, 19 is almost 20. So maybe, let's see if it will go 7 times. 7 times 9 is 63. 7 times 1 is 7. Plus 6 is 13. Let's see the difference here. Actually, I could have gone in one more time. So let's do it eight times. 8 times 9 is 72. 8 times 1 is 8. Plus 7 is 15. Yeah, you have a remainder here. So this doesn't go evenly. This isn't divisible by 19. And they don't share any other common factors, so we've simplified it about as much as we can. This is equal to 19/156.