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# Example of subtracting fractions with unlike denominators

If you conquered adding fractions with different denominators, then subtracting fractions will be a snap. Don't worry...we'll take it slow and explain every step. Created by Sal Khan.

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.