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## Adding and subtracting mixed numbers with unlike denominators

Current time:0:00Total duration:2:31

# Subtracting mixed numbers: 7 6/9 - 3 2/5

CCSS.Math:

## Video transcript

Let's try to evaluate 7
and 6/9 minus 3 and 2/5. So like always, I like to
separate out the whole number parts from the fractional parts. This is the same thing as 7
plus 6/9 minus 3 minus 2/5. And the reason why I'm
saying minus 3 minus 2/5 is this is the same thing
as minus 3 plus 2/5. And so you distribute
the negative sign. You're subtracting a 3, and
then you're subtracting the 2/5. And so now we can worry
about the whole number parts, 7 minus 3. Well, 7 minus 3 is
going to give us 4. So that's going to give us 4. And then we're going
to have 6/9 minus 2/5. So let me think about
what 6/9 minus 2/5 are. 6/9 minus 2/5, well,
we're going to have to find a common denominator. So this is going to
be the same thing. And I think the least
common multiple of 9 and 5 is going to be 45. Literally, you then multiply. They have no common factors. So it's going to be over 45. To go from 9 to 45, I
have to multiply by 5. So I'm going to have to
multiply the numerator by 5. So 6 times 5 is 30. Then I'm going to subtract. To go from 5 to 45, I
had to multiply by 9. So I have to multiply
the numerator by 9 if I don't want to
change the value. So 2 times 9 is 18. And 30/45 minus 18/45 is
going to be something over 45. 30 minus 18 is 12. If I subtract these two
fractions right over here, I get 12/45. So it's 4 plus 12/45. Or if we wanted to write
it as a mixed number, this is equal to 4 and 12/45. But we're not done yet. We can simplify this further. 12 and 45 have common factors. They're both divisible by 3. Actually, they're both
divisible by-- well, I think we can divide
more after that. So let's see. If we divide the numerator by
3 and the denominator by 3, we end up with 4. And 12 divided by 3 is 4. And 45 divided by 3 is 15. 4 and 4/15. And actually, we're done. These two can't be
simplified anymore. 4 and 4/15.