Welcome to "Working with Fractions"! Our focus today is on adding and subtracting
fractions. So, in our last video, "Operation Overview," we mentioned that in order to
add or subtract fractions they have to have the same denominator. This means
that if we had 2/5 and 1/5, for instance, what we would do was add
the top numbers — so 2 plus 1 gives us 3 — and keep the same denominator, giving
us 3/5. However, if the denominators were different, then we cannot do this. Why is
this? Well, think about it this way. Let's say you have one third of a chocolate bar. Your
friend comes along and says, "Hey, you're such a wonderful person. I'm gonna give
you half of mine." Well, now you have a lot of chocolate, but what exactly do you
have? Right now there is no way for us to express this quantity.
That's where the common denominator comes in. Looking at this one half of a
chocolate bar your friend gave you, you might notice that you can divide it up
into smaller sections. So we actually are getting
3/6. And for the one that you have, you can
divide it up again into similarly sized sections. So we're getting 2/6. And look
at that! Now we can actually count the number of pieces that we have: one ... two ... three ... four ... five sixths.
In summary, when you have two fractions with different denominators,
find a common denominator by multiplying each fraction. In our chocolate bar
example we had 1/3 and 1/2 — and notice that the number 6 was the product of
both 3 and 2. So we multiplied 1/3 by 2/2 to give
us 2/6. And, we multiplied 1/2 by 3/3 to give us 3/6.
Wait a minute. So you might be wondering if it's okay for us to multiply
something by 2/2 or 3/3, but this actually doesn't do anything to the
number — even if we were to multiply it by 1,000,000/1,000,000. See, it's the
same thing as multiplying something by 1 — meaning that the number stays the same —
because 2 divided by 2, or any number divided by any number, well, that just
gives us 1. So, essentially, this number is the same as THIS number, just in a
different form. After that, just as in our first example, we add the numerators — the
top numbers — and keep the denominator to give us 5/6. For subtraction it's the same
idea. So your friend came along, but was in a bad mood this time, and said, "Hey.
Give me 1/4 of your chocolate bar." You would have 1/3 minus 1/4. Right? Well, in
this case, with 1/3 and 1/4, the lowest common denominator would be — 3 times 4
equals — 12. So what we would do was multiply 1/3 by 4/4, multiply 1/4 by 3/3,
and this is really gonna give us 4/12 minus 3/12 — and this is equal to 1/12.
And that's it! When I was learning
fractions myself, one thing I always did was to look at the bottom number of the
fraction I wasn't working with and then just multiply my numerator and
denominator by that same number. Now, it won't give you the least common
denominator every time, but it's a good place to start. In the next part of the
series, we'll talk about multiplication and division, but in the meantime check
out the games on "Always Ice Cream" and "Clever Dragons" that were made
specifically for this material. I will see you soon!