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Welcome to the Student Academic Learning Services video on adding and subtracting fractions.
This video picks up right where the Introduction to Fractions video ends,
so if you have not watched the Introduction to Fractions video I strongly suggest you
watch that video first
before continuing on with this video.
Let's take a look at this example. Here we have 4 over 5 subtract 1 over 3. I included
our method up here in the corner so we can reference it.
The first step in our method is to check and see whether the denominators are equal. Here
we can see we have 5 and 3 so they are not equal, so we have
to go to step 2, which is finding the lowest common denominator.
In order to do that we need to list the multiples of both denominators, so the multiples of
5 are 5, 10, 15 and they just keep going.
And the multiples of 3 are 3, 6, 9, 12 and 15 and they just keep going.
So what we are looking for is the lowest common denominator. So were going to find the lowest
common multiple, here we see its 15.
So were going to rewrite these fractions with a denominator of 15. Now because we changed
the denominators we need to change the numerators as well.
In the first fraction 5 times 3 gave us 15 so were going to multiply the top by 3 as
well. In this fraction one third we multiplied the bottom by 5 to get 15
so were going to multiply the top by 5, so 1 times 5 gives us 5. So were left with 12
over 15 subtract 5 over 15.
Moving on to step 3 were going to add or subtract the numerators, here we are subtracting so
12 subtract 5 gives us 7 and we are just going to copy that denominator.
Moving on to step 4 figuring out whether or not this in lowest terms. We are going to
list the factors, just like we did in the last video.
So the factors of 7 are 1 and 7 and the factors of 15 are 1, 3, 5, and 15.
Here we can see they don't have anything in common other than the 1 and dividing by 1
is not going to change our fraction so we can state 7 over 15 is in lowest terms.
Let's take a look at another example. In this example we have 7 tenths plus 11 twelfths.
And as always we have our method located up here.
So step 1 is checking to see whether the denominators are equal.
Again we have 10 on one side and 12 on the other, so they are not equal.
So were going to move onto step 2. Step 2 being finding the lowest common denominator.
In order to do that we need to list the multiples of both denominators.
So the multiples of 10 are 10, 20, 30, 40, 50, 60 and so on.
And the multiples of 12 are 12, 24, 36, 48, 60 and so on.
And we can see that 60 is common in both lists here, so that's going to be our lowest common
denominator.
So were going to rewrite both these fractions with 60 as our new denominator.
And in order to get 60 we had to multiply 10 by 6 so we have to multiply 7 by 6
And likewise we have to multiply 12 by 5 so we have to multiply 11 by 5.
That's going to gives us 42 and 55.
So we have 42 over 60 plus 55 over 60.
Moving onto step 3 now and that's adding or subtracting the numerators and copying the
denominator.
So 42 plus 55 is 97 and we are going to copy the denominator down.
Lastly moving onto step 4, checking to see whether or not we are in lowest terms.
We have a rather unique situation here where we have the numerator being greater than the
denominator.
So in order to get that in terms we like we are just going to divide 60 into 97 and that
goes once with 37 left over.
So what were checking for lowest terms now is this 37 over 60. In order to do that were
going to list the factors of each
just like we have done in the other exercises.
So the factors of 37 are 1 and 37.
And the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
And we can see here in these two lists that the only thing common is the ones.
Dividing by one is not going to change our fraction so we can state that 1 and 37 60ths
is in lowest terms and that sour final answer.
That concludes our video on adding and subtracting fractions. If you have any questions regarding
the material covered
in this video I strongly encourage you to come to the SALS centre located in room 204
of the Student Services Building
and make an appointment with the appropriate learning skills advisor.
Thanks for watching.