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This video is provided as supplementary material for courses taught at Howard Community
College, and in this video I want to talk about adding fractions with different
denominators.
So here's the first problem.
I've got two fractions and I have to add them.
I've got 4/5
and 2/7.
They have different denominators. If the denominators were the same,
this would be an easy problem.
All I would have to do is add the numerators together
and that would be the new numerator,
and the denominator would stay the same.
But when the denominators are different, I have to do a little more work.
What I've got to do is find a common denominator both of these fractions.
Now the common denominator
is
a number that I can turn both of the denominators into
by multiplication.
I can turn a 5
into 35 if I multiply it by 7,
and I can turn 7 into 5 by multiplying it by 5. So 35 will
be my common denominator.
And here's how I'm going to get those fractions into a form with that common
denominator.
I'll take the first fraction,
4/5,
and remember, I want to multiply the denominator by 7
to make it 35.
Well, if I multiply the denominator
by 7, I've got to multiply the numerator
by 7 also.
I've got to multiply them both by the same thing,
otherwise I'm changing what the value of the fraction is.
So I'll multiply by 7 over 7.
Now if you think about it, 7 over 7 is just equal to 1.
So really, I'm just multiplying this fraction by 1.
So let's do the multiplication.
When we multiply two fractions, we multiply the numerators
to get the new numerator.
So 7 times 4
is 28.
And we multiply the denominators to get the new denominator, and 7 times 5
is 35.
Now I'm going to use a similar process for the second fraction, 2/7.
I'll take that 2/7 and
I want to turn the denominator into 35, so I will have to multiply
that by 5,
which means I'll multiply the whole fraction
by 5 over 5, which is just equal to 1.
So now I can do the multiplication.
5 times 2 is 10,
and 5 times 7 is 35.
Now I've got the same denominators for both of my fractions.
I've got 28
over 35 and 10 over 35.
So I can just add the numerators.
28 plus 10
is 38,
and the denominator
will be that common denominator that I had,
which is 35.
So I'm going to get 38 over 35
as
what happens when I add 4/5 plus 2/7.
I want to take quick look and make sure I can't reduce 38 over 35, which I
can't.
So that means that will be my final answer.
Now if you're given a subtraction problem,
you're basically going to do the same steps. So let's take all those plus signs
and turn them into minus, or subtraction, signs.
Now I've got 4/5
minus
2/7.
That's going to become 28 over 35
minus 10 over 35.
And now all I have to do is subtract the numerators. I have to take 28
and subtract 10.
And that will give me
18
over 35.
I can't reduce that ether, so that will be my answer.
Now I want to do one more,
just to make a point about common denominators.
So let's take this problem...
5/6
plus
3/4.
And I know a lot of times you're probably told to find
the lowest common denominator.
Well, I'm not going to do that.
So
I've got a 6 and a 4,
and I'm going to say that the common denominator I want
is 24. Now I know that's not the smallest denominator I can use,
but let's just see what happens.
So I have to take that 5/6, and I have to turn that six into
24,
which means I'm gonna multiply it by 4,
which basically means I'll multiply by the fraction
4 over 4.
And when I do that,
4 over 4 times 5 over 6,
I'll get
20
over
24.
And I have to go through the same process for the second fraction,
3/4.
So I want to turn the denominator into 24, which means I'll multiply
the denominator by 6.
So I'll multiply
by the fraction 6 over 6.
And now I'll do that multiplication.
6 times 3 is 18,
and 6 times 4 is 24.
And now I'll add the 20
and the 18.
That's 38.
and the denominator,
the common denominator, is 24.
Now these are both even numbers, 38 and 24, so I could reduce this
fraction.
I can divide
38 by 2
and I can divide 24 by 2,
and I would end up with
19
over
12.
Now I did that without using the lowest common denominator.
Let's do it again with the lowest common denominator and see if we get the same
answer.
So once again,
that was
5/6
plus
3/4. Now the lowest common denominator is actually 12.
Now if I want to take the 6, from 5 over 6, and turn it into 12,
I have to multiply it by 2.
So I'll multiply by the fraction
2 over 2.
And that's going to get me
10
over 12.
And now I'll do the same process for 3 over 4.
I'll have to multiply that
by
3 over 3.
That will give me a 12 as the denominator.
And 3 times 3 is 9,
3 times 4 is 12.
the denominators are the same
so I can add the numerators,
and I get
19
over 12,
and it's the same answer I got
when I used a denominator that was not the lowest common denominator.
So the reason I did this was to make the point
that if you get the lowest common denominator,
like I did when I chose 12, that's fine.
You probably won't have to reduce anything when you're done. If you don't get the lowest
common denominator,
such as when I used
24
as my common denominator,
then basically
you just go through with the process and just make sure that you're seeing if you can
reduce your answer, if you can simplify your answer. Once you've simplified it,
you'll get the same as you would have gotten if you'd used the lowest common
denominator.
So either way will get you the same result.
That's about it,
take care, I'll see you next time.