Tip:
Highlight text to annotate it
X
This video reviews how to order fractions, which means how to decide which fraction is smaller or larger
than another and how to add and subtract fractions. All of
these processes require finding a common denominator, so that's why they are all in one video together.
So the first question we have here is which fraction is larger, 4/7 or 7/11?
And if you estimate it,four out of a seven that's a little bit more than 1/2. Half of seven is 3.5 so 4 out of 7's a little bit more than 1/2. 7/11 well
let's see half of elevens about 5.5 so that's a little bit more than 1/2 also. So it is tough to
decide just by looking at the numbers that are given.
The trick is to rewrite each of these
4/7
and 7/11 and rewrite them with a common denominator so the common denominator of seven and 11
is 77. So I'm going to rewrite each of these
as 77ths. And then to rewrite 4/7 with the denominators 77 I have to decide what do I
multiply seven by to turn it into 77 and the answer to that is 11
So I'm going to multiply this by 11 and this by 11 and that's going to be 44/77
and then this one over here to turn the 11 and a 77 I need to multiply by seven
so that one's 49/77 so
this second fraction here is larger
and 49/77 came from seven
elevenths so 7/11 is larger
Here's a second question involving comparing the size of fractions . We've got 3/8
as a size of the drill bit
1/4 and 5/16 to let me write them down 3/8
one 4th
and 5/16
I look at all three of those fractions and I think about what the common denominator is. I think the common denominator for all of them is 16.
This last and your 5/16 that's already 16 so leave at the same
this first fraction 3/8
Let's see, to turn in eight into a 16 I need to multiply by two
so that's 6/16
and the 1/4, to turn the 4 into a 16 I have to multiply by four so that's 4/16. So that 6/16 4/16 and 51/6 so the largest
is this one right here which is 3/8
and the smallest
is this and right here. 4/16 which came from
one 4th
OK, the last two examples here are how to add
fractions. Again to add and subtract fractions we need to have a common denominator so what I'm going to do in each of these is
convert the seven and the three to a common denominator
so, the common denominator of seven and three is 21
and
in order to convert a 7 to 21 I have to introduce a multiplier of three
and remember you have to do that in the numerator and in the denominator. So this is 12/21
one 3rd to convert that three to a 21 I need to multiply by seven
so that's 7/21. Once you have the common denominator you leave that denominator alone
and you just add the numerator so 12 plus seven is 19
now typically what you would do is look to see if you can simplify that. Is there any number that will divide into both 19 and 21? Since there's
not that will just stop there and say that 4/7 plus one 3rd is 19/21
The last one here involves mixed numbers. there are different ways to add and subtract mixed numbers. The
method I'm going to show here is to convert everything to an improper fraction first.
so 2 2/5 if I convert that to an improper fraction five times two is 10 plus two is 12
leave the denominator the same
the second mixed number here 1 1/2. two times one is two plus one is three
leave the denominator the same
and then the last one is just a proper fraction so we don't need to convert that
Now I've got three denominators 5, 2 and 3. I'm looking to convert them to a common denominator. I'm looking for a number that all
three of those will divide into. If we just had the five and the two of the common denominator would be 10
we also have this three over here so the common denominator of 10
and three is 30. So I will convert all of these into 30ths.
Now I'm going to go back and decide how to convert all of these to 30. This first one here
to convert a five to a 30 I need to multiply by six
so this first one becomes 72/30. To convert a two to a 30 I have to multiply by 15
again notice I'm putting that factor in the numerator in the denominators so that's 45
and then to convert a three to a 30 I have to multiply by 10
so I end up withe 72/30 minus 45/30
plus 10/30 it's so I know my answer is going to be 30ths. I just need to figure out what 72
-45 plus 10 is and make sure you go left to right here
so 72 -45
that's gonna be 27
plus 10
is going to be 37
so this is 37/30 S and you can either leave it that way
or if you want to rewrite that as an improper fraction 30 divides into 37 1 time
with seven left over. Either of those answers is fine
Just remember to add and subtract fractions or to decide which is larger you need to have a common denominator.