Transcript Fractions - TeacherWeb

Fractions
3
4
By Mr. Walker
What is a Fraction?
A fraction is just a smaller part of something else.
If you have one piece of the pizza, you are only
eating a fraction of the pizza, not the whole
thing.
What do Fractions look like?
Parts of a Fraction
The top part of the
fraction is called the
The bottom part of
the fraction is called
the Denominator
_
1
4
Numerator
How Fractions Work
If you shade or take one piece
of the circle away, you are taking
1 of the 4 pieces. That fraction looks
like this…
1
4
3
4
This is a whole
circle with 4 pieces.
So the numerator (top #) is the part or parts
that you are working with…
1
4
and the denominator
(bottom #) is the number of total parts
the object has or used to have.
If you take away 1 of the 4 pieces
you will be left with 3 of the 4 pieces.
That fraction looks like this…
Try it Out
What fraction of the objects are shaded? Remember that the part you are
working with (the shaded part) goes on top and the total number of parts
goes on the bottom.
2
3
3
4
3
5
4
6
1
2
5
7
7
10
1
2
Comparing Fractions
With like denominators
>, <, or =
If the two fractions you are comparing have like denominators (the same),
your job is easy. Just look at the numerator and see which one is bigger.
1
4
3
4
<
The denominators are the same,
so just compare the numerators.
The 3 is bigger than the 1.
So the answer is …
7
8
>
5
8
The 7 is bigger than the 5.
So the answer is …
Try it Out
2
9
<
3
9
Answer
5
6
>
1
6
Answer
2
3
=
2
3
Answer
Comparing Fractions
With unlike denominators
>, <, or =
If the two fractions you are comparing have unlike denominators (different),
you need to do a little more work using multiplication.
3
4
3
5
3
4
The problem
15
3
5
The Denominators
are different
5X3=15
3
4
Starting on the bottom
Multiply diagonally up
across the middle
12
3
4
>
3
5
Answer
3
5
4X3=12
Which is bigger the 15 or the 12 ?
Comparing Fractions
With unlike denominators
Try it Out
>, <, or =
18
3
2
3
>
1
9
Answer
4
5
>
12
12
3
4
=
3
4
Answer
6
8
Answer
1
4
<
7
20
1
5
<
4
7
Answer
2
6
Answer
3
9
=
35
18
7
9
>
2
5
Answer
3
9
Answer
3
4
>
2
4
Answer
Adding & Subtracting Fractions
Adding fractions with like
Denominators means
adding the same size
pieces to the circle
Adding fractions with
unlike denominators
means adding different size
pieces to the circle
Adding & Subtracting Fractions
With like denominators
If the denominators are the same then adding and subtracting fractions is easy.
2 + 1 = 3
5 5
5
Denominators are the same so you just use that number in your answer on
the bottom.
Then you just add or subtract the numerators (top numbers).
Try it Out
3 + 2 = 5
8 8
8
Answer
6 - 3 = 3
7 7
7
Answer
1 + 1 = 2
3 3
3
Answer
Adding & Subtracting Fractions
With unlike denominators
2 + 1 =
5 3
If the denominators are different then we need to
do some work before we can add these two fractions.
1. Rewrite the problem so it looks like this
2
=
5
15
1 =
15
+ 3
2. Add some of these lines to make your work nice and neat
3. Take the denominators and count them both out to
find a number that they both have in common
5, 10, 15, 20, 25
3, 6, 9, 12, 15
15
4. They both have a 15 in common
So we will use that number as the
new denominator
Adding & Subtracting Fractions
With unlike denominators continued
2 X=3 = 6
5 X 3 = 15
1 X=5 = 5
+ 3 X 5 = 15
11
15
5. Now ask yourself how many times 5 goes into 15
3 times, 5x3=15
6. For the top fraction you used a X 3 on the denominator
Whatever you do to the denominator,
you also have to do to the numerator
So multiply the numerator by a 3, which looks like this…
7. Now ask yourself how many times does 3 go into 15
5 times, 3x5=15
8. For the bottom fraction you used a X 5 on the denominator
Whatever you do to the denominator,
you also have to do to the numerator
So multiply the numerator by a 5, which looks like this…
9. Now just add the numerators and you are done
Adding & Subtracting Fractions
Try it Out
4, 8, 12, 16, 20
7, 14, 21, 28, 35
2, 4, 6, 8, 10
3, 6, 9, 12, 15
5, 10, 15, 20, 25, 30, 35
3, 6, 9, 12, 15
1 X=3 = 3
4 X 3 = 12
1 X=4 = 4
+ 3 X 4 = 12
2 X=5 = 10
7 X 5 = 35
3 X=7 = 21
+ 5 X 7 = 35
1 X=3 = 3
2X 3 = 6
2 X=2 = 4
+ 3X 2 = 6
7
12
31
35
7
6
Reducing Fractions
Whenever possible you should reduce your fractions
To Reduce means to make the numbers in the fraction smaller.
The actual fraction does not change but the numbers do.
You reduce a fraction by dividing both the numerator and
the denominator by the same number. Remember…
Whatever you do to the denominator,
you also have to do to the numerator
_
:
3 = 1
_
6: 3 = 2
3 =
_
:
2 =2 = 1
_
4: 2 = 2
As you can see by the bars,
the numbers got smaller (reduced) but the
fraction shaded (amount) stayed the same.
Hints
Reducing Fractions
Try it Out
1. When you divide both the numerator and the denominator
it has to come out perfect, no remainders.
2. When you divide you can never divide by 1 because they would just be
the same numbers
3. If they are both even numbers you can always use 2 to divide
4. If you can use a bigger number to divide it is better, if not, you may have to
reduce several times to get the smallest numbers
_
6 :=2 = 3
_
8: 2 = 4
_
5 :=5 = 1
_
15 : 5 = 3
_
7 :=? = 7
_
8: ? = 8
Can’t, so it is
already as small
as it can get
_
4 :=4 =
_
8: 4 =
or
_
4 :=2 =
_
8: 2 =
1
2
2 _: 2 = 1
_
4 :2=2
Changing Fractions
Improper to Mixed
Some fractions are improper. Improper means that the numerator is bigger
than the denominator. They are top heavy with a bigger number on top.
They need to be changed so they will not fall over.
7
5
7
5
To change it, you just divide the top by the bottom.
A fraction is really just a division problem.
7
5
1 R2
5) 7
-5
2
The denominator stays the same.
The remainder becomes the numerator
1 25
The answer on top of the division
problem goes in front of the fraction.
It’s the whole number.
Changing Fractions
Improper to Mixed
Try it Out
3 =
2
1 R1
2) 3
=
-2
1
3 =
2
1
12
1 R1
2) 3
=
-2
1
1 12
3 =
2
1 R1
2) 3
=
-2
1
1 12
Changing Fractions
Mixed to Improper
Some fractions are mixed. Mixed means that the fraction also has a whole
number in front of it. Think, the whole number and fraction are mixed up together
to get a job done.
To change this mixed fraction to an improper is as easy as 1, 2, 3.
The fraction
1. Keep the bottom number the same
2
15
2. To get the top number, just take the
denominator (bottom #) and multiply it by the
whole number in front.
5X1=5
Whole number
+
1 25
x
=
7
5
3. Then add the numerator
(top number) to your answer.
5+2=7
Mixed and improper are just two ways to say the same fraction
Changing Fractions
Mixed to Improper
Try it Out
+
2 12
x
= 5
2
Answer
2 37 = 17
7
Answer
+
3 35
x
= 18
5
Answer
1 23 = 53
Answer
+
1 67
x
= 13
7
Answer
3 = 9 = 3
23 3
Answer
Answer