Transcript Multiplying Fractions

Multiplication Model
• A Fraction of a Fraction
• Length X Length = Area
We will think of multiplying fractions as
finding a fraction of another fraction.
3
4
We use a fraction
square to represent
3
the fraction 4 .
2
3
3
4
Then, we shade of .
We can see that it is the same as
2
3
But, of
same as
So,
3
4 is the
3
2
X 4.
3
3 = 6
2
X 4
12
3
.
6
12
2 of 3
4
3
3
1
To find the answer to 2 X 5,
model to find of 12 . 35
we will use the
3
5
We use a fraction
square to represent
3
the fraction 5 .
1
2
3
5
Then, we shade of .
We can see that it is the same as
.
3
10
1 of 3
5
2
So,
3
3
1
X 5 = 10
2
1
3
In this example, 2 of 4 has been shaded
1 of 3
4
2
1
3
What is the answer to 2 X 4 ?
In the second method, we will think of multiplying
fractions as multiplying a length times a length to
get an area.
3
This length is 4
In the second method, we will think of multiplying
fractions as multiplying a length times a length to
get an area.
3
4
2
This length is 3
We think of the rectangle having those sides. Its
area is the product of those sides.
3
4
2
3
2
3
This area is 4 X 3
We can find another name for that area by
seeing what part of the square is shaded.
3
4
2
3
2
3
This area is 4 X 3
6
It is also 12
We have two names for the same area. They
must be equal.
3
4
2 = 6
3
12
4 X 3
2
3
2
3
This area is 4 X 3
6
It is also 12
Length X Length = Area
1
2
3
4
1
3
This area is 4 X 2
3
It is also 8
1 = 3
3
8
4 X 2
What is the answer to 4 X 1?
5
1
4
4
5
4
Fraction Multiplication
And Cancelation
Fraction Multiplication
•
•
Here are some fraction
multiplication problems
Can you tell how to multiply
fraction from these examples?
2 5 10
 
3 7 21
1 1 1
 
3 3 9
4 1
4
 
5 7 35
2 5 10
 
3 1
3
3 5 15


4 12 48
6 4 24


5 10 50
Multiplication
•
•
Multiply numerator by numerator
And denominator by denominator
2 5 10
 
3 1
3
N1 N 2 N1  N 2


D1 D2 D1  D2
Try some.
• Multiply the following:
1 5
 
3 8
2 4
 
3 5
5 5
 
8 8
4 2
 
9 3
Answers
• Multiply the following:
1 5
5
 
3 8 24
2 4
8
 
3 5 15
5 5 25
 
8 8 64
4 2
8
 
9 3 27
Mixed Numbers
•
•
•
•
Because of the order of operations,
Mixed numbers cannot be multiplied as is
GET MAD!!!!!
Change mixed numbers to improper fractions, then multiply.
2 5
3 1 
5 8
17 13


5 8
17 13 221


5 8
40
221  40  5 with a remainder of 21
5
21
40
Try some
•
•
•
Change any whole or mixed numbers to improper.
Multiply straight across.
Simplify answers
2
1 7 
5
1
8 
5
•
•
•
Answers
Change any whole or mixed numbers to improper.
Multiply straight across.
Simplify answers
2
7 7 49
4
1 7   
9
5
5 1
5
5
1
1 8 8
3
8    1
5
5 1 5
5
Cancelling
Reduce before you multiply
•
Canceling
Reducing before mutiplying is called canceling.
25 12 300
 
32 35 1120
•
ICK! Instead think the following in your head.
25 12 25  12 5  5  4  3



32 35 32  35 8  4  7  5
5  5  4  3 5  3 15


8  4  7  5 8  7 56
Canceling on paper
•
Rules: One factor from any
numerator cancels with like
factor from the denominator.
11
4444
16 9 15
 
21 20 12
3
11
3
33
1
16
9
15
16
9
15
3
16
9
15
16
9
15
16  9  15 




7
21
20
12
7
4
21
21
123
21
120
20 12
20
21
4444
1
20
3
3
12
3 13 3
1
1
Try one
•
•
Say “--- goes into ____ this many times.”
As you cross each number out and write what is left after
canceling above the number.
5 1

3 10
Answer
•
•
Say “--- goes into ____ this many times.”
As you cross each number out and write what is left after
canceling above the number.
1
5
1
5


3
10 2 6
Try one more
•
•
•
•
Make whole and mixed numbers improper
Cancel if you can
Multiply Numerators and denominators straight across.
Simplify
10
1 14
4  4
21 2 15
Answer
•
•
•
•
Make whole and mixed numbers improper
Cancel if you can
Multiply Numerators and denominators straight across.
Simplify
10
1 14
4 
4
21
2 15
10 9 14 4
 
 8
21 2 15 1