Transcript Those Dynamic Fractions - Technology Resources-4

Those Dynamic Fractions
Dynamic:
Characterized by continuous change,
activity, or progress
 Fractions can change in many ways

– They can use larger numbers or smaller
numbers
– They can be changed to decimals or
percentages

But even when a fraction’s appearance
changes, its value must remain the same.
Fractions can use bigger numbers or
they can use smaller numbers…
1/2 can be called 2/4 or 3/6 or 50/100
but the top number is always half of
the bottom number
12/20 can be called
24/40,
3/5 or
6/10
but the top number is always a
multiple of 3 and the bottom number
is always a multiple of 5.
You try…
On your answer sheet, write some
other names for ¼ in the first space.
Try to think of at least 3 other names.
Remember the denominator (bottom
number) for these answers will
always be 4 times bigger than the
top number.
1/2, 1/4 and 3/5 are called Lowest
Terms because they cannot go any
lower.
Most people prefer to talk about
fractions in lowest terms. If a
fraction is not in lowest terms, you
have to reduce it.
To reduce a fraction, you divide.
And just as your mother and father try
to keep things fair between you and
your brothers and sisters, you have
to keep things fair between the
numerator (top number) and
denominator (bottom number).
To reduce 6/8, you divide the top and
bottom numbers by the same thing.
Ask yourself, which times tables have
both 6 and 8 for an answer.
The answer would be the twos times
tables. 3X2 = 6 and 4X2 =8.
I usually write it like this:
6÷ 2 = 3
8÷ 2 = 4
6/8 reduces to 3/4
Now you try: reduce 10/14 and write the
answer in the second space.
Remember to be fair to the numerator and
denominator.
To reduce a fraction to lowest terms,
you keep reducing it until you can’t
reduce anymore.
How do you tell when you can’t reduce
anymore? How do you tell when
your fraction is in lowest terms?
There are 5 ways to tell:
1. When the top number is a 1
2. When the numerator and denominator
are neighbors (like 2/3 or 5/6)
3. When both the numerator and
denominator are prime numbers
4. When the numerator is a prime number
and does not divide evenly into the
denominator
5. When the numerator and denominator
have no common factors.
Now you try…
How many of these fractions are in
lowest terms? Write your answer on
your answer sheet.
7/21
3/5
6/12
1/18
3/8
11/12
10/25
2/32
4/25
You don’t ALWAYS want fractions in
lowest terms.
When you compare fractions or add
and subtract them, you have to find
common denominators.
Common denominators aren’t usually
in lowest terms
When you reduce fractions, you divide.
When you find common denominators,
you multiply.
To find common denominators, for 1/2
and 3/5, you look at the 2 and the 5
(because those are the
denominators).
You look at the smaller denominator (the 2)
and you start saying your twos times
tables (2, 4, 6, 8, 10, 12, 14, 16, 18, etc.)
You stop when you find a number that the 5
will go into evenly – that would be 10 in
this case.
Our common denominator for 2 and 5 is 10
because 10 is in both the 2 and the 5
times tables.
This is how I write it:
1X=
_
2 X  = 10
AND
3X =
I call it “equal sign and a line”.
_
5 X  = 10
Copy these onto your answer sheet.
Those little boxes look like little elevators, don’t
they?
_
1X=
2 X  = 10
Now your fraction
looks like this:
1X5=5
2 X 5 = 10
Ask yourself, 2 times what
number equals 10?
5, right? Right. So 5 goes in
the elevator. The elevator goes
up to the second floor and the 5
is still there. So, 1 times 5 is
what?
5, right? Right. So 5 goes on
top of the 10.
5/10 is an equivalent fraction name for 1/2. We
know this is true because 5 is half of 10.
On your answer sheet, write 5/10 beside the
1/2.
Now let’s work with the 3/5…
3X=
_
5 X  = 10
3X2=6
5 X 2 = 10
This time, ask yourself, 5
times what number equals
10?
2, right? Right. So 2
goes in the elevator. The
elevator goes up to the
second floor and the 2 is
still there. So, 3 times 2
is what?
6, right? Right. So 6 goes
on top of the 10.
Write 6/10 beside the 3/5 on your
answer sheet.
This is what you should now have
written on your answer sheet. 1/2 and
3/5 now have common denominators.
1X5=5
2 X 5 = 10
3X2=6
5 X 2 = 10
Now we can compare them (which one
is bigger? Smaller?)
Or we can add them. If we put the
bigger one on top, we could subtract
them.
And when we get done, we might need
to reduce the answer.
THAT’S how you make dynamic
fractions.
Let’s try another one. Find common
denominators for 2/3 and 1/12 (What
number is in both the 3 and the 12
times tables?)
3X1 = 3
2X=?
3 X  = 12
3X 2 =6
3X 3 = 9
3 X 4 = 12
3 X 5…
1 X=?
12 X  = 12
Hey, wait a minute… 12 works
for both of them!
The common denominator is 12!
4 = ?
2X
3 X  = 12
4
1 = ?
1 X
1 = 12
12 X 
Next, I figure out the numerators (top
numbers).
Those boxes look like elevators.
3 times what number equals 12? That
would be 4. Put four in the elevator and
send it upstairs… 2 X 4 = 8. The top
number is 8!
Next, I figure out the numerator here.
Those boxes look like elevators.
12 times what number equals 12? That
would be 1. Put 1 in the elevator and
send it upstairs… 1 X 1= 1. The top
number is 1!
2X4=8
3 X 4 = 12
Now we can:
Compare
Add
1 X1=1
12 X 1 = 12
Subtract
Now you try. Write the answer on your
answer sheet.
What would be common denominators for
these fractions:
3
4
5
6
Did you do it?
Try these. Write these answers on
your answer sheet.
What are some other names for these
fractions?
1/2
1/4
2/10
6/21
And that’s how you
make dynamic
fractions!