Download Standard 4NF1

Standard 4NF1
I CAN EXPLAIN WHY A FRACTION A/B IS
EQUIVALENT TO A FRACTION (N X A) / (N X
B) BY USING FRACTION MODELS
Say What?
 Let’s try it with numbers instead of letters.
 ½ is equivalent to (2 x 1) / (2 x 2)
 So, ½ is equivalent to 2/4.
The Goose/Gander Rule
 With equivalent fractions, there is always one





important rule that must be followed.
I call it the Goose / Gander rule
What’s good for the goose is good for the gander.
BTW the goose is the girl and the gander is the boy.
FYI – a boy duck is called a drake.
With fractions this means that what you do to the
bottom number (the denominator) you must also do
to the top (the numerator).
Example:
 This is what you usually get in a math book.
1
3
 --- = --3
?
 1 x 3 = 3 on the top, so…
 3 x 3 = 9 on the bottom.
 9 is your missing denominator.
Working it out
 When you work the problem out, it should look
something like this:
 1 (x3)
3
 --- = -- 3 (x3) 9
 Since 1 x 3 = 3 on top, you multiply 3 x 3 to get 9 on
the bottom.
Sometimes you have to go backwards.
 Check this out:
?




8
 --- = --5
20
Don’t freak out! You’re doing the opposite of what
you did before.
So what’s the opposite of multiplying?
DIVIDING!
Feel better?
Working it out
 To solve this one, you must divide.
 20 divided by 4 is 5
 What you do to the bottom, you do to the top.
 8 divided by 4 is 2, so…
 The missing numerator is 2
Showing your work
 When you work this problem out, it should look kind
of like this:
8
(/4) 2
 --=
-- 20 (/4) 5
 I switched the fractions around, you don’t have to do
that, but what the hey.
 This is what you look like right now.
Model It!
 You should be able to do this with numbers, but…
 Drawing a picture can be very helpful.
Modeling
 Here’s a model of ½
 Notice that the top of the model is hued (darker) and
the bottom of the model is in pastel (lighter)
1
2
 Now, just imagine making an equivalent fraction of
this model by drawing a line down the middle.
 Ah heck, I’ll just show you on the next slide
The Next Slide
 Told you I’d show you
1
2
3
4
 Now you may notice that there are a total of 4 boxes
in the model…
 Only 2 of the 4 boxes are hued (darker), and…
 The model is still the same size as before, so…
 ½ is equivalent to 2/4
Your Turn!
 Solve these 2 equivalent fraction equations.
 ½ is equivalent to ?/10
 ?/24 is equivalent to ¼
 Take your time…
 I’ve got all day…
 You can do it…
 At least I think you can…
 Are we there yet???
How did you do?
 ½ is equivalent to 5/10
 6/24 is equivalent to ¼
 Here’s your yearbook picture