I CAN EXPLAIN WHY A FRACTION A/B IS EQUIVALENT TO A FRACTION (N
X A) / (N X B) BY USING FRACTION MODELS Standard 4NF1
Slide 3
Say What? Lets try it with numbers instead of letters. is
equivalent to (2 x 1) / (2 x 2) So, is equivalent to 2/4.
Slide 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 Whats 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).
Slide 5
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.
Slide 6
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.
Slide 7
Sometimes you have to go backwards. Check this out: ? 8 --- =
--- 5 20 Dont freak out! Youre doing the opposite of what you did
before. So whats the opposite of multiplying? DIVIDING! Feel
better?
Slide 8
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
Slide 9
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 dont have to do that, but what the hey. This
is what you look like right now.
Slide 10
Model It! You should be able to do this with numbers, but
Drawing a picture can be very helpful.
Slide 11
Modeling Heres a model of Notice that the top of the model is
hued (darker) and the bottom of the model is in pastel (lighter)
Now, just imagine making an equivalent fraction of this model by
drawing a line down the middle. Ah heck, Ill just show you on the
next slide 1 2
Slide 12
The Next Slide Told you Id show you 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
is equivalent to 2/4 12 34
Slide 13
Your Turn! Solve these 2 equivalent fraction equations. is
equivalent to ?/10 ?/24 is equivalent to Take your time Ive got all
day You can do it At least I think you can Are we there yet???
Slide 14
How did you do? is equivalent to 5/10 6/24 is equivalent to
Heres your yearbook picture
