mostly the how a little about the why or when 38 49 Step one what is this problem asking me to do Add fractions which means what You need a common denominator Multiplication and division dont ID: 201673
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Slide1
Adding Fractions with Different Denominators
(mostly the how, a little about the why or when)Slide2
3/8 + 4/9
Step one: “what is this problem asking me to do?”
Add fractions, which means what?
You need a common denominator. (Multiplication and division *don’t*) Slide3
But why??? Why??? Why???
Welp
, if I said I wanted to add 8 inches and 3 feet…
Would that be 11 miles?
I don’t think so.
It wouldn’t be 11 inches… it wouldn’t be 11 feet…It would be 3 feet and 8 inches… Slide4
We *can* put them together, though
One foot is exactly the same as 12 inches.
3 feet would have 12 + 12 + 12 inches, or 3 x 12 inches.
36 inches plus the other eight inches would mean we had 44 inches total. Slide5
Changing feet to inches meant
We were adding things of the same size. Slide6
Back to our original problem: 3/8 + 4/9
3/8 -------
4/9 -----
Slide7
Put ‘em
together…
Huh???? It isn’t
eigths
or ninths…
3/8
4/9
Slide8
The “denominator” – DOWN at the bottom – has to be the same.
Think of the denominator as shoes.
If the fractions aren’t wearing the same kinds of shoes, they can’t dance together.
Sorry, those are the rules
(and I did explain why, remember?)
OR… since you’ve been working with “like terms”… the denominator is like an “x” or a “y.” 3/8 + 4/9 is like adding 3x and 4y (but x would be 1/8 and 7 would be 1/9)… you can’t just put ‘
em together. Slide9
Here’s how to get *any* pair of fractions to have a common denominatorSlide10
Rewrite the Problem Vertically
3
8
+
4 9Slide11
Find the Common Denominator.Write
it in.
(You’re not *changing* the fraction, just
its
name. 2 quarters is worth the same amount as 5 dimes or 10 nickels; they just look different.)
3 ___ 8 72
+ 4 ___ 9 72
If you’re not sure what the *least* common denominator is, you can always *multiply the two denominators.* Slide12
What did you multiply by to get the new denominator?
3
x9 ___
8 x9 72+ 4 x8 ___ 9 x8 72
Slide13
To keep the fractions equivalent, treat the numerator the same as the denominator for each fraction.
3
x9
27 8 x9 72+
4 x8 32 9 x8 72
Slide14
Add the numerators, and keep that common denominator.
3
x9
27 8 x9 72+ 4
x8 32 9 x8 72
59
72(Reduce it if you can. You can’t
) Slide15
Find and write Common Denominator
Find the multiplication and write it down
Multiply across
Add down
Reduce
… when you’re an expert, you can skip copying the “x 8 x 8 x 9 x 9” part. Slide16
+
Copy Vertically
+
Write in Common Denominator (multiplying them always works)
72
72
Write in the multiplication,
TOP AND BOTTOM of fraction
(I do it bottom-up)
+
72
72
x8
x8
x9
x9
x8
x8
x9
x9
Multiply to get
New Numerators (finish the circle)
x8
x8
x9
x9
Add the top numbers.
Bottom one is the
“kind of shoe”
– it stays the same!
Reduce if you can… but you can’t this time