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Adding Fractions with Different Denominators. (mostly the how, a little about the why or when). 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*) .

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adding fractions with different denominators

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*)
but why why why
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…
we can put them together though
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.
changing feet to inches meant
Changing feet to inches meant
  • We were adding things of the same size.
the denominator down at the bottom has to be the same
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.
find the common denominator write it in
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.*

to keep the fractions equivalent treat the numerator the same as the denominator for each fraction
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

add the numerators and keep that common denominator
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

x9

x9

x9

72

x9

+

x8

+

x8

x8

72

x8

Write in the multiplication, TOP AND BOTTOM of fraction

(I do it bottom-up)

Copy Vertically

Add the top numbers. Bottom one is the “kind of shoe” – it stays the same!

x9

72

x9

+

x8

72

Reduce if you can… but you can’t this time 

x8

Write in Common Denominator (multiplying them always works)

Multiply to get

New Numerators (finish the circle)

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