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# Adding Fractions with Different Denominators - PowerPoint PPT Presentation

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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Presentation Transcript

### 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*)
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
• 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
• We were adding things of the same size.

4/9

3/8

• 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.
• (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.

3 x9 27

8 x9 72

+ 4 x8 32

9 x8 72

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 )

Find and write Common Denominator

• Find the multiplication and write it down
• Multiply across
• Reduce
• … when you’re an expert, you can skip copying the “x 8 x 8 x 9 x 9” part.

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)