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Adding Fractions with Different Denominators

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

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

  2. 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*)

  3. 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…

  4. 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.

  5. Changing feet to inches meant • We were adding things of the same size.

  6. Back to our original problem: 3/8 + 4/9 3/8 ------- 4/9 -----

  7. Put ‘em together…Huh???? It isn’t eigths or ninths… 4/9 3/8

  8. 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.

  9. Here’s how to get *any* pair of fractions to have a common denominator

  10. Rewrite the Problem Vertically 3 8 + 4 9

  11. 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.*

  12. What did you multiply by to get the new denominator? 3 x9 ___ 8 x9 72 + 4 x8 ___ 9 x8 72

  13. 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

  14. 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 )

  15. 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.

  16. 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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