# A DDING F RACTIONS WITH D IFFERENT D ENOMINATORS (mostly the how, a little about the why or when)

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A DDING F RACTIONS WITH D IFFERENT D ENOMINATORS (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*)

B UT WHY ??? W HY ??? W HY ??? 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…

W E * 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.

C HANGING FEET TO INCHES MEANT We were adding things of the same size.

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

P UT ‘ EM TOGETHER … H UH ???? I T ISN ’ T EIGTHS OR NINTHS … 3/8 4/9

T HE “ 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.

H ERE ’ S HOW TO GET * ANY * PAIR OF FRACTIONS TO HAVE A COMMON DENOMINATOR

R EWRITE THE P ROBLEM V ERTICALLY 3 8 + 4 9

F IND THE C OMMON D ENOMINATOR.W RITE 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.*

W HAT DID YOU MULTIPLY BY TO GET THE NEW DENOMINATOR ? 3 x9 ___ 8 x9 72 + 4 x8 ___ 9 x8 72

T O 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

A DD 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 Add down Reduce … when you’re an expert, you can skip copying the “x 8 x 8 x 9 x 9” part.

+ Copy Vertically + Write in Common Denominator (multiplying them always works) 72 Write in the multiplication, TOP AND BOTTOM of fraction (I do it bottom-up) + 72 x8 x9 x8 x9 Multiply to get New Numerators (finish the circle) x8 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

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