Adding Fractions with Different Denominators
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Transcript 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*)
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.
Back to our original problem: 3/8 + 4/9
3/8 -------
4/9 -----
PUT ‘EM TOGETHER…
HUH???? IT ISN’T EIGTHS OR NINTHS…
4/9
3/8
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.
HERE’S HOW TO GET *ANY* PAIR OF FRACTIONS
TO HAVE A COMMON DENOMINATOR
REWRITE THE PROBLEM VERTICALLY
3
8
+
4
9
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.*
WHAT DID YOU MULTIPLY BY TO GET THE
NEW DENOMINATOR?
3 x9
8 x9
+
4 x8
9 x8
___
72
___
72
TO KEEP THE FRACTIONS EQUIVALENT, TREAT
THE NUMERATOR THE SAME AS THE
DENOMINATOR FOR EACH FRACTION.
3 x9
8 x9
+
4 x8
9 x8
27
72
32
72
ADD THE NUMERATORS, AND KEEP THAT
COMMON DENOMINATOR.
3 x9
8 x9
+
4 x8
9 x8
27
72
32
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.
x9
x9
+
+
72
x9
x8
x8
Copy Vertically
x9
x8
72
Write in the multiplication,
TOP AND BOTTOM of fraction
(I do it bottom-up)
x9
72
+
72
Write in Common
Denominator (multiplying
them always works)
x8
Add the top
numbers.
Bottom one is the
“kind of shoe” – it
stays the same!
x9
x8
x8
Multiply to get
New Numerators
(finish the circle)
Reduce if you
can… but you
can’t this time