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 