# Adding and Subtracting FRACTIONS!!!! by vZy1so

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```									Adding and Subtracting
FRACTIONS!!!!

with good hints for you to learn.
First of all,
what makes up a Fraction?
   A fraction has two parts to it:
   A Numerator (the top number)
   And a Denominator (the bottom number)
Which section do you need help
with? Select an area to learn.

Subtracting Fractions
   First of all, you need          ½+¾
denominator”. This           together... Yet.
means the bottom
numbers of each
fraction must be the           2/4 + ¾
the denominators are
“common” (the same)
Test Time!!!!

See if you can get these
correct, and you will be
A.   ¾+¼               A.   YES
B.   ½ + 5/8           B.   NO
C.   3/16 + 5/16       C.   YES
D.   1½+3½             D.   YES
E.   10 3/16 + 3 5/8   E.   NO
F.   15/16 + 3 3/8     F.   NO
G.   2 7/8 + 2 3/8     G.   YES
How did you do?
To start any problem, you first need to
determine if you CAN add them together
as they are.

Or…if you need to change them somehow to
Making a Common
Denominator
How to make a common
denominator.
Here’s what you do if         Find the common
the denominators are         denominator for:
different:                          2 and 4

You first need to find a             16 and 4
number that BOTH                ANSWER: 16
denominators can
 4 and 8
divide into evenly.
HINT

   Did you notice that the common
denominator was ALWAYS the bigger of
the two denominators?

   Just remember that this rule ONLY applies
in woodworking. Not in your math class.
Converting the
Fractions
Step #1
Converting the Fraction
Step #1
   Let’s try an example together!
½+¾
 The ½ needs to be converted to match
the bigger denominator.
   So…(what number) x 2 = 4?
   Simple huh?
Converting the
Fractions
Step #2
Converting the Fraction
Step #2
 Take the answer (2) and multiply it by both the
numerator and denominator.
2x½
(OR) 2 x 1 = 2
2x2 = 4
Do you agree that ½ = 2/4?

So now…2/4 + 1/4 can be added together.

   Now…what do we do with 2/4 + 1/4?

   All that’s left is adding ONLY the
numerators. The denominator IS NOT

   So… 2/4 + 1/4 = 3/4 THE ANSWER!!!
Conclusions
   All addition problems take the same steps
to solve.
   The common denominator will ALWAYS be
the bigger denominator of the two.
   Don’t be afraid of the problem if it has big
numbers. It’s easy!
beginning of the slide show.
Subtracting
Fractions

Learn to Borrow
Subtraction

   Subtracting fractions begins exactly the
   The first thing you have to do is figure out
if you CAN subtract them as they are.
   If not, you will need to convert a
denominator so you can.
Test Time!!!
This should be a breeze.
Can these be subtracted?
   1½-¾                NO
   15/16 – 3/16        YES
 3 5/8 – 1 ½         NO
 5 2/4 – 3 ¼         YES

 10 5/8 – 7 15/16    NO

 3¼-1¼               YES

 7 7/8 – 3 13/16     NO
How did you do?
   Remember that all you need to know is if
they are able to be subtracted.
   If not, we need to convert one of the
fractions.
Make a common
denominator
Let’s do one together
   1½-¼
   You can see that one of them needs to be
converted so you can subtract them.
   What will the common denominator be?
Step #1                          Step #2
   Identify the common      Since ¼ already has a
denominator.              denominator of 4 you
   1½-¼                      don’t need to change
   But ½ needs to be
converted to 4’ths.
Step #2 (continued)
   How do you convert ½ into 4ths?
   (what number) x 2 = 4?
   Now, multiply both the numerator (top
number) and the denominator (bottom
number) by 2.
   1x2=2
2x2=4
Step #3
   So now ½ has been converted to 2/4.
   Now we have: 1 2/4 – ¼
   Go ahead and subtract ONLY the
numerators. What did you get?
Go again
Did you get the right answer?

If so, good job!!!
If not, you had better go over it
again.
BORROWING!!!
   Generally, borrowing is the most difficult
thing to do in subtracting fractions.
   There are 4 simple steps to follow and it
works for ANY fraction in ANY problem.
   Don’t worry, it’s easy once you learn the
steps.
Here is the problem
   Let’s say that you got a problem like this:
3     ¼ - 15/16
   First step: They can’t be subtracted as
they are.
   Second step: What is the common
   Third step: Convert a fraction.
Let’s go through it
   With a common denominator of 4 we need
to figure out: (what number) x 4=16?

   SO: 4 x 1 = 4
4 x 4 = 16
Oops! What’s this?
   The problem now       Normally you would
reads like this:       now subtract. The
problem is that 4 – 15
would be a negative
3 4/16 – 15/16        number. We can’t
have that!
   THUS, BORROWING
IS NEEDED!
Borrowing
   In this problem:
3 4/16 – 15/16
   Borrowing is having to increase the value
or amount of 4/16 so that it’s bigger than
15/16.
   In other words, we need to make 4/16
bigger so that we CAN subtract.
Here’s how to do it
   3 4/16 needs to be changed somehow.
   We’re going to take 1 whole number from the 3
   Would you agree that:

2 + 1 4/16 = 3 4/16?

   NOW COMES THE TRICKY PART.
The tricky part
   2 + 1 4/16 needs to        We can write 1 as:
be changed a bit               2/2 = 1
before we can                  3/3 = 1
subtract from it.              4/4 = 1
   Lets take 1 4/16 and       And so forth up to:
“fix” it.                      16\16 = 1
   Because 16 is the                SO NOW:
common denominator             16 + 4 = 20
we need to write 1 in
16 16 16
16ths.
Recap
3    ¼ -15/16 =
3    4/16 – 15/16 =
   (2 +1 + 4/16) – 15/16 =
   (2 + 16/16 + 4/16) – 15/16 =
   (2 + 20/16) – 15/16 =
   All of these expressions are equal to each
other.
Let’s pause and try a
couple problems.
test?
What fraction would you turn 1 into
to complete the problem?
 1 + 3/16         16/16
 1 + 1/8          8/8

 1 + 9/16         16/16

 1+½              2/2

 1+¾              4/4

 1 + 5/8          8/8
Back to the problem
2 + 1 4/16 we have: 2 20/16
   If we rewrite the problem now we have:

2 20/16 – 15/16
   Now it’s just a simple subtraction problem!
Don’t forget
2 20/16 – 15/16
   Remember that you only subtract the
numerator, not the denominator.

   WHEW!
If you’re not sure yet about
how to borrow, click below to
go through it again.

Borrowing
The End