Adding and Subtracting FRACTIONS!!!! by vZy1so

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									Adding and Subtracting
   FRACTIONS!!!!

       A helpful slide show
 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.

  Adding Fractions
Subtracting Fractions
    How do you ADD FRACTIONS?
   First of all, you need          ½+¾
    a “common                  Cannot be added
    denominator”. This           together... Yet.
    means the bottom
    numbers of each
    fraction must be the           2/4 + ¾
    same.                    Can be added because
                              the denominators are
                              “common” (the same)
 Test Time!!!!

See if you can get these
correct, and you will be
      on your way!
         Can These Be Added?
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
 add them.
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

                                   ANSWER: 4
You first need to find a             16 and 4
  number that BOTH                ANSWER: 16
  denominators can
                                      4 and 8
  divide into evenly.
                                   ANSWER: 8
                    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?
   Answer: 2
   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.
Adding the Fractions
    Adding the Converted Fraction

   Now…what do we do with 2/4 + 1/4?

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

   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!
            Click here to go back to the
            beginning of the slide show.
  Subtracting
   Fractions

Learn to Borrow
                 Subtraction

   Subtracting fractions begins exactly the
    same way as adding fractions.
   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?
   ANSWER: 4
    Step #1                          Step #2
   Identify the common      Since ¼ already has a
    denominator.              denominator of 4 you
   1½-¼                      don’t need to change
   ANSWER: 4                 it.
                             But ½ needs to be
                              converted to 4’ths.
         Step #2 (continued)
   How do you convert ½ into 4ths?
   (what number) x 2 = 4?
   ANSWER: 2
   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?
   ANSWER: 1 ¼
          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
    denominator? ANSWER: 16
   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?
   ANSWER: 4

   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
    and add it to 4/16.
   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.
  Ready for an easy
        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
   Now, instead of:
    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.


   The answer:   2 5/16
   WHEW!
 If you’re not sure yet about
how to borrow, click below to
     go through it again.



      Borrowing
      The End
Is your brain turned into
       mush yet?

								
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