Adding and Subtracting FRACTIONS!!!!

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Adding and SubtractingFRACTIONS!!!!

• A helpful slide show
• with good hints for you to learn.

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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)

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Which section do you need help with? Select an
area to learn.
Adding Fractions
Subtracting Fractions
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How do you ADD FRACTIONS?

• First of all, you need a common denominator.
  This means the bottom numbers of each fraction
  must be the same.

• ½ ¾
• Cannot be added together... Yet.
• 2/4 ¾
• Can be added because the denominators are
  common (the same)

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Test Time!!!!

• See if you can get these
• correct, and you will be
• on your way!

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Can These Be Added?

• ¾ ¼
• ½ 5/8
• 3/16 5/16
• 1 ½ 3 ½
• 10 3/16 3 5/8
• 15/16 3 3/8
• 2 7/8 2 3/8

1. YES
2. NO
3. YES
4. YES
5. NO
6. NO
7. YES

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How did you do?

• To start any problem, you first need to determine
  if you CAN add them together as they are.
• Orif you need to change them somehow to add
  them.

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Making a CommonDenominator
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How to make a common denominator.

• Heres what you do if the denominators are
  different
• You first need to find a number that BOTH
  denominators can divide into evenly.

• Find the common denominator for
• 2 and 4
• ANSWER 4
• 16 and 4
• ANSWER 16
• 4 and 8
• ANSWER 8

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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.

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Converting the Fractions

• Step 1

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Converting the FractionStep 1

• Lets 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?

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Converting the Fractions

• Step 2

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Converting the FractionStep 2

• Take the answer (2) and multiply it by both the
  numerator and denominator.
• 2 x ½
• (OR) 2 x 1 2
• 2 x 2 4
• Do you agree that ½ 2/4?
• So now2/4 1/4 can be added together.

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Adding the Fractions
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Adding the Converted Fraction

• Nowwhat do we do with 2/4 1/4?
• All thats left is adding ONLY the numerators.
  The denominator IS NOT added. It stays the same.
• So 2/4 1/4 3/4 THE ANSWER!!!

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Conclusions

• All addition problems take the same steps to
  solve.
• The common denominator will ALWAYS be the bigger
  denominator of the two.
• Dont be afraid of the problem if it has big
  numbers. Its easy!

Click here to go back to the beginning of the
slide show.
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Subtracting Fractions
Learn to Borrow
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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.

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Test Time!!!

• This should be a breeze.

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Can these be subtracted?

• 1 ½ - ¾
• 15/16 3/16
• 3 5/8 1 ½
• 5 2/4 3 ¼
• 10 5/8 7 15/16
• 3 ¼ - 1 ¼
• 7 7/8 3 13/16

• NO
• YES
• NO
• YES
• NO
• YES
• NO

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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.

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Make a common denominator
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Lets do one together

• 1 ½ - 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

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Step 1 Step 2

• Identify the common denominator.
• 1 ½ - ¼
• ANSWER 4

• Since ¼ already has a denominator of 4 you dont
  need to change it.
• But ½ needs to be converted to 4ths.

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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.
• 1 x 2 2
• 2 x 2 4

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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

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Did you get the right answer?
Go again

• If so, good job!!!
• If not, you had better go over it again.

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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.
• Dont worry, its easy once you learn the steps.

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Here is the problem

• Lets say that you got a problem like this
• 3 ¼ - 15/16
• First step They cant be subtracted as they
  are.
• Second step What is the common denominator?
  ANSWER 16
• Third step Convert a fraction.

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Lets go through it

• With a common denominator of 4 we need to figure
  out (what number) x 416?
• ANSWER 4
• SO 4 x 1 4
• 4 x 4 16

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Oops! Whats this?

• The problem now reads like this
• 3 4/16 15/16

• Normally you would now subtract. The problem is
  that 4 15 would be a negative number. We cant
  have that!
• THUS, BORROWING IS NEEDED!

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Borrowing

• In this problem
• 3 4/16 15/16
• Borrowing is having to increase the value or
  amount of 4/16 so that its bigger than 15/16.
• In other words, we need to make 4/16 bigger so
  that we CAN subtract.

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Heres how to do it

• 3 4/16 needs to be changed somehow.
• Were 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.

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The tricky part

• 2 1 4/16 needs to be changed a bit before we
  can subtract from it.
• Lets take 1 4/16 and fix it.
• Because 16 is the common denominator we need to
  write 1 in 16ths.

• We can write 1 as
• 2/2 1
• 3/3 1
• 4/4 1
• And so forth up to
• 16\16 1
• SO NOW
• 16 4 20
• 16 16 16

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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.

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Lets pause and try a couple problems.

• Ready for an easy test?

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What fraction would you turn 1 into to complete
the problem?

• 1 3/16
• 1 1/8
• 1 9/16
• 1 ½
• 1 ¾
• 1 5/8

• 16/16
• 8/8
• 16/16
• 2/2
• 4/4
• 8/8

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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 its just a simple subtraction problem!

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Dont forget

• 2 20/16 15/16
• Remember that you only subtract the numerator,
  not the denominator.
• The answer 2 5/16
• WHEW!

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If youre not sure yet about how to borrow, click
below to go through it again.
Borrowing
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The End

• Is your brain turned into mush yet?