Fractions Explained

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Fractions Explained

• By Graeme Henchel

http//hench-maths.wikispaces.com
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Index

• What is a fraction?
• Mixed Numbers method 1
• Mixed Numbers method 2
• Equivalent Fractions
• Special form of one Why
• Special form of one
• Finding equivalent fractions
• Simplifying Fractions
• Adding Common denominators
• Adding Different denominators
• Common denominators 1
• Common denominators 2
• ½1/3 with diagram
• 1/31/4 with diagram
• ½ 2/5 with diagram

• 3/72/3 No diagram
• Adding Mixed Numbers
• Multiplying Fractions
• Multiplying Mixed Numbers 1
• Multiplying Mixed numbers 2
• Multiplying Mixed diagram
• Dividing Fractions
• Fraction Flowchart .ppt
• Fraction Flowchart .doc (download)
• Decimal Fractions
• Fractionlt-gtDecimallt-gt
• 100 Heart (Percentages)

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What is a Fraction?
A fraction is formed by dividing a whole into a
number of parts
Im the NUMERATOR. I tell you the number of parts
Im the DENOMINATOR. I tell you the name of part
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Mixed numbers to improper fractions
Convert whole numbers to thirds
Mixed number
Improper fraction
5
Another Way to change Mixed Numbers to improper
fractions
In short 5x3217
Since 5/51 there are 5 fifths in each whole. So
3 wholes will have 3x515 fifths. Plus the 2
fifths already there makes a total of 15217
fifths
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Equivalent fractions
An equivalent fraction is one that has the same
value and position on the number line but has a
different denominator
Equivalent fractions can be found by multiplying
by a special form of 1
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Multiplying By a Special Form of One
Why does it work?

• Multiplying any number by 1 does not change the
  value 4x14, 9x19 .
• Any number divided by itself 1.

Multiplying a fraction by a special form of one
changes the numerator and the denominator but
DOES NOT CHANGE THE VALUE
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1
9
Finding equivalent fractions
Convert 5ths to 20ths
Thats 4 so I must multiply by
What do we multiply 5 by to get a product of 20?
Special form of 1
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Simplifying Fractions Cancelling

• Simplifying means finding an equivalent fraction
  with the LOWEST denominator by making a special
  form of 1 equal to 1

1
Another way of doing this
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Adding Fractions with common denominators
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Adding Fractions with different denominators
Problem You cant add fractions with different
denominators without getting them ready first.
They will be ready to add when they have common
denominators
Solution Turn fractions into equivalent
fractions with a common denominator that is find
the Lowest Common Multiple (LCM) of the two
denominators
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Finding the Lowest Common Denominator

• The lowest common multiple of two numbers is the
  lowest number in BOTH lists of multiples

Multiples of 2 are 2, 4, 6, 8, 10 Multiples of
3 are 3, 6, 9, 12, What is the lowest
common multiple?
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Finding the Lowest Common Denominator

• The lowest common multiple of two numbers is the
  lowest number they will BOTH divide into

2 divides into 2, 4, 6, 8.. 3 divides into 3, 6,
9. What is the lowest number 2 and 3 both
divide into?
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You cant add fractions with different
denominators

The Lowest Common Multiple of 2 and 3 is 6 so
turn all fractions into sixths
Special form of 1
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Lowest common denominator is 10 so make all
fractions tenths
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Turn both fractions into twelfths
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Finally the fractions are READY to add. I just
have to add the numerators 91423
It is 3/3 So I multiply 3/7 by 3/3
It is 7/7 So I multiply 2/3 by 7/7
What is the lowest number BOTH 3 and 7 divide
into? Hmmmmm??????
What special form of 1 will change 7 to 21.
Hmmmm?
What special form of 1 will change 3 to 21.
Hmmmm?
It is 21. So that is my common denominator
Now 3x39 and 2x714 Now I know the new numerators
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Adding Mixed Numbers

• Separate the fraction and the whole number
  sections, add them separately and recombine at
  the end

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Multiplying Fractions
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Multiplying Fractions
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Multiplying Mixed Numbers 1
Change to Improper fractions before multiplying
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Multiplying Mixed numbers 2
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(No Transcript)
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Division of Fractions

• By Graeme Henchel

http//hench-maths.wikispaces.com
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The Traditional Way

• Turn the second fraction upside down and multiply

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Division of fractions the short version
Invert the 2nd fraction and multiply
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Division with numbers onlythe full story
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An Alternative way

• Convert to equivalent fractions with a common
  denominator and then you just divide the
  numerators only

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A visual representation
Form equivalent fractions with common denominators
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(No Transcript)
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(No Transcript)
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Fraction Flowchart

• Decisions and Actions in evaluating fraction
  problems
• Graeme Henchel
• http//hench-maths.wikispaces.com

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FLOWCHART and Skill set
The following should be used with the Fraction
Flow chart word doc. Download from
http//hench-maths.wikispaces.com
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Decision What is the operation?
What is the operation?
x,
, -
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Decision Are there Mixed Numbers?
, -
For example is a mixed number
YES
Mixed Numbers?
NO
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ACTION Evaluate Whole numbers
, -
Evaluate the whole number part and keep aside
till later
437
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Decision Are there common Denominators?
, -
For example and have
the same (common) denominator
YES
Common Denominators?
NO
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Action Find equivalent fractions
, -
Find equivalent fractions with common (the same)
denominators
Multiply by a special form of 1
Multiply by a special form of 1
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Action Add or Subtract the numerators
, -
Add (or subtract) the numerators this is the
number of parts 235
Keep the Common Denominator. This is the name of
the fraction
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Decision Is the numerator negative?
, -
YES
Is numerator negative?
NO
This numerator is negative
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Action Borrow a whole unit
, -
Borrow 1 from the whole number part Write it as
an equivalent fraction Add this to your negative
fraction
Remember to adjust your whole number total
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Action Add any whole number part
, -
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Thats All Folks
, -
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Decision Are there Mixed Numbers?
x,
For example is a mixed number
YES
Mixed Numbers?
NO
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Action Change to improper fractions
x,
OR
4X520 and 20323
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Decision Is this a X or a problem?
x,
x
X or ?

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Action Invert the 2nd Fraction and replace
division with multiply x
x,
Invert the 2nd fraction and multiply
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Decision Is cancelling Possible?
x,

• Do numbers in the numerators and the denominators
  have common factors

Yes
Common factors in numerators and denominators
No
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Action Simplify by cancelling
x,
1
1
3
5
3
5
2
2
51
ACTION Multiply the numerators AND the
denominators
x,
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Decision Is the product improper (top heavy)
x,
Yes
Is the fraction improper ? (top heavy)
No
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Action Change to a mixed Number
x,
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Thats All Folks
x,
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Representing Decimal Fractions
1
1
1
1
?
decimal point
?
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Representing Decimal Fractions
1
3
5
2
?
decimal point
?
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Converting Fractions to decimals and

• Graeme Henchel
• http//hench-maths.wikispaces.com

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(No Transcript)
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Conversions
Divide 2 by 5 Find ?25
Multiply by a special form of 1
Write as a decimal using place value
Write as a fraction with 10 as denominator
0.4
Multiply by a special form of 1
Multiply by special form of 1
40
60
Conversions
Divide numerator and denominator by a common
factor of 2
Write as a fraction with 100 as denominator then
divide numerator and denominator by common factor
of 20
0.4
Write as a fraction with 100 as denominator then
divide numerator and denominator by common factor
of 10
40
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Conversions
0.4
Divide 40 by 100 ? Move decimal point 2 places
left
40

0
40
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Percentages100 hearts

• Graeme Henchel
• http//hench-maths.wikispaces.com

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Visual representations

• 100
• 1
• 5
• 10
• 20
• 25
• 33?
• 50

Percent per hundred
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100100/100
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11/100
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55/1001/20
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1010/1001/10
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2020/1001/5
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2525/1001/4
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33?33?/100?
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5050/100½