1. Fractions Explained By Graeme Henchel

2. Index 3/7+2/3 No diagram Adding Mixed Numbers Multiplying Fractions
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
½+1/3 with diagram
1/3+1/4 with diagram
½ +2/5 with diagram
3/7+2/3 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
Fraction<->Decimal<-> %
100 Heart (Percentages)

3. What is a Fraction?
A fraction is formed by dividing a whole into a number of parts
I’m the NUMERATOR. I tell you the number of parts
I’m the DENOMINATOR. I tell you the name of part

4. 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
5x3+2=17
Since 5/5=1 there are 5 fifths in each whole.
So 3 wholes will have 3x5=15 fifths.
Plus the 2 fifths already there makes a total of
15+2=17 fifths

6. 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

7. Multiplying By a Special Form of One
Why does it work?
Multiplying any number by 1 does not change the value 4x1=4, 9x1=9 ……….
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

8. 1

9. Finding equivalent fractions
Convert 5ths to 20ths
That’s 4 so I must multiply by
What do we multiply 5 by to get a product of 20?
Special form of 1

10. 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

11. Adding Fractions with common denominators

12. Adding Fractions with different denominators
Problem:
You can’t 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

13. 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?

14. 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?

15. You can’t 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

16. Lowest common denominator is 10 so make all fractions tenths

17. Turn both fractions into twelfths

18. What is the lowest number BOTH 3 and 7 divide into?
Finally the fractions are READY to add. I just have to add the numerators 9+14=23
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 3x3=9 and 2x7=14
Now I know the new numerators

19. Adding Mixed Numbers
Separate the fraction and the whole number sections, add them separately and recombine at the end

20. Multiplying Fractions

21. Multiplying Fractions

22. Multiplying Mixed Numbers 1
Change to Improper fractions before multiplying

23. Multiplying Mixed numbers 2

25. Division of Fractions By Graeme Henchel

26. Turn the second fraction upside down and multiply
The Traditional Way
Turn the second fraction upside down and multiply

27. Division of fractions the short version
Invert the 2nd fraction and multiply

28. Division with numbers only the full story

29. An Alternative way
Convert to equivalent fractions with a common denominator and then you just divide the numerators only

30. Form equivalent fractions with common denominators
A visual representation
Form equivalent fractions with common denominators

33. Decisions and Actions in evaluating fraction problems
Fraction Flowchart
Decisions and Actions in evaluating fraction problems
Graeme Henchel

34. FLOWCHART and Skill set
The following should be used with the Fraction Flow chart word doc. Download from

35. Decision: What is the operation?
x,÷
+ , -

36. Decision: Are there Mixed Numbers?
+, -
Decision: Are there Mixed Numbers?
For example is a mixed number
YES
Mixed Numbers? NO

37. ACTION: Evaluate Whole numbers
+, -
Evaluate the whole number part and
keep aside till later
4+3=7

38. Decision: Are there common Denominators?
+, -
For example and have the same (common) denominator
Common Denominators?
YES NO

39. 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

40. Action: Add or Subtract the numerators
+, -
Add (or subtract) the numerators this is the number of parts 2+3=5
Keep the Common Denominator.
This is the name of the fraction

41. Decision: Is the numerator negative?
+, -
Decision: Is the numerator negative?
Is numerator negative?
YES NO
This numerator is negative

42. Action: Borrow a whole unit
+, -
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

43. Action: Add any whole number part
+, -
Action: Add any whole number part

44. +, -
That’s All Folks

45. Decision: Are there Mixed Numbers?
For example is a mixed number
YES NO
Mixed Numbers?

46. Action: Change to improper fractions
x,÷
Action: Change to improper fractions OR
4X5=20
and 20+3=23

47. Decision: Is this a X or a ÷ problem?

48. Action: Invert the 2nd Fraction and replace division ÷ with multiply x
Invert the 2nd fraction and multiply

49. Decision : Is cancelling Possible?
x,÷
Decision : Is cancelling Possible?
Do numbers in the numerators and the denominators have common factors
Yes No
Common factors
in numerators
and denominators

50. Action Simplify by cancelling
x,÷
Action Simplify by cancelling 1 1
÷ 3
÷ 5
÷ 3
÷ 5 2 2

51. ACTION: Multiply the numerators AND the denominators
x,÷
ACTION: Multiply the numerators AND the denominators

52. Decision: Is the product improper (top heavy)
x,÷
Decision: Is the product improper (top heavy)
Yes No
Is the fraction
improper ?
(top heavy)

53. Action: Change to a mixed Number

54. x,÷
That’s All Folks

55. Representing Decimal Fractions1 1 1 1 ●
decimal point ●

56. Representing Decimal Fractions1 3 5 2 ●
decimal point ●

57. Converting Fractions to decimals and %
Graeme Henchel

59. Conversions 0.4 40% Multiply by a special form of 1 Divide 2 by 5
Find 2÷5
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. Divide numerator and denominator by a common factor of 2
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%

61.  Move decimal point 2 places left
Conversions
0.4
Divide 40 by 100
 Move decimal point 2 places left 40 %
40%

62. Graeme Henchel http://hench-maths.wikispaces.com
Percentages 100 hearts
Graeme Henchel

63. Visual representations
100% 1% 5%
10%
20%
25%
33⅓%
50%
Percent = per hundred

64. 100%=100/100

65. 1%=1/100

66. 5%=5/100=1/20

67. 10%=10/100=1/10

68. 20%=20/100=1/5

69. 25%=25/100=1/4

70. 33⅓%=33⅓/100=⅓

71. 50%=50/100=½