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# Fractions Explained

Fractions Explained. By Graeme Henchel. http://hench-maths.wikispaces.com. 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

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## Fractions Explained

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1. Fractions Explained By Graeme Henchel http://hench-maths.wikispaces.com

2. 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) Index

3. A fraction is formed by dividing a whole into a number of parts What is a Fraction? 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. 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

24. Division of Fractions By Graeme Henchel http://hench-maths.wikispaces.com

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

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

27. Division with numbers onlythe full story

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

29. A visual representation Form equivalent fractions with common denominators

30. Fraction Flowchart Decisions and Actions in evaluating fraction problems Graeme Henchel http://hench-maths.wikispaces.com

31. FLOWCHART and Skill set The following should be used with the Fraction Flow chart word doc. Download from http://hench-maths.wikispaces.com

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

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

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

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

36. +, - 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

37. +, - 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

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

39. +, - 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

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

41. +, - That’s All Folks

42. x,÷ Decision: Are there Mixed Numbers? For example is a mixed number YES Mixed Numbers? NO

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

44. x,÷ Decision: Is this a X or a ÷ problem? x X or ÷ ? ÷

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

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

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

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