1. FRACTIONS & RATIONAL NUMBERS
Chapter 6
FRACTIONS
&
RATIONAL NUMBERS

2. 6.1 Basic Concept of a Fraction
A Fraction is “a part of a whole”
Must first agree on the unit (the whole).
Understand that we are subdividing the unit into b equal parts.
Consider a of the parts of the unit.
a is the numerator
b is the denominator
Activity 1

3. Activity 1
Pattern blocks
Cuisenaire Rod

4. Fraction
A fraction is an ordered pair of integers a and b, b ≠ 0, written a/b. The integer a is called the numerator of the fraction and the integer b is called the denominator of the fraction.
1/3, 4/3, -2/-3, 0/3

5. Folded fractions
1/8
1/6
Pattern Blocks Equivalent Fraction Worksheet2
Activity 2

6. Pattern Block Worksheet (what is 1?)
Set Model Pg 347
Fraction Strips showing ½ = 3/6

7. Number line model = ruler.
What is the unit?
How many equal parts is the unit divided into?
Label each mark with the correct fraction 2 1

8. Label each mark with the correct fraction2 1

9. Label each mark with the correct fraction1 2

10. Equivalent fractions
Fraction Strips to show 2/3 =4/6 = 6/9 = 8/12

11. Properties of Fractions
a/b = an/bn for any integer n
a/b = c/d are equivalent if and only if ad = bc
a/b is in simplest form if a and b have no common divisors larger than 1.

12. B 7 Denominator is bigger Improper Fractions A 9 Numerator is bigger
A Numerator is smaller
B Denominator is bigger
Improper Fractions
A Numerator is bigger
B Denominator is smaller
Confusion about improper fractions 9/8 of a pie. In a bakery with a lot of identical pies 9/8 of a pie would be the pies all cut into 8 equal pieces so that we could take 9 of the equal pieces.

13. Common Denominators Finding common denominators is finding the LCM.
Fraction Strips.

14. Order of Fractions a/b is less than c/d if and only if ad < bc.
Mickey Mouse.
Fraction strips Pg 355
Diagrams.
Activity 5
Comparing fraction by Reasoning

15. Rational Numbers
A rational number is a number THAT CAN be represented by a fraction a/b, where a and b are integers and b 0. Two rational numbers are equal if and only if they can be represented by equivalent fractions.
Pg 355 ex.
What is not a rational number?

16. Homework Pg 357 # 1,2,3,4all,5,7,9all14,17all,39,43-46

17. 6.2 Addition & Subtraction of Fractions
You can only add like things.
3 Apples + 2 apples = 5 apples
3 Apples + 4 oranges = ??????
MUST HAVE COMMON DEONMINATORS BEFORE YOU CAN ADD FRACTIONS.
2/8 + 3/8 = 5/8

19. Adding & Subtracting Fractions with different denominators.
Pattern Block Worksheet.
Activity 7 wkst.

21. Subtraction of Fractions
Just like addition, subtraction can only be done with like objects.
5 apples – 3 apples
7/6 – 3/6

22. Mixed Numbers & Their Equivalents

25. Homework
Pg 372 # 1,3,4,5,7,8,9,10,11,12 a-e,31-32

26. Multiplication & Division of Fractions
Meaning of multiplication
A x B represents the total number of objects in A groups of B objects in each group.
3 x 2/3
We have 3 groups of 2/3 of a candy bar = 6/3 = 2

27. X =

29. 3 1/7 x 5 1/4

30. 3 1/7 x 5 1/4

32. 3 1/7 x 5 ¼
22/7 x 21/4
22 x 21 / 7 x 4 = 662/ 28
16 14/28
16 1/2

33. Activity 8 Multiplying Fractions
Worksheet

34. Division of Fractions

36. Division with Fractions
Dividing by a fraction is the same as multiplying by it’s reciprocal.
Reciprocals The reciprocal of a fraction is found by inverting the fraction. The reciprocal of is

37. Division with Fractions

38. Activity 9
Worksheet

39. Homework
Pg 387 # 1a-c,2,3,4,5,7, 15,

40. Properties of Rational Numbers
Addition
Closure
Commutative
Associative
Zero is an Additive Identity
Existence of Additive Inverse

41. Properties of Rational Numbers
Subtraction
Closure
NOT Commutative
NOT Associative
Zero is an Identity

42. Properties of Rational Numbers
Multiplication
Closure
Commutative
Associative
One is an Multiplicative Identity
Existence of Multiplicative Inverse
Multiplication by 0

43. Properties of Rational Numbers
Division
Closure
NOT Commutative
NOT Associative

44. Density Property
For any 2 rational numbers there will be a rational number between them.
If then there exist such that

45. Find a rational number between: