View
225
Download
1
Embed Size (px)
Citation preview
Chapter 6
FRACTIONS &
RATIONAL NUMBERS
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
Activity 1
• Pattern blocks• Cuisenaire Rod
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
• Folded fractions• ¼• 1/8• 1/6• Pattern Blocks Equivalent Fraction
Worksheet2• Activity 2
• Pattern Block Worksheet (what is 1?)• Set Model Pg 347
• Fraction Strips showing ½ = 3/6
1 2
Label each mark with the correct fraction
Number line model = ruler.What is the unit?How many equal parts is the unit divided into?
1 2
Label each mark with the correct fraction
1 2
Label each mark with the correct fraction
Equivalent fractionsFraction Strips to show 2/3 =4/6 = 6/9 = 8/12
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.
• Proper Fractions • A 4 Numerator is smaller • B 7 Denominator is bigger • Improper Fractions A 9 Numerator is bigger B 7 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.
Common Denominators
• Finding common denominators is finding the LCM.
• Fraction Strips.
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
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?
• Homework Pg 357 # 1,2,3,4all,5,7,9all14,17all,39,43-46
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
• Adding & Subtracting Fractions with different denominators.
• Pattern Block Worksheet.• Activity 7 wkst.
Subtraction of Fractions
• Just like addition, subtraction can only be done with like objects.
• 5 apples – 3 apples• 7/6 – 3/6
Mixed Numbers & Their Equivalents
Homework
• Pg 372 # 1,3,4,5,7,8,9,10,11,12 a-e,31-32
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
X =
3 1/7 x 5 1/4
3 1/7 x 5 1/4
• 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
• Activity 8 Multiplying Fractions• Worksheet
Division of Fractions
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
Division with Fractions
•
• Activity 9• Worksheet
Homework
• Pg 387 # 1a-c,2,3,4,5,7, 15, 35 - 37
Properties of Rational Numbers
• Addition• Closure• Commutative• Associative• Zero is an Additive Identity• Existence of Additive Inverse
Properties of Rational Numbers
• Subtraction• Closure• NOT Commutative• NOT Associative• Zero is an Identity
Properties of Rational Numbers
• Multiplication• Closure• Commutative• Associative• One is an Multiplicative Identity• Existence of Multiplicative Inverse• Multiplication by 0
Properties of Rational Numbers
• Division• Closure• NOT Commutative• NOT Associative
Density Property
• For any 2 rational numbers there will be a rational number between them.
• If then there exist such that
•
Find a rational number between:
•