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:

•