FRACTIONS & RATIONAL NUMBERS 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

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

Label each mark with the correct fraction 2 1

Label each mark with the correct fraction 1 2

Equivalent fractions Fraction 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.

B 7 Denominator is bigger Improper Fractions A 9 Numerator is bigger 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: