Transcript Chapter 6
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 1 2 Label each mark with the correct fraction 1 2 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. • • • • 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: •