Pre Algebra Chapter 4 Rational Numbers and Fractions

Pre- Algebra Chapter 4: Rational Numbers and Fractions

Chapter Project – 50 points �Group Work – Teams of 3 �Your groups will conduct surveys to at least 20 students. �You will create your own survey, asking at least 10 questions. � Answer types could include: �Yes or No �Like or Dislike �A scale of 0 -5 �Favorites

Schedule of Events Monday Tuesday Wednesday Thursday Friday Nov. 23 Chapter 4 Introduction 24 25 Lesson 1 & 2 – Proper, Improper and Mixed Numbers Homework: Pg. 85 1 -10, Pg. 89 2 -34 EVEN 26 No School – Thanksgiving 27 No School – Thanksgiving 30 Dec. 1 3 4 Lesson 3 – Equivalent Fractions Homework: Pg. 91 -93 #1 -20 Lesson 4 – Simplest Form Homework: Pg. 95 #1 -25 2 QUIZ 1 st Team Meeting Lesson 5 – Comparing and Ordering Fractions Lesson 6 & 7 – Like and Unlike Denominators Homework: Pg. 98 -99 #1 -25 Homework: Pg 102 -103 #2 -24 even Pg. 106 -107 #2 -24 even 7 8 QUIZ 2 nd Team Meeting 9 10 Lesson 9 – Multiplying Fractions and Mixed Numbers Lesson 10 – Dividing Fractions and Mixed Numbers 11 Chapter Review Pg. 117 – 119 all Homework: Pg 111 1 -25 Homework: Pg 114 1 -20 14 15 16 17 18 Supplementary Problems 374 -375 all Begin review for Semester Exam Review for Semester Exam 21 Semester Exams HR 14 Exam Ch 1 -4 Projects Due 22 Semester Exams HR 5 -8 23 No School – Begin break 24 No School – Christmas Eve 25 No School – Christmas Day Lesson 8 – Subtracting Fractions with Regrouping Homework: Pg 109 1 -20 2: 30 Dismissal

Goals for Learning �To learn proper and improper fractions and mixed numbers �To write equivalent fractions �To express fractions in their simplest form �To compare and order fractions �To add and subtract fractions and mixed numbers with like or unlike denominators �To multiply and divide fractions and mixed numbers

Lesson 1 & 2 – Proper and Improper Fractions and Mixed Numbers �Vocabulary – � Proper Fraction – � Improper Fraction – � Mixed Number -

Proper Fractions What part is shaded red? Shade each shape using the given fraction.

Improper Fractions �TO change an improper fraction to a mixed number, DIVIDE

Mixed Numbers �To change a mixed number to an IMPROPER FRACTION � Step 1: Multiply the WHOLE NUMBER by the DENOMINATOR � Step 2: ADD the NUMERATOR

Homework �Lesson 1 & 2 – Proper, Improper and Mixed Numbers �Homework: Pg. 85 1 -10, Pg. 89 2 -34 EVEN

Lesson 3 - Equivalent Fractions � Name the same amount but have different numerators and denominators. =

Equivalent Fraction Models = =

Equivalent Fraction Models = =

Equivalent Fraction Models 1 2 =

Equivalent Fraction Models 3 4 =

Equivalent Fraction Models 2 3 =

What are the missing numbers? 1 2 = =

What are the missing numbers? 1 2 = =

What are the missing numbers? 1 2 =

What are the missing numbers? 3 4 =

What are the missing numbers? 2 3 =

To Find Equivalent Fractions � Multiply the numerator and the denominator by the same number. 1 x 3 3 = 9

To Find Equivalent Fractions � Divide the numerator and the denominator by the same number. 4 ÷ 12 1 = 3

Homework �Lesson 3 – Equivalent Fractions �Homework: Pg. 91 -93 #1 -20

Lesson 4 – Simplest Form �First, lets recall finding the GCD (Greatest common Divisor) � GCD (9, 21) � GCD (10, 15) � GCD (30, 36)

Simplifying Using the GCD �Express each fraction in lowest terms using the GCD method.

Homework: �Lesson 4 – Simplest Form �Homework: Pg. 95 #1 -25 �Tomorrow: QUIZ st � 1 Team Meeting

Lesson 5 – Comparing and Ordering Fractions �Activity – Creating fraction strips. � 1 st – Fold your paper in half. Label the crease ½. � 2 nd – Fold your paper into halves twice. Label these ¼ and ¾. � 3 rd – Fold your paper into fifths. �Continue as instructed…

Cont… �In order to compare and order fractions, they need to have the same denominator. �To change unlike fractions to like fractions we use MULTIPLICATION and LCM (Least Common Multiple).

Order the following fractions from LEAST TO GREATEST

Homework: �Lesson 5 – Comparing and Ordering Fractions �Homework: Pg. 98 -99 #1 -25

Lesson 6 & 7 – Fractions with Like and Unlike Denominators �Important Side Notes: � In algebra, 1 x and x are the same value. You will see several letters written without the 1 present. � 1 m = m � 1 p = p �K = 1 k �X = 1 x � Recall that the fraction bar that separates a numerator from a denominator means “DIVIDE”

Like Denominators �When fractions have the same denominator, all you have to do is ADD or SUBTRACT the numerator.

Like Denominators with Variables

Unlike Denominators

Unlike Denominators with Variables

Homework: �Lesson 6 & 7 – Like and Unlike Denominators �Homework: �Pg 102 -103 #2 -24 even �Pg. 106 -107 #2 -24 even

Lesson 8 – Subtracting Fractions with Regrouping

Practice with Common Denominators

Practice with Unlike Denominators

Homework �Lesson 8 – Subtracting Fractions with Regrouping �Homework: Pg 109 1 -20 � Tomorrow: QUIZ nd � 2 Team Meeting

Lesson 9 – Multiplying Fractions, Mixed Numbers �Quick Recap: � Changing Mixed Numbers to Improper Fractions:

Multiplying Background �Unlike addition and subtraction, when you multiply fractions: �you DO NOT NEED a common denominator. �you DO NOT write them up and down. �you DO MULTIPLY LEFT TO RIGHT! Numerators and Denominators. �ALWAYS SIMPLIFY

Examples:

Homework: �Lesson 9 – Multiplying Fractions and Mixed Numbers �Homework: Pg 111 1 -25

Lesson 10 – Dividing Fractions, Mixed Numbers �Vocabulary – � Reciprocal – the reciprocal of any non-zero number 3 is 1/3, sometimes called the multiplicative inverse of that number. �What is the reciprocal of ½? �What the is reciprocal of y/3? �What is the reciprocal of 5?

Rules � 1 st – Always make sure that you change any mixed numbers to improper fractions. � 2 nd – always reciprocate the 2 nd fraction, and multiply. � 3 rd – You may have to SIMPLIFY. DO NOT LEAVE any IMPROPER FRACTIONS!

Examples:

Homework: �Lesson 10 – Dividing Fractions and Mixed Numbers �Homework: Pg 114 1 -20