Slide 1 / 114 Slide 2 / 114 New Jersey Center for Teaching and Learning Fractions Progressive Mathematics Initiative Presentation Part 1 This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course 2011-11-29 materials to parents, students and others. www.njctl.org Click to go to website: www.njctl.org Slide 3 / 114 Slide 4 / 114 Table of Contents · Meaning of Fractions · Equivalent Fractions · Lowest Term Fractions Fractions · Improper Fractions and Mixed Numbers · Using Fractions in Measurement Presentation 1 · Adding Fractions with Common Denominators · Adding Mixed Numbers with Common Denominators · Subtracting Fractions with Common Denominators · Subtracting Mixed Numbers with Common Denominators · Finding Common Denominators · Comparing Fractional Numbers Slide 5 / 114 Slide 6 / 114 Table of Contents for Presentation 2 · Adding Fractions with Unlike Denominators · Subtracting Fractions with Unlike Meaning of Denominators · Adding Mixed Numbers with Unlike Fractions Denominators · Subtracting Mixed Numbers with Unlike Denominators · Multiplying Fractions · Multiplying Fractions and Whole Numbers · Multiplying with Mixed Numbers · Dividing Fractions Return to · Dividing with Whole Numbers and Mixed Table of Numbers Contents
Slide 7 / 114 Slide 8 / 114 Key Terms Key Terms Proper Fraction - A fraction where the Fraction - An expression that indicates the numerator (top number) is less than the quotient ( ) of two quantities. denominator (bottom number) Numerator - The number above the fraction bar. The numerator answers the question 5 7 11 "How many parts?" 9 13 17 Denominator - The number below the fraction Improper Fraction - A fraction where the bar. The denominator answers the question numerator (top number) is greater than or "How many total?" equal to the denominator (bottom number) 8 12 9 Numerator 3 Fraction = = 3 7 9 Denominator 7 Slide 9 / 114 Slide 10 / 114 Key Terms Equivalent Fractions - Fractions that represent the same number or are equal to each other. 2 4 6 8 10 12 14 = = = = = = 3 6 9 12 15 18 21 Mixed Number - A fraction with a whole number and a proper fraction. 5 1 2 2 2 Improper Mixed Fraction Number Slide 11 / 114 Slide 12 / 114 Fractions are used to measure ingredients What fractions are represented below? for baking and cooking.
Slide 13 / 114 Slide 14 / 114 Halves Thirds Pull Slide 15 / 114 Slide 16 / 114 Fifths Fourths Slide 17 / 114 Slide 18 / 114 Sevenths Sixths
Slide 19 / 114 Slide 20 / 114 1 What fraction of the whole is shaded? Eighths Slide 21 / 114 Slide 22 / 114 Internet links for more practice 2 What fraction of the whole is white? Fractions Naming Model link Fractions Parts of a Whole Model link Slide 23 / 114 Slide 24 / 114 What do you notice about the denominators in each set of equivalent fractions? Equivalent Fractions 1 1 1 9 9 9 Return to Table of Contents
Slide 25 / 114 Slide 26 / 114 Use the multiplication table to make equivalent Click below to use this interactive number line. fractions. 2 ? = 5 ? Pull Slide 27 / 114 Slide 28 / 114 3 Which set of fractions is equivalent? To create equivalent fractions, multiply (or divide) the numerator and denominator by the same number. 1 3 1 2 A C = = 3 6 2 2 2 x 3 6 x 2 12 x 3 36 = = = 7 x 3 21 x 2 42 x 3 126 3 9 4 1 B = D = 36 / 6 6 / 3 2 = = 7 21 8 4 126 / 6 21 / 3 7 Slide 29 / 114 Slide 30 / 114 3 5 Which fraction is equivalent to ? 4 4 Write a fraction equivalent to 8 7 16 12 A C 6 24 12 9 B D 32 16
Slide 31 / 114 Slide 32 / 114 6 Which set of fractions is equivalent? 5 7 Write a fraction equivalent to 9 6 1 3 9 A C = = 18 3 4 16 3 9 9 2 B = D = 12 3 7 14 Slide 33 / 114 Slide 34 / 114 Reducing Fractions to Lowest Terms Once you complete operations with fractions, you must write your answer in lowest terms. Lowest Term The easiest way to determine if your answer is in simplest form is to check: Fractions 1. Do the numerator and denominator have any common factors? 2. If they do not, the answer is in simplest form. 3. If they do, divide both the numerator and denominator by common factors until there are none left. Return to 40 10 4 2 2 = = Table of 220 10 22 2 11 Contents Slide 35 / 114 Slide 36 / 114 Remember: Whatever you do to the numerator, If you divide by 2 and 3 (common factors), then you must do to the denominator. you will reach the simplest form in two steps. Either way, the simplest form is the same. 18 24 18 3 6 2 3 = = In this problem, 18 and 24 are divisible by 2, 3 24 3 8 2 4 and 6. If you divide by 6 (the GCF), you will reach the simplest form in one step. 18 6 3 = 24 6 4
Slide 37 / 114 Slide 38 / 114 8 Simplify to lowest terms. 21 35 Slide 39 / 114 Slide 40 / 114 9 Simplify to lowest terms. 10 Simplify to lowest terms. 3 21 9 29 Slide 41 / 114 Slide 42 / 114 11 Simplify to lowest terms. 12 Simplify to lowest terms. 17 24 51 96
Slide 43 / 114 Slide 44 / 114 Internet links for more practice Simplifying Fractions link (interactive at bottom of page) Improper Fractions and Rename in Lowest Terms interactive Mixed Numbers Return to Table of Contents Slide 45 / 114 Slide 46 / 114 Proper or Improper? Mixed Numbers An improper fraction can be expressed as a whole In a proper fraction, the numerator is always less number and a fraction. This is called a mixed number. than the denominator. The value of a proper fraction is always less than 1. "Seven Halves" Seven halves can fill up 3 whole strips 3 1 and of another whole strip. That's 5 2 and we say "three and one half", 3 1 2 meaning "three plus one half". In an improper fraction, the numerator is equal to or greater than the denominator. The value of an improper fraction is equal to or greater than 1. 7 3 1 = 5 7 2 2 5 5 Slide 47 / 114 Slide 48 / 114 Converting Improper Fractions to Mixed Numbers Let's look at another example. Remember, the fraction bar symbolizes division! 2 13 13 2 3 Therefore: = 5 13 5 5 5 -10 · Divide the numerator by the denominator to see how 3 many "wholes" there are. · Write the remainder over the denominator 5 Let's look at "seven halves" again. 3 7 7 3 1 2 7 = Now try this one. 2 2 2 -6 1 17 2 8
Slide 49 / 114 Slide 50 / 114 Converting Mixed Numbers Let's look at another example. into Improper Fractions To do this, complete a multiplication problem. 4 2 = 12 + 2 14 = 3 3 3 3 · Multiply the whole number by the denominator to create an improper fraction (of the original whole number). · Add the new fraction to the original fraction (from the mixed number). Now try this one. Let's look at "seven halves" again. 6 3 7 3 1 = 6 + 1 7 = 2 2 2 2 Slide 51 / 114 Slide 52 / 114 8 15 14 Change to a mixed number. 13 is a proper fraction. 5 8 True 1 7 A 8 False 2 7 B 8 1 3 C 8 Slide 53 / 114 Slide 54 / 114 15 Change this mixed number to an 16 Change this mixed number to an improper fraction. improper fraction. 1 3 3 9 4 10
Slide 55 / 114 Slide 56 / 114 17 Change this improper fraction to a mixed number. Using Fractions 28 6 in Measurement Return to Table of Contents Slide 57 / 114 Slide 58 / 114 Fraction Ruler Move the pink arrows to two locations on the ruler. Then hit the large blue arrow for the distance between the arrows to be Each one inch segment on this ruler is like measured. one strip folded into four parts. For every 1 1 3 inch, there are , and inch markings. 4 4 2 1 1 1 1 4 4 4 4 Slide 59 / 114 Slide 60 / 114 18 What is the length between the two arrows? 19 What is the length between the two arrows? 1 9 1 5 13 3 in. in. C in. C in. A A 8 4 16 16 1 3 3 7 1 in. in. in. in. B D B D 4 4 8
Slide 61 / 114 Slide 62 / 114 Adding Fractions with Common Denominators To add fractions with common denominators, add the numerators and leave the denominator Adding Fractions the same. Make sure your answer is in simplest form. with Common The denominator indicates the number of parts Denominators of the whole. If the fractions have a common denominator, they are the same "size" so we can add the numerators (or number of parts). 2 6 3 + Return to 6 Table of 5 Contents 6 Slide 63 / 114 Slide 64 / 114 Try these! Move the boxes to see work and answers. 3 20 Be sure to simplify all answers. 10 2 + 10 11 3 2 5 30 7 4 12 13 1 1 4 + + + + 30 7 4 12 24 3 4 9 30 7 4 12 4 3 5 4 Slide 65 / 114 Slide 66 / 114 5 7 21 22 8 14 1 3 + + 8 14
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