Fractions Return to Table of Contents Slide 5 / 305 Slide 6 / - PDF document

Slide 1 / 305 Slide 2 / 305 Table of Contents 7th Grade Math Click on the topic to go to that section Fractions Review of 6th Grade Decimal Computation Statistics Number System Expressions 2012-07-31 Equations and Inequalities Geometry www.njctl.org Ratios and Proportions Slide 3 / 305 Slide 4 / 305 List what you remember about fractions . Hint Fractions Return to Table of Contents Slide 5 / 305 Slide 6 / 305 Greatest Common Factor 1 Find the GCF of 18 and 44. Pull Pull We can use prime factorization to find the greatest common factor (GCF). 1. Factor the given numbers into primes. 2. Circle the factors that are common. 3. Multiply the common factors together to find the greatest common factor.

Slide 7 / 305 Slide 8 / 305 2 Find the GCF of 72 and 75. 3 Find the GCF of 52 and 78. Pull Pull Pull Pull Slide 9 / 305 Slide 10 / 305 A multiple of a whole number is the product of the number There are 2 ways to find the LCM: and any nonzero whole number. 1. List the multiples of each number until you find the first A multiple that is shared by two or more numbers is a one they have in common. common multiple . 2. Write the prime factorization of each number. Multiply Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ... all factors together. Use common factors only once (in other words, use the highest exponent for a repeated Multiples of 14: 14, 28, 42, 56, 70, 84,... factor). The least of the common multiples of two or more numbers is the least common multiple (LCM) . The LCM of 6 and 14 is 42. Slide 11 / 305 Slide 12 / 305 4 Find the least common multiple EXAMPLE: 6 and 8 of 10 and 14. Pull Pull Multiples of 6: 6, 12, 18, 24, 30 A 2 Multiples of 8: 8, 16, 24 B 20 LCM = 24 70 C 140 D Prime Factorization: 6 8 2 3 2 4 2 2 2 2 3 2 3 LCM: 2 3 3 = 8 3 = 24

Slide 13 / 305 Slide 14 / 305 5 Find the least common multiple 6 Find the LCM of 24 and 60. Pull Pull Pull Pull of 6 and 14. A 10 B 30 C 42 D 150 Slide 15 / 305 Slide 16 / 305 The Distributive Property allows you to: Which is easier to solve? 1. Rewrite an expression by factoring out the GCF. 28 + 42 7(4 + 6) 2. Rewrite an expression by multiplying by the GCF. Do they both have the same answer? EXAMPLE You can rewrite an expression by removing a common factor. This Rewrite by factoring out the GCF: is called the Distributive Property. 45 + 80 28 + 63 5(9 + 16) 7(4 + 9) Rewrite by multiplying by the GCF: 3(12 + 7) 8(4 + 13) 36 + 21 32 + 101 Slide 17 / 305 Slide 18 / 305 7 In order to rewrite this expression using the Distributive 8 In order to rewrite this expression using the Distributive Property, what GCF will you factor? Property, what GCF will you factor? Pull Pull Pull Pull 56 + 72 48 + 84

Slide 19 / 305 Slide 20 / 305 9 Use the distributive property to rewrite this expression: 10 Use the distributive property to rewrite this expression: Pull Pull Pull Pull 36 + 84 88 + 32 A 3(12 + 28) A 4(22 + 8) B 4(9 + 21) B 8(11 + 4) C 2(18 + 42) C 2(44 + 16) D 12(3 + 7) D 11(8 + 3) Slide 21 / 305 Slide 22 / 305 Adding Fractions... 3 11 10 Pull Pull 1. Rewrite the fractions with a common denominator. 2. Add the numerators. 2 + 3. Leave the denominator the same. 10 4. Simplify your answer. Adding Mixed Numbers... 1. Add the fractions (see above steps). 2. Add the whole numbers. 3. Simplify your answer. (you may need to rename the fraction) Link Back to List Slide 23 / 305 Slide 24 / 305 13 Find the sum. 5 12 Pull Pull 8 Pull Pull 1 + 5 3 + 7 5 8 10 10

Slide 25 / 305 Slide 26 / 305 A quick way to find LCDs... 14 Is the equation below true or false? Pull Pull List multiples of the larger denominator and stop False True when you find a common multiple for the smaller denominator. 1 8 1 2 12 Ex: and 3 5 + 1 5 Click For reminder 12 Multiples of 5: 5, 10, 15 Don't forget to regroup to 3 1 the whole number if you 12 end up with the numerator 3 2 Ex: and larger than the 4 9 denominator. Multiples of 9: 9, 18, 27, 36 Slide 27 / 305 Slide 28 / 305 Common Denominators 2 15 Another way to find a common denominator is to 5 Pull Pull multiply the two denominators together. 1 + 3 1 2 Ex: and 3 x 5 = 15 3 5 x 5 x 3 5 6 1 2 = = 3 15 15 5 x 5 x 3 Slide 29 / 305 Slide 30 / 305 3 5 16 17 10 8 Pull Pull Pull Pull 2 3 + + 5 5

Slide 31 / 305 Slide 32 / 305 18 19 Pull Pull 5 3 + 2 7 2 3 + 5 5 Pull = Pull = 4 12 8 12 8 1 7 8 7 16 7 19 A C A C 3 12 12 24 B 8 4 7 5 8 7 7 8 B D D 8 12 12 20 Slide 33 / 305 Slide 34 / 305 Subtracting Fractions... 20 Pull Pull 3 1 + 2 1 = 1. Rewrite the fractions with a common denominator. 4 6 2. Subtract the numerators. 3. Leave the denominator the same. 4. Simplify your answer. 5 1 5 2 C A 2 10 Subtracting Mixed Numbers... 1. Subtract the fractions (see above steps..). 6 5 5 5 (you may need to borrow from the whole number) B D 12 2. Subtract the whole numbers. 12 3. Simplify your answer. (you may need to simplify the fraction) Link Back to List Slide 35 / 305 Slide 36 / 305 6 4 22 7 21 7 5 Pull Pull 8 Pull Pull 4 8

Slide 37 / 305 Slide 38 / 305 24 Is the equation below true or false? 2 1 23 3 5 Pull Pull Pull Pull True False 4 5 9 3 9 3 2 9 Slide 39 / 305 Slide 40 / 305 25 Is the equation below true or false? 26 Find the difference. Pull Pull Pull Pull True False 4 7 2 3 8 8 2 7 9 1 1 9 1 2 3 Slide 41 / 305 Slide 42 / 305 6 27 A Regrouping Review Pull Pull 7 3 When you regroup for subtracting, you take 5 one of your whole numbers and change it into a fraction with the same denominator as the fraction in the mixed number. 3 3 = 2 5 3 = 2 8 5 5 5 5 Don't forget to add the fraction you regrouped from your whole number to the fraction already given in the problem.

Slide 43 / 305 Slide 44 / 305 28 Do you need to regroup in order 5 1 Pull Pull 5 3 4 12 3 4 15 to complete this problem? 4 12 12 12 12 Yes or No 3 7 3 7 3 7 3 7 12 12 12 12 3 1 1 8 2 12 1 1 2 4 3 Slide 45 / 305 Slide 46 / 305 29 Do you need to regroup in order 3 30 What does 17 become when regrouping? Pull Pull 10 Pull Pull to complete this problem? 7 2 3 3 6 4 Slide 47 / 305 Slide 48 / 305 5 31 What does 21 become when regrouping? 32 4 1 2 1 Pull Pull 8 Pull Pull = 6 4 2 1 1 11 A C 12 12 1 22 1 1 B D 24 12

Slide 49 / 305 Slide 50 / 305 33 34 6 2 3 2 8 10 Pull Pull 15 Pull Pull = = 7 3 12 3 8 2 2 7 5 7 1 A A C C 21 6 3 6 3 13 2 13 6 1 6 2 D D B B 21 21 6 12 Slide 51 / 305 Slide 52 / 305 Multiplying Fractions... 35 1 x 2 Pull 1. Multiply the numerators. Pull = 5 3 2. Multiply the denominators. 3. Simplify your answer. Multiplying Mixed Numbers... 1. Rewrite the Mixed Number(s) as an improper fraction. (write whole numbers / 1) 2. Multiply the fractions. 3. Simplify your answer. Link Back to List Slide 53 / 305 Slide 54 / 305 36 37 ( ) 4 3 2 x 3 Pull Pull = = 9 8 Pull Pull 3 7

Slide 55 / 305 Slide 56 / 305 38 39 Pull Pull Pull Pull x 1 5 x 1 x 4 5 3 = 2 1 2 7 True 1 5 12 A C 7 21 False 12 3 5 B D 7 7 Slide 57 / 305 Slide 58 / 305 40 Pull 41 Pull ( ) ( 3 ) Pull Pull 5 2 1 3 1 2 6 3 5 x = 8 4 8 5 8 True 20 3 15 1 C A 8 4 False 18 1 19 1 D B 8 8 Slide 59 / 305 Slide 60 / 305 To divide fractions, multiply the first fraction by Dividing Fractions... the reciprocal of the second fraction. Make sure 1. Leave the first fraction the same. you simplify your answer! 2. Multiply the first fraction by the reciprocal of the second fraction. Some people use the saying "Keep Change Flip" 3. Simplify your answer. to help them remember the process. Dividing Mixed Numbers... 1. Rewrite the Mixed Number(s) as an improper fraction(s). 3 7 3 x 8 = 3 x 8 = 24 (write whole numbers / 1) = 5 8 5 7 2. Divide the fractions. 5 x 7 35 3. Simplify your answer. 1 1 1 x 2 = 1 x 2 = 2 = 5 2 5 1 5 x 1 5

Slide 61 / 305 Slide 62 / 305 42 43 Pull Pull 4 8 = 5 x 8 3 2 2 7 = Pull Pull 8 5 10 4 10 4 7 True True False False Slide 63 / 305 Slide 64 / 305 45 44 Pull Pull 8 4 = 5 10 Pull Pull 1 A 39 B 40 40 C 42 Slide 65 / 305 Slide 66 / 305 To divide fractions with whole or mixed 46 numbers, write the numbers as an improper Pull Pull fractions. Then divide the two fractions by 1 2 2 1 = 2 using the rule (multiply the first fraction by the 3 reciprocal of the second). Make sure you write your answer in simplest form. 2 1 1 5 7 3 5 x 2 = 10 = = 3 2 3 2 3 7 21 1 6 3 = 4 6 1 6 x 2 = 12 = = 2 2 1 1 3 3