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Slide 2 / 115 5th Grade Fraction Operations Part 1 2015-10-08 www.njctl.org
Slide 3 / 115 Table of Contents Fractions as a form of division Finding Common Denominators Comparing Fractional Numbers Adding Fractions with Unlike Denominators Subtracting Fractions with Unlike Denominators Adding Mixed Numbers with Unlike Denominators Subtracting Mixed Numbers with Unlike Denominators
Slide 4 / 115 Fractions as a form of division Return to Table of Contents
Slide 5 / 115 (Derived from Imagine you have 2 sandwiches. Use your two pieces of paper to represent the sandwiches. Share the sandwiches equally between 2 people. ( How many sandwiches did each person get? Write a division sentence to show represent this.
Slide 6 / 115 Fractions can be used to show the division operation. 2 2 = 1 can also be written as 2 2 = 1 The fraction bar is a division click bar.
Slide 7 / 115 (Derived from Now imagine that there is only 1 sandwich. Use your paper and the scissors to show how you would share the sandwich equally between 2 people. ( How many sandwiches did each person get? click Write a division sentence to show represent this.
Slide 8 / 115 (Derived from Now imagine that there is 1 sandwich and 3 people. Use your paper and the scissors to show how you would share the sandwich equally between 3 people. ( Person 1 Person 2 Person 3 How many sandwiches did each person get? click Write a division sentence to show represent this.
Slide 9 / 115 (Derived from Now lets take 3 sandwiches and share them equally with 2 people. Turn and talk about how you can share these sandwiches. Use your paper and the scissors to show how you would share them. ( Person 1 Person 2 How many sandwiches did each person get? click Write a division sentence to show represent this.
Slide 10 / 115 (Derived from Imagine you have 2 different sandwiches. There are 5 people sharing them, and each person wants a taste of each sandwich. Use your two pieces of paper to represent the sandwiches. Share the sandwiches equally between 5 people. ( To give everyone part of each sandwich, each sandwich must be divided into fifths. Each person can have 1/5 of each sandwich. 1/5+1/5=2/5 How many sandwiches did each person get? click Write a division sentence to show represent this.
Slide 11 / 115 1 Which picture shows the division? (Derived from ( A B C
Slide 12 / 115 2 Which pictures show the division? (Derived from ( A D B E C
Slide 13 / 115 3 What division expression does the picture represent? Write your answer as a fraction. (Derived from (
Slide 14 / 115 (Derived from 4 Carla was drawing a picture to show how 2 children can equally share 3 cookies. She then wrote an equation, and expressed her answer as a fraction. ( 3 2 = 1 and 1 half = 1 1/2 Is her work correct? Yes No If not, explain on your paper how to correct her answer.
Slide 15 / 115 (Derived from ( 5 Hillary was solving the same problem, but she did it differently. 3 2 = six thirds = 6/3 = 2 Is her work correct? Yes No If not, explain on your paper how to correct her answer.
Slide 16 / 115 This fraction line represents division. It can be read as: 27 over 5 27 out of 5 27 divided by 5
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Slide 24 / 115 Finding Common Denominators Return to Table of Contents
Slide 25 / 115 How many halves make a whole circle?
Slide 26 / 115 How many fourths make half of this circle?
Slide 27 / 115 How many sixths make 1/3 of this circle?
Slide 28 / 115 How many eighths can fit in 1/4 of this circle?
Slide 29 / 115 How many different combinations can you make to fill the circle? Keep track of what pieces you use. (You may need to rotate your pieces.) 1/8 1/5 1/3 1/2 1/7 1/4 1/6
Slide 30 / 115 Fix the Sticks You can use the set of Skip Counting Sticks to find common denominators for two fractions with unlike denominators. If you don't have a set of sticks, you can create them by listing the multiples of the denominator. 3 For the fractions 4 and 6, line up the sticks this way for the denominator of each fraction: 3 4 1 6 1 4 8 12 16 20 24 28 32 36 6 12 18 24 30 36 42 48 54...... Find the smallest number in the "denominator" sticks that is common in both fractions. It's 12. The least common denominator of and is 12. 3 4 1 6
Slide 31 / 115 A quick way to find LCDs... List multiples of the larger denominator, and stop when you find a common multiple for the smaller denominator. 1 Ex: and 3 2 5 Multiples of 5: 5, 10, 15 3 Ex: and 4 2 9 Multiples of 9: 9, 18, 27, 36
Slide 32 / 115 11 Find the LCD of this pair of fractions. 2 4 1 6
Slide 33 / 115 12 Find the LCD of this pair of fractions. 3 5 5 6
Slide 34 / 115 13 Find the LCD of this pair of fractions. 2 9 1 3
Slide 35 / 115 14 Find the LCD of this pair of fractions. 3 4 3 7
Slide 36 / 115 15 Find the LCD of this pair of fractions. 5 6 3 8
Slide 37 / 115 Comparing Fractional Numbers Return to Table of Contents
Slide 38 / 115 Comparing Fractional Numbers Common Denominators When you have two fractions with common denominators, all you have to do is compare the numerators. 8 9 > 7 9 Unlike Denominators To compare fractions with unlike denominators, you have to rewrite both fractions with a common denominator. Then, compare the numerators. 2 2 = 20 3 3 30 2 7 7 7 10 10 = 21 3 30 < 10
Slide 39 / 115 Compare the fractions 1. 4 2 7 5 4 7 = 20 35 4 > 2 7 5 click 2 5 = 14 35 2. 11 13 17 17 11 13 < 17 17 click 3. 4 3 5 4 4 5 = 16 20 4 > 3 5 4 click 3 4 = 15 20
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Slide 41 / 115 16 True or false? 4 7 > 2 3
Slide 42 / 115 17 True or false? 5 6 > 5 8
Slide 43 / 115 18 Compare the two fractions. 8 11 3 4 A > B < C =
Slide 44 / 115 19 Compare the two fractions. 3 12 1 4 A > B < C =
Slide 45 / 115 20 Compare the two fractions. 4 9 5 8 A > B < C =
Slide 46 / 115 21 Ali has completed of his essay, and Veronica has completed of her essay. A B C Ali has completed more (>) than Veronica. Ali has completed less (<) than Veronica. Ali and Veronica have completed the same amount (=).
Slide 47 / 115 22 Sasha has eaten of her lunch, and Cloe has eaten of her lunch. A Sahsa has eaten more (>) than Cloe. B Sasha has eaten less (<) than Cloe. C Sasha and Cloe have eaten the same amount (=).
Slide 48 / 115 23 Liam knows of this weeks vocabulary words, and Joshua knows of the words. A B C Liam knows more (>) words than Joshua. Liam knows less (<) words than Joshua. Liam and Joshua know the same amount (=) of words.
Slide 49 / 115 Internet links for more practice Finding fractions on a number line link Comparing Fractions Model
Slide 50 / 115 Adding Fractions with Unlike Denominators Return to Table of Contents
Slide 51 / 115 Adding Fractions with Unlike Denominators To add fractions with unlike denominators, rewrite the fractions as equivalent fractions with a common denominator. Then, add the fractions. (Using the LCD is often the fastest method, as it requires the least amount of simplification.) Make sure your answer is in simplest form. 4 9 + 5 8 + 4 9 5 8 + 32 72 45 72 77 72 = 1 5 72
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Slide 53 / 115 Try these! Click the boxes to see work and answers. Be sure to simplify all answers. 2 3 4 + 5 1 4 + 7 2 8 + 5 7 8 8 24 32 + 20 5 20 + 56 14 56 + 40 35 40 13 20 38 56 = 19 28 67 40 = 1 27 40
Slide 54 / 115 Internet Link for Practice Adding Fractions with Unlike Denominators link
Slide 55 / 115 24 2 5 + 1 3
Slide 56 / 115 25 3 10 + 2 5
Slide 57 / 115 26 5 8 + 3 5
Slide 58 / 115 27 3 4 + 7 9
Slide 59 / 115 28 5 7 + 1 3
Slide 60 / 115 29 Two friends get their hair cut. Natasha gets of a foot cut off, and Briar gets of a foot cut off. What is the total length of hair the two friends get cut off?
Slide 61 / 115 30 On Monday Bobby completes of his science project. On Thursday he completes of the project. What fraction of the project is completed after these two days of work?
Slide 62 / 115 31 Yolanda used of her new beads to make a necklace. She then used of the beads to make a bracelet. What fraction of her beads has she used so far?
Slide 63 / 115 Subtracting Fractions with Unlike Denominators Return to Table of Contents
Slide 64 / 115 Subtracting Fractions with Unlike Denominators To subtract fractions with unlike denominators, rewrite the fractions as equivalent fractions with a common denominator. Then, subtract the fractions. (Using the LCD is often the fastest method, as it requires the least amount of simplification.) Make sure your answer is in simplest form. 4 3 4 32 9 8 9 3 72 27 8 72 5 72
Slide 65 / 115 Try these! Click the boxes to see work and answers. Be sure to simplify all answers. 2 5 1 4 8 20 5 20 3 20 3 7 2 8 24 56 14 56 10 56 = 5 28 4 5 3 8 32 40 15 40 17 40
Slide 66 / 115 32 4 5 1 7
Slide 67 / 115 33 2 3 1 6
Slide 68 / 115 34 6 7 3 5
Slide 69 / 115 35 3 4 5 9
Slide 70 / 115 36 3 5 1 6
Slide 71 / 115 37 It is of a mile to Alyssa's best friend's house. So far she has walked of a mile to her friend's house. How much farther does she have to walk?
Slide 72 / 115 38 A recipe for pancakes calls for of a cup of milk. Deven only has of a cup of milk. How much more milk does Deven need?
Slide 73 / 115 39 Use the chart to solve the problem. How much less rain fell on Wednesday than on Thursday? Wednesday Thursday Friday Rainfall in inches
Slide 74 / 115 AMAZING FRACTIONS Quick Review
Slide 75 / 115 A few reminders... 1. If the problem is written in a horizontal format, rewrite the fractions in a vertical format. 2. Check for a common denominator. Rewrite with a common denominator if necessary. 3. Double check the sign to see if you are doing addition or subtraction. 4. Make sure you write your answer in simplest form.
Slide 76 / 115 40 4 5 + 3 5
Slide 77 / 115 41 4 9 + 2 9
Slide 78 / 115 42 6 8 4 8
Slide 79 / 115 43 6 7 4 5
Slide 80 / 115 44 2 3 1 5
Slide 81 / 115 45 3 4 + 2 3
Slide 82 / 115 46 Rebecca painted of a mural. Justina painted of it. How much of the mural did the girls paint?
Slide 83 / 115 47 Mr. Phillips class completed of their project for the science program on Monday. On Tuesday, they completed another of it. How much more did they complete on Tuesday than on Monday?
Slide 84 / 115 48 On Saturday of the plants in Ms. Drake's flower bed had flowers on them. On Sunday another of them had flowers on them. What fraction of her plants have flowers on them now?
Slide 85 / 115 Adding Mixed Numbers with Unlike Denominators Return to Table of Contents
Slide 86 / 115 Adding Mixed Numbers with Unlike Denominators To add mixed numbers with unlike denominators, rewrite the fractions as equivalent fractions with a common denominator. Add the fractions. Then, add the whole numbers. Make sure your answer is in simplest form. 2 1 6 2 5 30 5 7 9 5 7 9 + 1 2 5 + 1 12 30 + 2 2 3 + 2 6 9 3 17 30 7 13 9 = 8 4 9
Slide 87 / 115 Steps to add and simplify. + 9 1 3 8 3 4 9 4 2nd- Add Fractions x 4 = 1stx 4 Find 12 Common Denominator x 3 = (click + 8here) 9 x 3 12 3rd- Rename Fraction 17 13 12 = 18 1 12 (click here) (click here) 12 12 + 1 12 = 13 12
Slide 88 / 115 Try this... 9 1 2 + 7 10 click 10 1 5
Slide 89 / 115 Try this... 3 5 12 + 3 2 4 click 6 1 6
Slide 90 / 115 49 5 3 4 + 2 7 12 = A 7 16 12 C 8 1 3 B 8 4 12 D 7 5 8
Slide 91 / 115 50 2 3 8 + 5 5 12 = A 7 19 24 C 7 8 12 B 7 8 20 D 8 7 12
Slide 92 / 115 51 3 1 4 + 2 1 6 = A 5 2 10 C 5 1 2 B 5 5 12 D 6 5 12
Slide 93 / 115 52 9 2 5 + 5 5 6 = A 14 37 30 C 14 37 40 B 14 7 11 D 15 7 30
Slide 94 / 115 53 1 2 3 + 2 1 2 =
Slide 95 / 115 54 Find the sum. 5 2 10 + 7 4 10
Slide 96 / 115 55 A recipe for sugar cookies needs cups of flour. A recipe for oatmeal cookies needs cups of flour. How much flour altogether are needed to make the two recipes?
Slide 97 / 115 56 Jasmin made a necklace that is inches long. Diandra made one that is inches long. What is the total length of the two necklaces?
Slide 98 / 115 57 A recipe calls for cups of peanuts and cups of walnuts. How many cups of nuts in all are needed for the recipe?
Slide 99 / 115 Subtracting Mixed Numbers with Unlike Denominators Return to Table of Contents
Slide 100 / 115 Subtracting Mixed Numbers with Unlike Denominators To subtract mixed numbers with unlike denominators, the fractions as equivalent fractions with a common denominator. Subtract the fractions. Then, subtract the whole numbers. Make sure your answer is in simplest form. 2 1 5 2 6 30 5 7 9 5 7 9 1 1 6 1 5 30 2 1 3 2 3 9 1 1 30 3 4 9
Slide 101 / 115 1 1 3-2 3 In this problem, you can not subtract two thirds from one third, because the first numerator is smaller than the second. When this happens, you need to borrow from the whole number. How many thirds are in 1 whole? Pull How many fifths are in 1 whole? How many ninths are in 1 whole?
Slide 102 / 115 To borrow a whole number: 3 3 5 Take one from the whole number and write it as a fraction. (Click the denominator) 3 = 2 + 5 5 Then, add the new mixed # and the fraction. 2 5 + 5 3 5 = 2 8 5 So, 3 3 5 = 2 8 5
Slide 103 / 115 5 1 4 5 3 12 4 12 Click 3 12 12 4 15 12 3 7 12 3 7 12 3 7 12 3 7 12 1 8 12 1 2 3
Slide 104 / 115 9 8 8 8 Click 4 5 8 4 5 8 4 3 8
Slide 105 / 115 58 Can this problem be solved without borrowing? Yes or No 3 1 2 1 4
Slide 106 / 115 59 Can this problem be solved without borrowing? Yes or No 7 2 3 6 3 4
Slide 107 / 115 60 What does 17 become when borrowing? 3 10
Slide 108 / 115 61 What does 9 become when borrowing? 2 5
Slide 109 / 115 62 4 1 6 2 1 4 = A 2 1 12 C 1 11 12 B 1 22 24 D 1 1 12
Slide 110 / 115 63 6 2 7 3 2 3 = A 3 8 21 C 2 2 3 B 3 13 21 D 2 13 21
Slide 111 / 115 64 15 8 10 12 = A 7 5 6 C 7 1 6 B 6 1 6 D 6 2 12
Slide 112 / 115 65 Two items in a package have a combined weight of pounds. If one item weighs pounds, how much does the other item weigh?
Slide 113 / 115 66 My brother is years old. My sister is years younger than my brother. How old is my sister?
Slide 114 / 115 67 Keith bought pounds of dried fruit. He ate pounds of it. How much dried fruit is left?
Slide 115 / 115 68 A board is 8 feet long. If you cut off feet of it, how much is left?