My Fractions Handbook

Transcription

1 My Fractions Handbook By Mrs. Tiffany Howard Graphics from the pond: What fraction of Ms. Lady s spots are yellow?

2 Table of Contents: What is a fraction?...1 How can I find a fraction of an object?...2 How can I find a fraction of a set of objects?...4 How can I make equivalent fractions?...5 What are mixed numbers and improper fractions?...6 How can I change between mixed numbers and improper fractions?...7 What Is a Fraction? A fraction is a part out of a whole object or set of objects. We write the part on top, then draw a line underneath it to represent out of. Lastly, we write the total on the bottom. Example: There are 4 purple parts out of a total of 6 parts. 4 6 How can I compare and order fractions?...8 the part Numerator How can I simplify fractions?...11 How can I add and subtract fractions and decimals?...12 How can I change a fraction into a decimal?...13 How can I change a decimal into a fraction?...14 How can I multiply fractions?...14 the whole Denominator Practice: 1. What fraction of these hearts is green? Blue? Green Blue 2. Write your own fraction representation below. How can I divide fractions?

3 How Can I Find a Fraction of an Object? Let s use this bar of chocolate as an example: How many pieces is 1/5 of this whole bar of chocolate? Practice finding a fraction of an object: 1. How many squares are 2/3 of this figure? Remember, 1/5 is read as 1 piece out of 5 total. Does this bar of chocolate have a total of 5 pieces right now? No, we have too many pieces! We can fix that by breaking the chocolate into groups so that each group has a total of How many pieces of pizza is 1/2 of the pizza? There are now 5 total pieces in each of my groups. It matches the total in the fraction I am looking for: 1/5. Now shade in the pieces (1) out of the total (5) for each group:1/5 There are 2 pieces shaded in of my object; so 1/5 of my bar of chocolate is 2 pieces Challenge: How many pepperonis are 1/3 of the pepperonis on the pizza? - 4. Double Challenge: You had a birthday party yesterday. Your birthday cake was cut into 24 total pieces before the party started. Your mom said 1/8 of your cake was leftover. How many pieces of cake are left? (hint: you can draw a picture of the cake) 3

4 How Can I Find the Fraction of a Set of Objects? How many clouds are 1/3 of this set of clouds? How can I make an equivalent fraction? *Link to Comparing Fractions: Remember you can use a picture when comparing 2 fractions to see if the fractions are equal to each other. You can also cross multiply to see if they are equal. An equivalent fraction is a fraction that is equal to the original fraction. 1. Group your objects (by circling them) into what the fraction has as the total (the denominator). 1/3 When making an equivalent fraction you can chose to either multiply or divide the numerator and the denominator by the same number. Examples: Shade in or place an X over the amount in the numerator for each group of objects you have. 1/3 3 x 11 = = 3 5 x 11 = = 5 Remember whatever you do to the top, you do to the bottom also! Practice: /3 of the clouds equals 2 clouds 9 12 Practice: Draw 10 coins. How much is 4/5 of the coins? 4 5

5 What are mixed numbers and improper fractions? A mixed number is a number that is in between two whole numbers. It is represented by a whole number and a fraction or a whole number and a decimal ½ 2 3 An improper fraction is a fraction whose numerator is equal to or larger than its denominator. It is improper because the bottom number should be the biggest number. Pie Example: 11 pieces left over 5 Or 1 whole and 6 total pieces per whole 6 Practice: Draw your own pies, pizzas, or bars of chocolate with some pieces already eaten on a half sheet of paper (split with your neighbor). Write your name on the paper and ball it up. When the teacher says go, begin a 10 second snowball fight. Remember the rules: 1. You can t move your feet, and 2. You can t aim at someone in close range. When 10 seconds are up, grab a snowball and write the improper fraction and mixed number for the picture on the paper. Return it to the owner to check and discuss. 6 How Can I Change Between Mixed Numbers and Improper Fractions? Mixed Number to Improper Fraction: = x 2 2 Multiply the denominator by the whole number. Then add the numerator to your answer. This number is the numerator of your improper fraction. Then you get to steal the same bottom of the original fraction (Remember the only time you can steal is with fractions!). Improper Fraction to Mixed Number: 7 3 r Divide the big number (numerator) by the small number (denominator). Your whole number answer is your whole number in front of the fraction. Your remainder is the top of the fraction, and you steal the same bottom for the fraction as in the original fraction. Practice: Create 1 mixed number problem and 1 improper fraction problem. Write them on a sheet of paper. Switch papers with the person next to you. Solve the problems, return the paper, and check each other s work. Discuss and help each other when checking. 2 7

6 How Can I Compare and Order Fractions? 3 Options: Cross Multiply Battle Logic, rewrite each fraction with a common denominator, or draw a visual representation of each Cross Multiply Battle Logic: For ordering 3 fractions battle the first 2 fractions against each other and order them on a number line. Example: 1/2, 1/3, and 3/ /3 1/2 2 3 Then, cross multiply the third fraction with the first fraction on the number line. If the third fraction is smaller it will be the smallest number (the first number) on the number line. If the third fraction won the battle and was bigger, battle it against the next fraction on the number line. If it is smaller it will go in the middle; if it is larger it goes on the end. The third fraction has 3 possible places it can go (orange arrows); you must use your logic! 8 Example: 3/4 is bigger than 1/3 and bigger than 1/ /3 1/2 3/4 4 3 least greatest How Can I Compare and Order Fractions? Rewrite each fraction with a common (same) denominator: You can change the bottoms around by either multiplying the bottoms all by each other or finding a number that they all have in common by being able to either multiply or divide by to get to it. Remember, whatever you do to the bottom of each individual fraction, you have to do to the top of that fraction (they are like a jealous brother and sister). What you may do to one fraction may be different than what you do to the other fractions when you are trying to fix them to all have the same bottoms. Once the bottoms are the same, you can look at the tops to order the fractions. Example: Order 2/7, 3/5, and 1/ x 5 x 2 = 70 this will be the common denominator for all of the fractions.now let s fix the tops! I multiplied my first denominator, 7, by 5 and 2 so I must also multiply my numerator, 2, by 5 and 2. 2x5x2=20. That turns 2/7 into 20/70 (equivalent fractions)! I multiplied my 5 by 7 and 2; so I must multiply my 3 by 7 and 2 also 3x7x2=42. 3/5 turns into 42/70! I multiplied my 2 by 5 and 7; so I must multiply my 1 by 5 and 7 also.1x5x7=35. 1/2 turns into 35/70! Least to Greatest: 20/70, 35/70, 42/70 or 2/7, 1/2, 3/5 9

7 How Can I Compare and Order Fractions? Drawing a Visual Representation to compare 2 or more fractions: Remember the 2 rules when you draw the representations of each fraction: 1. The rectangle or circle must be the same size for each fraction: NOT: 2. The parts inside the representation must be the same size within the shape: NOT Example: Which is greater, 2/4 or 1/2? They re equal! How Can I Simplify Fractions? A simplified (or reduced) fraction is a fraction in its lowest term. Think of how much more simple it is to draw a visual representation of 1/2 versus 25/50! Step 1: Write out all the multiples next to each number (1x10, 2x5) 15 - (1x15, 3x5) Step 2: Circle all the numbers that are in both sets. 10 (1x10, 2x5) 15 (1x15, 3x5) Step 3: If there is any number other than the 1 circled, the fraction is currently not in its simpliest form. Select the largest number you circled to divide both the top and bottom by = 2 2/3 is the simpliest form of 10/15 Section Practice: Practice all 3 strategies to order fractions 2/5, 4/10, and 1/2 least to greatest = 3 Don t forget these are eqivalent fractions! (Cross Multiply if you don t believe me!) Practice: Simplify each fraction if needed

8 How Can I Add and Subtract Fractions and Decimals? Adding and Subtracting Fractions: 1. Make sure the bottoms (denominators) of each fraction are the same. If they are not, rewrite them with a common denominator. (refer to page 9 for how to do this) 2. Add or subtract just your top numbers (numerators). Steal the denominator from the original fractions. Examples: = x 2 = = x 2 = Adding and Subtracting Decimals: 1. Line up your decimals, and add or subtract like usual. 2. Remember.1 is the same as.10 How Can I Change a Fraction Into a Decimal? Option 1: 10, 100, 1000 bottoms If you have a fraction whose bottom can reach 10, 100, or 1000 by either multiplication or division, rewrite the fraction with this bottom by making an equivalent fraction. Then write your top number in the decimal position of the bottom number (the tenths spot if a 10 is on the bottom, the hundredths spot if a 100 is on the bottom, etc.) Example: 2 x 2 = 4 This fraction is read as four tenths 5 x 2 = 10 Therefore, a 4 is written in the tenths spot of a decimal: 0.4 (also read as four tenths) Remember they are the same amount, just written in different formats! Option 2: Divide and Conquer! Divide the numerator by the denominator. When you first set up the division problem add a decimal followed by 2 zeros to the numerator. Also add a 0. in front of your answer. Ignore the decimal while you divide. Practice: Example: Practice: Change to Decimals = /25 = 2/5 = /20 = 12 13

9 How Can I Change a Decimal Into a Fraction? Write the number without the decimal in your numerator position. Read your original decimal. If it is a tenths, write a 10 in the denominator. If it is a hundredths, write a 100 in the denominator. If it is in the thousandths, write a 1000 in the denominator position. Examples: 0.69 = 69/ = 7 and 5/ = 3/ = 891/1000 How Can I Multiply Fractions? Multiply the tops across. Multiply the bottoms across. Simplify if needed. 3 x 8 = = 1 10 x 12 = = 5 Practice: Prank or Real? Turn to page 15 for directions. Practice Continued From Page 14: Prank or Real? Fold a clean sheet of paper into fourths. Number each box on one side 1-4. In each square write a math problem. You should include 2 problems where you have to change a decimal into a fraction and 2 problems where you have to multiply fractions. On the back, number 1-4 for the same problems to write the answer to each (show your work). Return to the front side, here you can choose to write the real answer or a prank answer with each question. Exchange papers with your neighbor. Your neighbor should solve each of the 4 problems on the front side and write either Real or Prank for each square. Once your neighbor has completed the front side he can check his work using the answer sheet you created for him on the back. You follow the same procedures for his paper. How Can I Divide Fractions? 1. Change any mixed numbers to improper fractions. 2. Flip your second fraction (called the reciprocal). 3. Multiply the tops across and the bottoms across. 4. Simplify if needed. Change improper to proper (mixed number). Example: x 3 = 12 2 and 2/ x 1 = 5 Practice: 1. 6/11 1/9 = 2. 3 and 4/5 1/4 = 14 15

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