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D IVIDING F RACTIONS

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W ARM - UP How can you write (84 + 48) in distributive form? How can you write (64 + 16) in distributive form? 12(7 + 4) 16(4 + 1)

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S TANDARD MCC6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because ¾ of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share ½ lb. of chocolate equally? How many ¾ - cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length ¾ mi and area ½ square miles?

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I MPORTANT V OCABULARY !! Numerator: top number of the fraction (parts of the whole) Denominator: bottom number of the fraction (whole) Vinculum: line that separates the numerator and denominator Reciprocal: inverse of the fraction; when you “flip” the fraction

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R EVIEW : S IMPLIFYING F RACTIONS The easiest way is to divide the numerator and denominator by their GCF! 18 24 18: 1, 2, 3, 6, 9, 18 24: 1, 2, 3, 4, 6, 8, 12, 24 GCF: 6 ÷ ÷ 6 6 = 3 4 Simplest Form http://www.brainpop.com/math/numbers andoperations/reducingfractions/

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S PEED R OUND !!! Simplify these fractions as fast as you can!! 10 15 16 20 17 34 12 20 2 3 4 5 1 2 3 5

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Y OU MAY ALSO NEED TO KNOW … How do you change a mixed number into an improper fraction? 4 7 5 First, multiply the whole number by the denominator. Second, add the numerator to the product of the whole number and denominator. 39 7 +

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F INALLY, IN ORDER TO DIVIDE FRACTIONS YOU MUST BE ABLE TO … Multiply Fractions!!! When you are multiplying, all you do is multiply the numerators together then multiply the denominators together! 8 9 6 7 Option #1 Multiply across first and then simplify! = 48 63 = 16 21

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Option #2 Simplify/Cross Simplify first and then multiply across 8 9 6 7 3 2 16 21 Your answer will be the same no matter what method you use!

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W ARM -U P 1. What is 3/4 times 12/18? 2. What is 8 ½ times 6/7? 1/2 7 2/7

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Brainstorm!! Why is it important to know how to divide fractions? One of the biggest ways you will use this skill is when you are dealing with measurements. -Cooking -Construction -Time -Dividing up food evenly (very important )

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F RACTION M ODELS Problem: Jeremy has a wooden board that is 2/3 yard long. He wants to cut the board into pieces that are 1/9 yard long. How many pieces will Jeremy cut? Step One: Write out the division sentence. 2 3 1 9 ÷

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S TEP TWO : DRAW A FRACTION BAR OF THE FIRST FRACTION IN YOUR DIVISION SENTENCE Draw a rectangle and divide it into thirds. Then shade in two of the thirds to represent the fraction 2/3. 2 3

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S TEP 3: D IVIDE THE RECTANGLE INTO THE NUMBER OF PIECES THAT EQUALS THE DENOMINATOR OF THE SECOND FRACTION 1 9 So…how many 1/9s are there in 2/3? Jeremy will be able to cut the board into 6 pieces.

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N OW YOU CAN TRY ONE ! Jessica is making a cake and the recipe calls for ¾ of a cup of milk. She can only find the 1/8 measuring cup. How many times will she have to fill up her 1/8 measuring cup to get enough milk in the cake batter? Jessica will have to fill up the measuring cup 6 times.

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M ORE P RACTICE Spencer drew the model below to represent a division sentence. What division sentence does this model represent? 3/4 ÷ 1/12

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I MPORTANT V OCABULARY Reciprocal: when you “flip” a fraction over; the product of the original number and its reciprocal is always 1

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W ARM -U P Sasha has a piece of ribbon that is 4/5 of a yard long. She needs 1/10 of a yard to make a hair ribbon for her friends. How many hair ribbons can she make? Draw a model to answer the question. Sasha can make 8 hair ribbons.

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W ARM -U P C HALLENGE P ROBLEMS Compare different pay scales. Decide if it is better to receive $300 a week or to be paid hourly at a rate of $7.50 per hour. What factors could affect your decision? Three watermelons and two cantaloupes weigh 32 pounds. Four watermelons and three cantaloupes weigh 44 pounds. All watermelons weigh the same and all cantaloupes weigh the same. What is the weight of two watermelons and one cantaloupe?

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B ASIC A LGORITHM 1. Leave 2. Change 3. Flip It’s just that easy!

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E XAMPLE #1 3 4 ÷ 9 Leave the first fraction! Change the division sign to multiplication! Flip: What is the reciprocal of 9? 3 4 1 9 1 12

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E XAMPLE #2 Jake has 6 pounds of coconut. He will use 2/3 pound of the coconut to make one cake. How many cakes can he make? How do you set up the problem? 6 ÷ 2 3 Jake will be able to make 9 cakes.

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E XAMPLE #3 Stacy is making a recipe that calls for 3/4 teaspoon of cinnamon. Her only measuring spoon holds 1/8 teaspoon. How many times will she need to fill his measuring spoon to get enough cinnamon for the recipe? 3 4 ÷ 1 8 She will have to fill up the measuring spoon 6 times.

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J EOPARDY G AME !!! http://www.superteachertools.com/jeopardy/userg ames/Oct201040/game1286214246.php

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W HAT ABOUT IF THERE ’ S A MIXED NUMBER ? You have to change the mixed number to an improper fraction before you can leave, change, flip! Diego practices guitar for a total of 9 ¾ hours each week. He practices for 1 ½ hour each time. How many times does Diego practice guitar each week? 39 4 91 1 2 = = 3 2 3 4

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Leave the first fraction! Change the division sign to multiplication! Flip: What is the reciprocal 3/2? = Diego practices guitar for a total of 9 ¾ hours each week. He practices for 1 ½ hour each time. How many times does Diego practice guitar each week? 39 4 2 3 13 2 = 1 2 6 He practices guitar 6 ½ times each week.

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