1. Fraction Applications! Created by Katie Graves

2. What is a Fraction?  Fraction: A Part of a Whole  Fractions have 2 components:  Numerator (Top Number)  How many pieces are being discussed  Denominator (Bottom Number)  How many pieces something has been divided N2D3N2D3 1 3 1 3

3. Who Cares About Fractions?  You should! Fractions are used everyday in…  Conversation  That baseball team is only half as good as it was last year!  Baking  Add ½ Cup of Sugar, followed by 1/3 Cup Crisco…  Weather  Did you hear we got a half inch of rain last night? Oh my!  Music  Half Notes… Whole Notes… Quarter Notes…etc!

4. Reducing Fractions  Reducing a fraction means that both the numerator and the denominator become smaller  Reduced fractions are equal to the original fraction  When reducing a fraction, both the numerator and the denominator are divided by the same number  For example, can be reduced.  If you take 6÷2 for the numerator, and 8÷2, for the denominator, the reduced fraction is 6 8 3 4

5. Practice Reducing Fractions  How can we reduce…? . 2 6 7 14 6 10

6. Mixed Number Fractions  Mixed Number Fraction: A Whole Number with a Fraction  2  5  What can we do with these types of fractions?  Turn them into Improper Fractions 1 2 3 4

7. Turning Mixed Number Fractions into Improper Fractions  Turning Mixed Number Fractions into Improper Fractions Involves 3 Steps:  First Step: Multiply the denominator (bottom) number and the whole number together  Second Step: Add the numerator to the result you got in the first step to obtain the new numerator  Third Step: Put your new nominator on top of the original denominator 2 First Step: 2x4=8 Second Step: 8+1=9 Third Step: 5 First Step: 5x8=40 Second Step: 40+3=43 Third Step: 1 4 3 8 43 8 9 4

8. Practice Changing Mixed Number Fractions to Improper Fractions  How do we change 2 into an improper fraction?  How do we change 7 into an improper fraction? 6 7 1 4

9. Making Common Denominators  In order to make a common denominator, multiplication takes place.  Our result needs to have the denominators the same.  When multiplying, we multiply each fraction by a different number. However, the denominator and numerator are multiplied by the same number.  For example, if we are trying to make and have a common denominator, we would want both fractions to have 4 as the denominator. We would multiply by 2. Our result would be (1x2)/(2x2)= 1 2 3 4 2 4 1 2

10. Practice: Common Denominators  Make a common denominator for these fractions:  and  Be careful, this problem requires both fractions to change! 3 4 5 9 1 3 4 8 4 5 3 4

11. Multiplying Fractions  When multiplying fractions, one must multiply the numerators together to create a new numerator and the denominators together to create a new denominator  For example, × = =  Real Life Applications:  Making a Double or Triple Batch of Chocolate Chip Cookies 7 8 21 32 3 4 3×7 4×8

12. Practice Multiplying Fractions  × =  Baking Problem:  If I am making banana bread for a bake sale using a recipe for one loaf, and I want to make 2 loafs, what should I do?  If the same recipe calls for cup of sugar, and I want to make 2 loaves, how much sugar do I add? 3 4 1 2 5 8 2 3 1 4

13. Dividing Fractions  When dividing fractions, you first change the division sign to a multiplication sign.  After changing the sign, you invert the second fraction (change the numerator into the denominator and vice-versa)  For example, inverted is  Example: ÷  ÷ = ×  × = 4 3 3 4 3 4 3 5 3 4 3 5 3 4 5 3 3 4 5 3 15 12

14. Practicing Dividing Fractions  Try these practice problems:  ÷ 3 4 6 7 2 3 7 8

15. Activity  Listen to the statements  If the statement applies to you, stand up!

16. #1: My Favorite Color Is…  Stand up if your favorite color is blue  What fraction of the class’s favorite color is blue?  If half of the individuals standing changed their minds and sat down, what fraction of the class’s favorite color is blue?

17. #2: Something Fishy…  Stand if at some point in your life, you have had a pet fish.  What fraction of the entire class has had a pet fish?  What would happen if twice as many people stood up? What fraction of the class would that be?

18. #3: Movies  Stand up if you watched a movie this weekend.  What fraction of the class stood up?  What would happen if we had 3 times as many individuals stand up? What fraction would that be?

19. Adding Fractions  When adding fractions, it is important to make sure that both of the fractions have a common (same) denominator  For example, we would be able to take +  However, we would not be able to take + without first making a common denominator  When fractions do share a common denominator, we add their numerators and leave the denominator the same  For example + =  How can we reduce this fraction? 3 8 1 8 2 3 3 8 1 4 1 8 4 8

20. Practice: Fraction Addition  + =  Careful, this question requires an extra step! 2 6 5 6 1 2 3 4 1 5 3 5

21. Subtracting Fractions  Subtracting fractions is similar to adding in the sense that using common denominators is essential  When we subtract fractions, we subtract the numerators, while leaving the denominators the same  – = = 1 5 4 5 4 - 1 5 3 5 6 7 4 7 2 7 6 - 2 7

22. Practice Subtracting Fractions  - =  After subtracting, can the answer be reduced? If so, to what?  - =  Be careful with the positive/negative signs on this problem!  - =  This problem requires a common denominator. Don’t forget to find that before solving! 5 9 2 9 6 10 9 2 3 1 5

23. Fraction Blackjack Game!  I will number you into groups of three. Each group will have their own deck of fraction cards.  The same rules as Blackjack apply, but instead of trying to get to 21, try and get close to 1 without going over.  Each student starts the game by being dealt one card face up. The dealer has to have at least 7/10 or higher before he can stop. The other players’ goal is to get as close to 1 without going over.  Once everyone is satisfied with their hand, all the players show their cards, and the one with the closest total to 1 without going over is the winner.  If the players all go over, the dealer is the automatic winner.

24. Let’s Review!  Adding and subtracting fractions requires a common denominator and only the numerator changes  Multiplying fractions affects both the numerator and the denominator  Dividing fractions requires the numerator and denominator to be inverted. From there, apply the same steps as in multiplication

25. Individual Assessments  Next, I’m going to pass out an amazing review worksheet on FRACTIONS!  Try your best!  Feel free to ask questions!