Fractions describe parts of a whole and are composed of a numerator and denominator. The numerator tells how many parts are showing, and the denominator tells the total number of parts. Fractions can be added, subtracted, multiplied, and reduced to their simplest form. Converting between improper fractions and mixed numbers involves dividing the numerator by the denominator to get a whole number part and remaining numerator part.

1. All About Fractions Kelsey Charnawskas EDU 290 – Technology in Education 3-1-11

2. Fractions “describe a part of a whole after the whole is cut into equal parts.”¹ Fractions can tell, in a group of various objects, how many objects are the same thing. Ex: You have 4 blue marbles and 5 green marbles. 49 of the marbles are blue. What Are Fractions?

3. Fractions are composed of two numbers, one of top of the other, separated by a horizontal line. The top number is called the numerator. This tells “how many parts are showing.”¹ Parts of a Fraction

4. The bottom number is called the denominator. It tells the “number of parts in the whole.”¹ 34 Parts of a Fraction numerator denominator

5. Fractions can be added together but they must have the same denominator. If the denominators are the same, then the numerators can be added together. The denominator will remain the same. Adding Fractions

6. 68+ 18= 78 Example

7. In order for fractions with different denominators to be added together, the least common denominator needs to be found. The least common denominator is the smallest multiple that both numbers have in common.² Whatever you multiply the bottom number by to get the least common denominator, you have to multiply the numerator by. Adding Fractions with Different Denominators

8. 45 + 23 = ? The lowest common denominator is 15. The first fraction must be multiplied by 33, giving 1215. The second fraction must be multiplied by 55, giving 1015. The equation becomes: 1215+1015= 2215 Example

9. Just like with addition, when subtracting, the denominators have to be the same. If the denominators are the same, then the numerators can be subtracted from one another. The denominator will remain the same. Subtracting Fractions

10. 68 − 18= 58 Example

11. The least common denominator has to be found. Once the least common denominator is found, you figure out what the denominator had to be multiplied by to get that common number. Whatever the bottom number is multiplied by, the numerator also has to be multiplied by. Subtract Subtracting Fractions with Different Denominators

12. 45 − 23= ? The least common denominator is 15. The first fraction must be multiplied by 33, giving 1215. The second fraction must be multiplied by 55, giving 1015. 1215 − 1015= 215 Example

13. There are two ways that fractions can be multiplied. 1. They can be turned into decimals and multiplied. Example: 34 𝑥 12=0.75 𝑥 0.5=0.375 Multiplying Fractions

14. 2. The fractions can be left as fractions and multiplied together. First, the fractions have to be set up so the numerators and denominators align with each other. Next, see if the numbers diagonal from each other have a greatest common factor (GCF). Reduce these numbers using the GCF to the smallest they can be. Then, multiply straight across. Multiplying Fractions

15. 89 𝑥 1824= ? Looking diagonally: Between the 9 and 18, the greatest common factor is 9. Therefore, the 9 and 18 are both divided by 9. Between the 8 and 24, the greatest common factor is 8. Therefore, the 8 and 24 are both divided by 8. 11 𝑥 23= 23 Example

16. Reducing fractions, or simplifying, is when a fraction is in its lowest terms. This means that “there is no number, except 1, that can be divided evenly into both the numerator and denominator” (www.math.com). Divide both the numerator and denominator by their greatest common factor and it will be in simplest/reduced form. Reducing Fractions

17. 2040 reduced to ? The greatest common factor is 20. Therefore, the top and bottom numbers get divided by 20. After they are both divided, the fraction is reduced to 12. 2040 reduced to 12 Reducing Fractions Example

18. Improper fractions are fractions where the numerator is larger than the denominator. (98) A mixed number is composed of a whole number and a fraction. (114) To change: divide the top number by the bottom to get the whole number. The remainder from that division becomes the new numerator of the fraction. Converting from Improper Fractions to Mixed Numbers

19. 98 as a mixed number is ? 8 goes into 9 one time. The whole number is 1. There is a remainder of 1 from the division. The denominator stays the same and the remainder becomes the new numerator. Therefore, the fraction is 18. 98 as a mixed number is 118 Example

20. The denominator gets multiplied by the whole number. The numerator is then added to that new number. The denominator remains the same. Converting Mixed Numbers to Improper Fractions

21. 129 as an improper fraction is ? The denominator gets multiplied by the whole number. 9 x 1 = 9 The numerator is added: 9 + 2 = 11. This new number is put over the same denominator. 129 as an improper fraction is 119 Example

22. Add 18+ 36= 46+ 13= Subtract 45 − 12= 38 − 26= Convert to Improper Fraction or Mixed Number 114= 219= 7. 97= 8. 157= Practice Problems Multiply 12. 48 𝑥16= 13. 910 𝑥59= 14. 65 𝑥 159= Reduce 9. 515= 10. 624= 11. 3010=

23. 1524 66=1 310 124 54 199 127 Answers to Practice Problems 227 14 13 3 224= 112 15 63=2

24. 1. Information and direct quotes on slides 2-4 from “Understanding Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm Information on slides 5 and 7 from “Understanding Fractions: Adding Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm Information on slides 9 and 11 from “Understanding Fractions: Subtracting Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm Information on slides 13 and 14 from “Understanding Fractions: Multiplying Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm Works Cited

25. Information on slide 16 from “Reducing Fractions” http://www.math.com/school/subject1/lessons/S1U4L2GL.html Information on slides 18 and 20 from “Understanding Fractions: Other Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm 2. Definition of “Least Common Denominator” on slide 7 from http://www.google.com/search?hl=en&rlz=1T4TSNA_enUS386US388&defl=en&q=define:Least+Common+Denominator&sa=X&ei=BkppTeqNDJPQgAeV5t3LCg&ved=0CBQQkAE Image on slide 3 from http://spfractions.wikispaces.com/file/view/proper+fraction.bmp All of the examples are my own including slide 22 with the various practice problems. Works Cited Continued