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- 1. All About Fractions<br />Kelsey Charnawskas<br />EDU 290 – Technology in Education<br />3-1-11<br />
- 2. Fractions “describe a part of a whole after the whole is cut into equal parts.”¹<br />Fractions can tell, in a group of various objects, how many objects are the same thing. <br />Ex: You have 4 blue marbles and 5 green marbles. 49 of the marbles are blue.<br /> <br />What Are Fractions?<br />
- 3. Fractions are composed of two numbers, one of top of the other, separated by a horizontal line. <br />The top number is called the numerator. <br />This tells “how many parts are showing.”¹<br />Parts of a Fraction<br />
- 4. The bottom number is called the denominator. <br />It tells the “number of parts in the whole.”¹<br />34<br /> <br />Parts of a Fraction<br />numerator<br />denominator<br />
- 5. Fractions can be added together but they must have the same denominator.<br />If the denominators are the same, then the numerators can be added together. <br />The denominator will remain the same. <br />Adding Fractions<br />
- 6. 68+ 18= 78<br /> <br />Example<br />
- 7. In order for fractions with different denominators to be added together, the least common denominator needs to be found. <br />The least common denominator is the smallest multiple that both numbers have in common.²<br />Whatever you multiply the bottom number by to get the least common denominator, you have to multiply the numerator by.<br />Adding Fractions with Different Denominators<br />
- 8. 45 + 23 = ?<br />The lowest common denominator is 15.<br />The first fraction must be multiplied by 33, giving 1215.<br />The second fraction must be multiplied by 55, giving 1015.<br />The equation becomes:<br />1215+1015= 2215<br /> <br />Example<br />
- 9. Just like with addition, when subtracting, the denominators have to be the same.<br />If the denominators are the same, then the numerators can be subtracted from one another.<br />The denominator will remain the same.<br />Subtracting Fractions<br />
- 10. 68 − 18= 58<br /> <br />Example<br />
- 11. The least common denominator has to be found.<br />Once the least common denominator is found, you figure out what the denominator had to be multiplied by to get that common number.<br />Whatever the bottom number is multiplied by, the numerator also has to be multiplied by.<br />Subtract<br />Subtracting Fractions with Different Denominators<br />
- 12. 45 − 23= ?<br />The least common denominator is 15.<br />The first fraction must be multiplied by 33, giving 1215.<br />The second fraction must be multiplied by 55, giving 1015.<br />1215 − 1015= 215<br /> <br />Example<br />
- 13. There are two ways that fractions can be multiplied.<br />1. They can be turned into decimals and multiplied.<br />Example:<br /> 34 𝑥 12=0.75 𝑥 0.5=0.375<br /> <br />Multiplying Fractions<br />
- 14. 2. The fractions can be left as fractions and multiplied together.<br />First, the fractions have to be set up so the numerators and denominators align with each other.<br />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.<br />Then, multiply straight across.<br />Multiplying Fractions<br />
- 15. 89 𝑥 1824= ?<br />Looking diagonally:<br />Between the 9 and 18, the greatest common factor is 9. Therefore, the 9 and 18 are both divided by 9.<br />Between the 8 and 24, the greatest common factor is 8. Therefore, the 8 and 24 are both divided by 8.<br />11 𝑥 23= 23<br /> <br />Example<br />
- 16. Reducing fractions, or simplifying, is when a fraction is in its lowest terms.<br />This means that “there is no number, except 1, that can be divided evenly into both the numerator and denominator” (www.math.com).<br />Divide both the numerator and denominator by their greatest common factor and it will be in simplest/reduced form.<br />Reducing Fractions<br />
- 17. 2040 reduced to ?<br />The greatest common factor is 20. Therefore, the top and bottom numbers get divided by 20. <br />After they are both divided, the fraction is reduced to 12.<br />2040 reduced to 12<br /> <br />Reducing Fractions Example<br />
- 18. Improper fractions are fractions where the numerator is larger than the denominator. (98)<br />A mixed number is composed of a whole number and a fraction. (114)<br />To change: divide the top number by the bottom to get the whole number.<br />The remainder from that division becomes the new numerator of the fraction.<br /> <br />Converting from Improper Fractions to Mixed Numbers<br />
- 19. 98 as a mixed number is ?<br />8 goes into 9 one time. <br />The whole number is 1.<br />There is a remainder of 1 from the division. The denominator stays the same and the remainder becomes the new numerator.<br />Therefore, the fraction is 18.<br />98 as a mixed number is 118<br /> <br />Example<br />
- 20. The denominator gets multiplied by the whole number. <br />The numerator is then added to that new number.<br />The denominator remains the same.<br />Converting Mixed Numbers to Improper Fractions<br />
- 21. 129 as an improper fraction is ?<br />The denominator gets multiplied by the whole number.<br />9 x 1 = 9<br />The numerator is added: 9 + 2 = 11.<br />This new number is put over the same denominator.<br />129 as an improper fraction is 119<br /> <br />Example<br />
- 22. Add<br />18+ 36=<br />46+ 13=<br />Subtract<br />45 − 12=<br />38 − 26=<br />Convert to Improper Fraction or Mixed Number<br />114=<br />219=<br /> <br />7. 97=<br />8. 157=<br /> <br />Practice Problems<br />Multiply<br />12. 48 𝑥16=<br />13. 910 𝑥59=<br />14. 65 𝑥 159=<br /> <br />Reduce<br />9. 515=<br />10. 624=<br />11. 3010=<br /> <br />
- 23. 1524<br />66=1<br />310<br />124<br />54<br />199<br />127<br /> <br />Answers to Practice Problems<br />227<br />14<br />13<br />3<br />224= 112<br />15<br />63=2<br /> <br />
- 24. 1. Information and direct quotes on slides 2-4 from “Understanding Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm<br />Information on slides 5 and 7 from “Understanding Fractions: Adding Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm<br />Information on slides 9 and 11 from “Understanding Fractions: Subtracting Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm<br />Information on slides 13 and 14 from “Understanding Fractions: Multiplying Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm<br />Works Cited<br />
- 25. Information on slide 16 from “Reducing Fractions” http://www.math.com/school/subject1/lessons/S1U4L2GL.html<br />Information on slides 18 and 20 from “Understanding Fractions: Other Fractions” http://library.thinkquest.org/J002328F/understanding%20fractions.htm<br />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<br />Image on slide 3 from http://spfractions.wikispaces.com/file/view/proper+fraction.bmp<br />All of the examples are my own including slide 22 with the various practice problems.<br />Works Cited Continued<br />

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