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# Fractions

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1. Fractions By: Lisa Fogle

2. What are fractions? • They are part of a whole. • Comes from the Latin word fractio meaning to break or break apart. • Have numerator and a denominator • They are written as a over b or a/b, the a is the numerator and b is the denominator. • There will always be a fraction between two fractions, this is called density of fractions.

3. Models for Fractions • Part-to Whole concept • Is used to show part of a whole object. • The fraction a/b, a is the part of the whole and b is the whole. • The example to the right is 2/8. Having the whole as eight and the two as part of the whole reduces to ¼.

4. Models continued • Division Concept • Is also called the measurement or sharing concept. • Trying to divide a whole with bars by a certain number. • The example to the right shows that 2/5 equals 4/10.

5. Models continued • Ratio concept • It’s used to compare one amount to another. • Example is a girl’s height is ½ of her mother’s height. • Can use rods to compare the weights or size or amount.

6. Equality of Fraction • Shows how fractions are equal and how they represent the same amount. • With this you can use simplification of fractions by finding a common factor between the two numbers. This will help reduce the fraction to it’s simplest form. • An example is, 8/20 = 2/5 because 2 times 4 is 8 and 5 times 4 is 20 giving you 8/20.

7. Common Denominators • Show that two fractions can have the same denominator to determine their Inequality. • An inequality is to determine which fraction are greater then or less than of each other. • Example, a/b<c/d if and only if ad<bc • Or if a/b>c/d if and only if ad>bc.

8. Mixed Numbers Are when improper fractions are written as a whole number and a fraction combined. An example would be 2 1/3. Improper Fractions They are fraction with a numerator greater than or equal to the denominator. An example would be 7/4 or 4/4. Different types of Fractions

9. Adding Fractions • Concepts to use • Combining two sets of objects • Example, 1/3+1/5 would be 5/15+3/15 because you need to find the common denominator of the two. The answer would be 8/15. • 1/3+1/3, can be added across since they have a common denominator giving you the answer of 2/3. • For mixed numbers first add the fractions then the whole numbers in order to get the answer. • http://pittsford.monroe.edu/jefferson/calfieri/fractions/AddFrac.html • Provides visual example on how to add fractions Virtual Manipulative: Fractions – Adding - Is a good source to see how fractions are added.

10. Subtracting Fractions • Can use the take-away concept, missing addend or the partitioning. • Fraction bars or number lines can be used to display models. • Finding the common denominator can be beneficial when you subtract two fraction that have different denominators. • http://cne.gmu.edu/modules/dau/algebra/fractions/frac3_frm.html • This site is good for adding and subtracting fractions

11. Multiplying Fractions • Repeated addition is used when you multiply a whole number by a fraction. • Example, 4*3/4 shows that the product is 3. This answer was solved my cross multiplying. Having the fours cancel each other. • Fraction times a fraction by dividing a rectangle by the denominator, then shade in the region where the fractions take place. The answer will be the area that was shaded twice. • Example, a/b x c/d= ac/bd

12. Dividing Fractions • Can be represented by using the repeated subtraction concept. • Want to use the terms “How many times,” does one number go into the other. • Example, a/b divided by c/d=a/b x d/c=ad/bc. • Fraction bars are one of the models that represents division.

13. Fraction operations websites • http://www.visualfractions.com/ • Gives example of adding, subtracting, multiplying and dividing fractions by using concrete examples. • http://www.aaamath.com/B/fra.htm • Provides various concepts of fractions and allows the students to practice the operations of fractions. • http://library.thinkquest.org/J002328F/adding.htm?tqskip1=1&tqtime=0422 - Provides visual experiences on how to add fractions and lets you know what they are about. • http://cne.gmu.edu/modules/dau/algebra/fractions/fractions_frm.html • Is a good source to provide information about fractions with visual aids, definitions along with some of the concepts.