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Fractions. By: Lisa Fogle. 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.

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Fractions

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Fractions l.jpg

Fractions

By: Lisa Fogle


What are fractions l.jpg

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.


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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.


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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.


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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.


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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.


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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.


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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


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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.


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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


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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


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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.


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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.


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