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Fractions

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Fractions

By: Lisa Fogle

- 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.

- 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.

- 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.

- 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.

- 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.

- 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.

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.

- 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.

- Provides visual example on how to add fractions

- Combining two sets of objects

- 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

- 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

- 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.

- 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.