Fractions

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
• Its used to compare one amount to another.
• Example is a girls height is ½ of her mothers
  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
  its 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/bltc/d if and only if adltbc
• Or if a/bgtc/d if and only if adgtbc.

8
Different types of Fractions

• 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.

9
Adding Fractions

• Concepts to use
• Combining two sets of objects
• Example, 1/31/5 would be 5/153/15 because you
  need to find the common denominator of the two.
  The answer would be 8/15.
• 1/31/3, 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/fra
  ctions/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/f
  rac3_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, 43/4 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/da/b x d/cad/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?
  tqskip11tqtime0422
• - Provides visual experiences on how to add
  fractions and lets you know what they are about.
• http//cne.gmu.edu/modules/dau/algebra/fractions/f
  ractions_frm.html
• Is a good source to provide information about
  fractions with visual aids, definitions along
  with some of the concepts.