1. An Introduction to Fractions!
Defining, visualizing, comparing and finding equivalent fractions

2. Fractions A fraction is part of a whole number.
Can you think of examples of fractions?
The following numbers are all fractions: 1/2, 3/7, 6/10, 4/99

3. Definitions of Fractions
A fraction is a way of representing division of a 'whole' into 'parts'. It has the form
Numerator
Denominator

4. Numerators and Denominators
Numerator is the number of parts chosen
and the
Denominator is the total number of parts.
Another way which fractions are represent is in the form or a/b, where a and b are whole numbers, and the number b is not 0. In this example, a is the numerator and b is the denominator.

5. Representation of Fractions
In this example 3 of the 7 parts of the pie chart are shaded. Therefore the numerator is 3 and the denominator is 7.

6. Now You Decide: How many of the pieces are in the circle?
How many pieces are shaded in?
What fraction could be used to represent the amount of the circle which is shaded in?

7. Comparing Fractions
When comparing fractions, you will be given two fractions to compare as in the example below:
You are to choose which of the two fractions is the larger.
Keep this in mind as you make your choice - the larger the numerator the larger the fraction and the larger the denominator the smaller the fraction. If the denominators are the same, the fraction with the larger numerator is larger and if the numerators are the same, the fraction with the larger denominator is smaller.

8. Visualizing the fraction
One method is to visualize the fractions, as pictured below in red:

9. Discussion of two fractions
As you can see 1/4 is less than half the circle while 5/6 is more than half the circle - so 5/6 is larger.
Here, the idea of the least common denominator or LCD is used.  LCD is an idea we have discussed that can be used in comparing fractions. The LCD is the smallest number that both 4 and 6 will divide into evenly. 12 is the LCD for the fractions 1/4 and 5/6 because both 4 and 6 divide evenly into 12. 

10. Now You compare: Which is greater 2/7 or 1/11 ?
Which is less 6/11 or 22/51 ?
Which is greater 1/2 or 4/8 ?
What do you notice about the last pair of fractions we compared?

11. Equivalent Fractions
Fractions are equivalent if they represent the same amount of the whole or the same value
Why are these two fractions equivalent? Can you think of more equivalent fractions?

12. More Equivalent Fractions
Is this fraction equivalent to 2? How can you tell?

13. Why do you think fractions are useful?
If Jimmy at 3 of the 9 pieces of pizza how much of the pizza did he eat?
If Rieta drove 2 of the 5 miles to school how much of the trip to school has she traveled?
If Andy read 22 of the 55 pages in his book how much of the book has he read?
Can you think of other examples of fractions?

14. Exploring Fractions on the Internet
A great site to compare and find equivalent fractions:
Virtual Manipulative: Fractions

15. GREAT!

16. TRY AGAIN

17. THEY ARE EQUAL!

18. According to the Ohio Department of Education’s content standards for middle school math, 6th graders should be able to explain why a number is rational and recognize that the expression a/b can represent a parts of size 1/b and use models and pictures to represent the ideas of ratios. This idea of fractions can be difficult for 6th graders to comprehend because they are comfortable working with whole numbers. Therefore, this PowerPoint presentation was designed to define fractions, compare fractions, and discuss equivalent fractions through class discussions, application of fractions to the real world, and the use of visual images to illustrate fractions.
When presenting each slide to the class, I will ask them questions in order to get them involved in the lecture. For example, I will ask “What is a fraction?” and “Can you think of any examples of fractions?” In addition, I will ask the students to relate their new knowledge of fractions to the real world by asking them to think of any examples of fraction they might encounter in their lives. Finally, this presentation is full of pictures which will help students visualize and understand fractions. These pictures are especially useful when comparing fractions and studying equivalent fractions. Students can see for themselves why one fraction is greater than the other or why two fractions are equal.
This lesson was designed to present information about fractions, which meet the content standards for Ohio, in an organized manner. This presentation also will appeal to students because the information will be presented both visually and verbally. Finally, the presentation will get students actively involved in the lesson by having them discuss fractions and visualize fractions throughout the lesson.

19. References
Interactive Math Lessons, Tutorials, and Games Online: Fractions, Decimals,
Percents, and Integers. (n.d.) Retrieved on August 1, 2005, from
Middle School Math. (n.d.) Retrieved on August 1, 2005, from