1. Section 6.1 The Basic Concepts of Fractions and Rational Numbers
MTH 231
Section 6.1
The Basic Concepts of Fractions and Rational Numbers

2. Need I Say More?

3. Applications of Fractions
Measurement

4. Applications of Fractions
Music

5. Applications of Fractions
3. Ratio and Proportion

6. The Worst Thing Ever

7. Important Interpretations of the Fraction a/b:
Agree on the unit (describe, in words, how something is being measured or what one of something is)
Understand that the unit is subdivided into b parts of equal size.
Understand that we are considering a of those parts of the unit.

8. Everybody Likes Pizza!

9. Colored Regions

10. Number Lines

11. Strips

12. Sets

13. Equivalent Fractions

14. Fractions in Simplest Form
A fraction is in simplest form when the numerator and denominator have no common divisor larger than 1.
To reduce a fraction to simplest form (or lowest terms), divide both the numerator and the denominator by the greatest common divisor.
Divisibility rules can play an important role in reducing fractions.
Two fractions are equivalent if, when reduced to simplest form, they are equal.

15. Examples

16. Least Common Denominators
As we shall see in a later section, a (least) common denominator is required to add and subtract fractions.
Least common denominator = least common multiple.

17. Examples

18. Comparing and Ordering Fractions
If two fractions have the same denominator, the larger fraction will have a larger numerator.
If two fractions have the same numerator, the larger fraction will have a small denominator.

19. An Example