1. Set of Rational Numbers
Section 6.1
Set of Rational Numbers
numerator
denominator

2. Uses of Rational Numbers
Example
Division problem or solution to a multiplication problem
2x = 3, x = 3/2
Part of a whole
Joe received ½ of Mary’s salary
Ratio
The ratio of girls to boys is 9/6 or 3/2
Probability
When you toss a coin, the probability of landing on heads is ½

3. Rational Number Models

4. Definition Proper fraction A fraction where Improper fraction
A fraction such that

5. Equivalent or Equal Fractions
Equivalent fractions are numbers that represent the same point on a number line.

6. Fraction Strips

7. Fundamental Law of Fractions
Let be any fraction and n a nonzero whole
number, then

8. Example
Find a value for x such that

9. Example
Write each of the following fractions in simplest form if they are not already so: a. b. c. d.

10. Equality of Fractions
Two fractions and are equal if and only if ad = bc.

11. Ordering Rational Numbers
If a, b, and c are integers and b > 0, then if and only if a > c.
If a, b, c, and d are integers
and b > 0, d > 0, then
if and only if ad > bc.

12. Denseness of Rational Numbers
Given rational numbers there is another rational number between these two numbers.
Find two fractions between

13. Addition of Rational Numbers
Section 6.2
Addition of Rational Numbers
Area model

14. Addition/Subtraction with Like Denominators
If are rational numbers, then

15. Addition/Subtraction with Unlike Denominators
If are rational numbers, then

16. Example
Find each of the following sums: a. b.

17. Example (continued) c. d.

18. Example
Find each difference. a. b.

19. Mixed Numbers
Numbers that are made up of an integer and a fractional part of an integer.
A mixed number is a rational number, and therefore, it can always be written in the form

20. Example
Change each of the following mixed numbers to improper fractions. a. b.

21. Example
Change to a mixed number.

22. Properties of Addition for Rational Numbers
Properties of the additive inverse for rational numbers are analogous to those of the additive inverse for integers.

23. Example
Add or subtract. Write answers in simplest form. a.

24. Example (continued) b.

25. Example (continued) c.

26. Estimation
A sixth-grade class is collecting cans to take to the recycling center. Becky’s group brought the following amounts (in pounds). About how many pounds does her group have all together?
The front-end estimate is = 9.
The adjustment is
The adjusted estimate is = 11.

27. Example
Estimate each of the following. a. b.