1. 3
Chapter
Chapter 2
Fractions and Mixed Numbers

2. Introduction to Fractions and Mixed Numbers
Section
3.1
Introduction to Fractions and Mixed Numbers

3. Identify the Numerator and the Denominator of a Fraction.
Objective A
Identify the Numerator and the Denominator of a Fraction.

4. Identifying Numerators and Denominators
In a fraction, the top number is called the numerator and the bottom number is called the denominator. The bar between the numbers is called the fraction bar.
Names
Fraction
Meaning
Numerator number of parts being considered
Denominator number of equal parts in the whole
Objective A 4

5. Example
Identify the numerator and denominator of each fr action. a. b.

6. Write a Fraction to Represent Parts of Figures or Real-Life Data.
Objective B
Write a Fraction to Represent Parts of Figures or Real-Life Data.

7. Example Write the fraction to represent the shaded part of the figure.
In this figure, 4 out of the 7 equal parts are shaded. Thus the fraction is .
Objective A 7

8. Example
Write the fraction to represent the shaded part of the diagram.
In this diagram, 3 out of the 10 equal parts are shaded. Thus the fraction is .
Objective A 8

9. Example
Draw a figure and then shade a part of it to represent the fraction .
Since the denominator is 6, we divide the rectangle into 6 equal parts. Then we shade 5 of the equal parts.
Objective A 9

10. Example Draw and shade a part of a figure to represent the fraction.
The figure consists of 11 circles of the same size.
We will shade 7 of the circles.
Objective A 10

11. Example
Of the eight planets in our solar system, five are farther from the Sun than Earth is. What fraction of the planets are farther from the Sun than Earth is?

12. Identify Proper Fractions, Improper Fractions, and Mixed Numbers.
Objective C
Identify Proper Fractions, Improper Fractions, and Mixed Numbers.

13. Identifying Proper Fractions, Improper Fractions and Mixed Numbers
Proper Fraction: A fraction whose numerator is less than its denominator.
Numerator
Denominator
Improper Fraction: A fraction whose numerator is greater than or equal to its denominator.
Objective A 13

14. Example
Identify each number as a proper fraction, improper fraction, or mixed number. a. b. c. d. e. f.
proper fraction
improper fraction
improper fraction
proper fraction
mixed number
improper fraction

15. Graph Fractions on a Number Line.
Objective D
Graph Fractions on a Number Line.

16. Fractions on Number Lines
Chapter 1 / Whole Numbers and Introduction to Algebra
Fractions on Number Lines
Another way to visualize fractions is to graph them on a number line. 3
5 equal parts 1

17. Example
Graph the proper fraction on a number line. Divide the distance from 0 to 1 into 4 parts. Then start at 0 and count over 3 parts. 3 4

18. Example
Graph the improper fraction on a number line. 8 3

19. Review Division Properties of 0 and 1.
Objective E
Review Division Properties of 0 and 1.

20. Division Properties of 0 and 1
Chapter 1 / Whole Numbers and Introduction to Algebra
Division Properties of 0 and 1
If n is any integer other than 0, then
If n is any integer, then

21. Examples
Simplify.
a. b.
c. d.
e. f.
Objective A 21