1. Introduction to Fractions and Mixed Numbers
Section
2.1
Introduction to Fractions and Mixed Numbers

2. 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 2

3. Example
Identify the numerator and denominator of each fraction. a. b.

4. Division Properties of 0 and 1
Chapter 1 / Whole Numbers and Introduction to Algebra
Division Properties of 0 and 1
If n is any whole number, except 0.

5. Examples
Simplify.
a. b.
c. d.
e. f.
Objective A 5

6. 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 6

7. 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 7

8. 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 8

9. 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 9

10. 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?

11. 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 11

12. 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

13. Writing a Mixed Number as an Improper Fraction
To write a mixed number as an improper fraction: Step 1: Multiply the denominator of the fraction by the whole number. Step 2: Add the numerator of the fraction to the product from Step 1. Step 3: Write the sum from Step 2 as the numerator of the improper fraction over the original denominator.

14. Example
Write each as an improper fraction. a. b.

15. Writing an Improper Fraction as a Mixed Number or a Whole Number
To write an improper fraction as a mixed number or a whole number: Step 1: Divide the denominator into the numerator. Step 2: The whole number part of the mixed number is the quotient. The fraction part of the mixed number is the remainder over the original denominator.

16. Example
Write each as a mixed number of whole number. a. b.