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Math 008 - Cooley
Prealgebra
OCC
Section 4.2 – Understanding Fractions
Definition – Fraction
A numerical representation indicating the quotient of two numbers (a numerator and a denominator). This
3
representation is a number that can represent part of a whole. For example: . Here, 3 is called the numerator, 5
5
is called the denominator, and both are separated by a line called the fraction bar.
Division Involving the Number 1 and the Number 0
9
1
9
7
2) Any number divided by 1 remains unchanged. Example:
7
1
1) Any nonzero number divided by itself is 1. Example:
3) Zero may be divided by any nonzero number; the result is always zero. Example:
4) You cannot divide by zero. Example:
0
0
5
3
0
is undefined. (Note:
is indeterminate.)
0
0
Proper Fraction
A fraction whose numerator is always less than the denominator. Examples:
3 4 9
, ,
5 7 31
Improper Fraction
A fraction whose numerator is always greater than or equal to the denominator. Examples:
6 7 8 13
, , ,
5 3 8 9
Mixed Number
3 7
8
The sum of a whole number greater than zero and a proper fraction. Examples: 2 ,4 ,13
5 9 13
Picture Representations of Improper Fractions
Changing a Mixed Number to an Improper Fraction
1. Multiply the whole number by the denominator of the fraction.
2. Add the numerator of the fraction to the product found in step 1.
3. Write the sum found in step 2 over the denominator of the fraction.
Changing an Improper Fraction to a Mixed Number
1. Divide the numerator by the denominator.
2. Write the quotient followed by the fraction with the remainder over the denominator.
quotient
remainder
denominator
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Math 008 - Cooley
Prealgebra
OCC
Section 4.2 – Understanding Fractions
 Exercises:
What fraction is represented by the darker shaded portion of the following figures?
1)
2)
3)
Divide, if possible. Assume all variables in the denominators are nonzero.
4)
4
0
5)
0
6
6)
9
9
7)
x
x
Answer the questions in the following applications.
8)
Jillian earned $165 over the weekend at her waitressing job. She used $48 of it to repay a loan to her
sister. What fractional part of her earnings did Jillian use to repay her sister?
9)
In 2010, Orange Coast College had 21 full-time math instructors and 38 part-time math instructors.
What fractional part of the faculty are part time?
Change each mixed number to an improper fraction.
10)
2
3
5
11)
6
6
7
9
10
12)
7
16)
59
7
1
9
13)
6
17)
106
9
Change each improper fraction to a mixed number.
14)
13
5
15)
19
3
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