Suppose that you and two of your friends went out to lunch and that you ate
Guidance
Rational numbers include fractions, integers and whole numbers. The definition below shows that all rational numbers can be written in the form of a fraction:
Definition:
A
rational number
is a number that can be written in the form
An integer, such as the number
A Review of Fractions
You can think of a rational number as a fraction of a cake. If you cut the cake into
There are three main types of fractions:
 Proper fractions are rational numbers where the numerator is less than the denominator. A proper fraction represents a number less than one. With a proper fraction you always end up with less than a whole cake!
 Improper fractions are rational numbers where the numerator is greater than the denominator. Improper fractions can be rewritten as a mixed number – an integer plus a proper fraction. An improper fraction represents a number greater than one.

Equivalent fractions
are two fractions that give the same numerical value when evaluated. For example, look at a visual representation of the rational number
24 .
The visual of
Therefore,
Example A
Classify and simplify the following rational numbers .
a)
b)
c)
Solution:
a) Because both 3 and 7 are prime numbers,
b) The numerator is larger than the denominator; therefore, this is an improper fraction.
c) This is a proper fraction;
Ordering Rational Numbers
To order rational numbers is to arrange them according to a set of directions, such as ascending (lowest to highest) or descending (highest to lowest). Ordering rational numbers is useful when determining which unit cost is the cheapest.
Example B
Cans of tomato sauce come in three sizes: 8 ounces, 16 ounces, and 32 ounces. The costs for each size are $0.59, $0.99, and $1.29, respectively. Find the unit cost and order the rational numbers in ascending order.
Solution:
Use proportions to find the cost per ounce:
Example C
Which is greater,
Solution:
Begin by creating a common denominator for these two fractions. Which number is evenly divisible by 7 and 9?
Because
Video Review
Guided Example
For the fractions
a.) Determine whether these are proper or improper fractions.
b.) Simplify if necessary.
b.) Order the two fractions.
Solution:
a.) For both fractions, the numerator is smaller than the denominator, so they are both proper fractions.
b.) For
For
c.) To order the fractions, we'll use the simplified versions:
Since
then
Practice
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK12 Basic Algebra: Integers and Rational Numbers (13:00)
 What are the three types of fractions?
In 2 – 4, determine what fraction of the whole each shaded region represents.
In 5 – 8, place the following sets of rational numbers in order from least to greatest.

12,13,14 
1112,1211,1310 
3960,4980,59100 
711,813,1219
In 9 – 14, find the simplest form of the following rational numbers.

2244 
927 
1218 
315420 
19101 
9911
Mixed Review

Evaluate the following expression:
56d+7a2 ; usea=(−1) and d=24 .  The length of a rectangle is one more inch than its width. If the perimeter is 22 inches, what are the dimensions of the rectangle?

Determine if
x=−2 is a solution to4x+7≤15 . 
Simplify:
(7+3)÷2×32−5(58−8) .