Download Rational Numbers

Student Academic Learning Services
Page 1 of 2
Rational Numbers
What is a Rational number?
A rational number is any number that can be written as a fraction of two integers. This
includes any fraction whose numerator and denominator are both integers as well as any
decimal number with a finite number of decimal places, or even any repeating decimal
number. (All repeating decimals can be written as fractions. E.g. 0.33333… is equal to 1/3).
A fraction is a type of ratio that allows you to compare two numbers. Fractions are effective
because they allow you to express numbers clearly and efficiently without approximating.
Examples of Rational Numbers
4.2
-32.6666…
3/7
0.2/0.3
Signed Fraction
It is worth a quick mention of what happens when you have a fraction with a negative sign.
The problem is that both the numerator and denominator can be either positive or negative.
When this occurs, it is helpful to remember that a fraction represents a division (the
numerator divided by the denominator).
When it comes to fractions, the sign can be in front of the fraction (as if adding and
subtracting) or on the numerator, the denominator or both.
If you have a negative in the numerator or the denominator (but not both) then the fraction
will be negative. This is because the division will be composed of a negative divided by a
positive or vice versa, which will result in a negative quotient. For the same reason, if both
the numerator and denominator are negative then the fraction is positive.
The next page will discuss how to use rational numbers in expressions and in equations.
www.durhamcollege.ca/sals
Student Services Building (SSB), Room 204
905.721.2000 ext. 2491
This document last updated: 12/22/2010
Student Academic Learning Services
Page 2 of 2
Expressions with Rational Numbers
Solving Equations with Rational Numbers
When solving equations with rational numbers the same rules again apply. Here are two
examples of equations where we are solving for the variable ‘x.’
www.durhamcollege.ca/sals
Student Services Building (SSB), Room 204
905.721.2000 ext. 2491
This document last updated: 12/22/2010