- Events, Workshops and Programs
- Resources by Discipline
-
Support and Resources by Topic
- - Statistics Help (General)
- - Statistics Help (R Commander)
- - Arithmetic
- - Standard Derivatives
- - Standard Integrals
- - Hyperbolic Trigonometric Functions
- - Remainders and Quotients
- - SPSS Help
- - Logic Basics: AND, OR, NOT
- - Approximations: rounding and truncation
- - Mathematical Terminology
- - Proportional Reasoning
- - Number Sense
- - I Don't Get It
- - Percentages
- Contact the MESH team
- MESH Research
- Resources for Staff
Rational Numbers
When you divide one integer by another the answer is not always another integer.
For example $3 \div 2$, $2$ goes into $3$ once but there is a remainder of $1$, so the result of this division is NOT an integer.
$3 \div 2$ can also be written as $\displaystyle{\frac32}$ or $\displaystyle{1\frac12}$ or $1.5$.
When an integer is divided by another integer (not zero) the answer is a rational number. The word rational comes from ‘ratio’.
The symbol used to represent rational numbers is $\mathbb{Q}$.
A rational number can be written as a fraction (or ratio) of integers.
Examples:
$$\frac14,\; \frac12,\; -\frac23,\; \frac51$$
Look at the last example above $\displaystyle{\frac51 = 5}$.
All integers are rational numbers as they can be written as a fraction with a denominator (bottom number of the fraction) of $1$.
Rational numbers can be written as decimals that either terminate (finish) or recur (repeat).
Example:
$$\frac14 = 0.25\quad\text{terminates,}$$ $$-\frac23 = -0.666666666666\ldots\text{ which we write as } -0.\dot{6},\text{ repeating or recurring.}$$
Click here to continue to explore the properties of fractions.
Mobile options: