58 Part 1: The World of Numbers
The Rational Numbers ............................................................................................................
The counting numbers, or natural numbers, are the numbers you use to count. When you find
that you need a symbol for nothing and add 0 to the counting numbers, you form the set called
the whole numbers. When you introduce negative numbers, you have the integers. Now you’re
turning your focus to numbers that represent parts of a whole, so what language do you use to
describe all of this?
Fractions are the names our number system gives to symbols representing parts of a whole. A frac-
tion is what we produce when we break a whole number into parts. Common fraction is the name
we give to a way of writing a fraction as one number divided by another. The number^12 is an
example of a common fraction, although usually it’s just called a fraction.DEFINITION
A fraction is a symbol that represents part of a whole. Decimal fractions are written in
the base ten system, with digits to the right of the decimal point. Common fractions
are written as a quotient of two integers.The set of numbers that includes all the integers plus all the fractions is called the rational
numbers. The name rational comes from ratio, another name for a fraction or a comparison of two
numbers by dividing. The rational numbers include any number you can write as a quotient of
two integers. So
1
2 is a rational number, but so is 2, because you can write it as2
1. Other examples
of rational numbers are
-4
13 ,163
71 , and 0.DEFINITION
Rational numbers are the set of all numbers that can be written as the quotient of
two integers.Proper Fractions and Improper Fractions
When we talk about fractions, we are usually talking about rational numbers written as a
quotient of two integers. When a fraction is written this way, the top number is called the
numerator, and the bottom number is called the denominator.DEFINITION
The denominator of a fraction is the number below the division bar. It tells how many
parts the whole was broken into, or what kind of fraction you have. The numerator is
the number above the bar, which tells you how many of that sort of part you actually
have. In the fraction^12 , 2 is the denominator and 1 is the numerator.