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Chapter 1 | Review of Basic Arithmetic 23
1.3 Fractions
Definition of Fractions and Types of Fractions
A fraction is a rational number written as one integer divided by another non-zero integer. It is usually
If the denominator of a written as a pair of numbers, with the top number being called the numerator and the bottom number
fraction is zero, then the the denominator. A fraction bar (horizontal bar indicating division) separates the numerator and the
fraction is undefined.
denominator. The use of fractions is another method of representing numbers.
3 numerator
fraction bar
8 denominator
3
For example, f p is a fraction. It is read as "three divided by eight", "three-eighths", or "three
8
over eight", which all indicate that 3 is the numerator and 8 the denominator.
A proper fraction is a fraction in which the absolute value of the numerator is less than the absolute
value of the denominator; i.e. the absolute value of the entire fraction is less than 1.
For example,
The absolute value of
a number refers to the 3
positive sign of ■ f p is a proper fraction.
that number. 8
For example, the
2
absolute value of –2 is 2. ■ –2 in absolute value is f p, which is a proper fraction. Therefore, –2 is a proper fraction.
i.e. |–2| = 2. 5 5 5
An improper fraction is a fraction in which the absolute value of the numerator is greater than the
absolute value of the denominator; i.e. the absolute value of the entire fraction is more than 1.
7 –3
For example, f p and f p are improper fractions.
4 2
(seven quarters) (negative three halves)
If the numerator and denominator are equal, then the fraction is equal to 1.
7
For example, = 1.
7
If the absolute value of the numerator and denominator are equal but with opposite signs, then the
fraction is equal to –1.
9 –8
For example, = –1 or = –1.
–9 8
To reduce a fraction, divide the numerator and denominator by a number by which they are both
divisible.
A mixed number consists of both a whole number and a proper fraction, written side-by-side, which
implies that the whole number and proper fraction are added.
5
For example, 3 implies 3 + 5 Mixed Number
8
8
5
three five-eighths 3 8 Fraction
Whole Number