Page 44 - Mathematics of Business and Finance

24 Chapter 1 | Review of Basic Arithmetic

A complex fraction is a fraction in which one or more fractions are found in the numerator or
denominator.
2 5
1 d n 3 6
3
For example, , , and are complex fractions.
3 6 1
d n d n
4 8

Whole Number as a Fraction

Any whole number can be written as a fraction by dividing it by 1 (i.e. 1 is the denominator).
7
For example, 7 = .
1
Reciprocal of a Fraction

Two numbers whose product is equal to 1 are called reciprocals of each other.
4 7 4 7
For example, and are reciprocals of each other because × = 1
7 4 7 4
When the numerator and denominator of a fraction are interchanged, the resulting fraction is called
the reciprocal of the original fraction.
7 1
For example, the reciprocal of 7, which is equal to , is .
1 7

To determine the reciprocal of a mixed number, it must first be converted to an improper fraction.

2 17 2 5
For example, 3 = 5 , therefore the reciprocal of 3 is 17 .
5
5
Note: The reciprocal of a fraction is not an equivalent fraction.

Converting a Mixed Number into an Improper Fraction

Follow these steps to convert a mixed number into an improper fraction:

■ Multiply the whole number by the denominator of the fraction and add the result to the numerator
of the fraction.
■ The answer is the numerator of the improper fraction.
■ The denominator of the improper fraction is the same as the denominator of the original fraction
in the mixed number.
5
For example, 3 = 3(8) + 5 = 24 + 5 = 29
8
8
8
8
3 × 8 = 24 pieces 5 pieces
Thus, there is a total of 29 pieces,
each piece being one-eighth in size.