Fundamentals of Mathematics, 2008a

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Thus,
CHAPTER 4.
INTRODUCTION TO FRACTIONS AND MULTIPLICATION
AND DIVISION OF FRACTIONS
6
3 = 2
Improper fraction = whole number.
The following important fact is illustrated in the preceding examples.
Mixed Number = Natural Number + Proper Fraction
Mixed numbers are the sum of a natural number and a proper fraction. Mixed number = (natural number)
+ (proper fraction)
For example 1 1 3 can be expressed as 1 + 1 3 The fraction 5 7 8 can be expressed as 5 + 7 8 .
It is important to note that a number such as 5 + 7 8
does not indicate multiplication. To indicate multiplication,
we would need to use a multiplication symbol (such as ·)
note: 5 7 8 means 5 + 7 8
and not 5 · 7
8 , which means 5 times 7 8 or 5 multiplied by 7 8 .
Thus, mixed numbers may be represented by improper fractions, and improper fractions may be represented
by mixed numbers.
4.3.6 Converting Improper Fractions to Mixed Numbers
To understand how we might convert an improper fraction to a mixed number, let's consider the fraction,
4
3 .
4
3
= 1 3 + 1 3 + 1 } {{
3
}
1
= 1 + 1 3
= 1 1 3
Thus, 4 3 = 1 1 3 .
+ 1 3
We can illustrate a procedure for converting an improper fraction to a mixed number using this example.
However, the conversion is more easily accomplished by dividing the numerator by the denominator and
using the result to write the mixed number.
Converting an Improper Fraction to a Mixed Number
To convert an improper fraction to a mixed number, divide the numerator by the denominator.
1. The whole number part of the mixed number is the quotient.
2. The fractional part of the mixed number is the remainder written over the divisor (the denominator
of the improper fraction).
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