Fundamentals of Mathematics, 2008a

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CHAPTER 4.
4.8 Summary of Key Concepts 8
4.8.1 Summary of Key Concepts
INTRODUCTION TO FRACTIONS AND MULTIPLICATION
AND DIVISION OF FRACTIONS
Fraction (Section 4.2)
The idea of breaking up a whole quantity into equal parts gives us the word fraction.
Fraction Bar, Denominator, Numerator (Section 4.2)
A fraction has three parts:
1. The fraction bar
2. The nonzero whole number below the fraction bar is the denominator.
3. The whole number above the fraction bar is the numerator.
Proper Fraction (Section 4.3)
Proper fractions are fractions in which the numerator is strictly less than the denominator.
4
5
is a proper fraction
Improper Fraction (Section 4.3)
Improper fractions are fractions in which the numerator is greater than or equal to the denominator.
Also, any nonzero number placed over 1 is an improper fraction.
5
4 , 5 5 , and 5 1
are improper fractions
Mixed Number (Section 4.3)
A mixed number is a number that is the sum of a whole number and a proper fraction.
1 1 5 is a mixed number ( 1 1 5 = 1 + )
1
5
Correspondence Between Improper Fractions and Mixed Numbers (Section 4.3)
Each improper fraction corresponds to a particular mixed number, and each mixed number corresponds to
a particular improper fraction.
Converting an Improper Fraction to a Mixed Number (Section 4.3)
A method, based on division, converts an improper fraction to an equivalent mixed number.
5
4 can be converted to 1 1 4
Converting a Mixed Number to an Improper Fraction (Section 4.3)
A method, based on multiplication, converts a mixed number to an equivalent improper fraction.
5 7 8 can be converted to 47 8
Equivalent Fractions (Section 4.4)
Fractions that represent the same quantity are equivalent fractions.
3
4 and 6 8
are equivalent fractions
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