Beginning Algebra, 11th Edition

(Marvins-Underground-K-12) #1

The fraction bar represents division


A fraction is classified as being either a proper fractionor an improper fraction.


Proper fractions

Improper fractions

3


2


,


5


5


,


11


7


,


28


4


1


5


,


2


7


,


9


10


,


23


25


A


a

babB.


2 CHAPTER 1 The Real Number System


OBJECTIVES In everyday life, the numbers seen most often are the natural numbers,


the whole numbers,


and fractions,such as


and


The parts of a fraction are named as shown.


Fraction bar


4


7


15


7


.


2


3


,


1


2


,


0, 1, 2, 3, 4,Á,


1, 2, 3, 4,Á,


Fractions


1.1


1 Learn the definition
of factor.
2 Write fractions in
lowest terms.
3 Multiply and divide
fractions.
4 Add and subtract
fractions.
5 Solve applied
problems that
involve fractions.
6 Interpret data in a
circle graph.

Numerator
Denominator

Numerator is less thandenominator.
Value is less than 1.

A mixed numberis a single number that represents the sum of a natural number and


a proper fraction.


Mixed number

OBJECTIVE 1 Learn the definition of factor.In the statement


the numbers 3 and 6 are called factorsof 18. Other factors of 18 include 1, 2, 9, and 18.


The result of the multiplication, 18, is called the product.We can represent the prod-


uct of two numbers, such as 3 and 6, in several ways.


Products

We factora number by writing it as the product of two or more numbers. Fac-


toring is the reverse of multiplying two numbers to get the product.


Multiplication Factoring

Factors Product Product Factors

NOTE In algebra, a raised dot is often used instead of the symbol to indicate


multiplication because may be confused with the letter x.


A natural number greater than 1 is primeif it has only itself and 1 as factors.


“Factors” are understood here to mean natural number factors.


2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 First dozen prime numbers


*


*


3 # 6 = 18 18 = 3 # 6


3 *6, 3 #6, 132162 , 132 6, 3162


3 * 6 =18,


5


3


4


= 5 +


3


4


Numerator is greater than or equal
todenominator. Value is greater
than or equal to 1.

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