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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The symbols, notations, and properties of numbers that form the basis of algebra, as well as exponents and the rules of exponents, are introduced in this chapter. Each property of real numbers and the rules of exponents are expressed both symbolically and literally. Literal explanations are included because symbolic explanations alone may be difficult for a student to interpret.This module contains the proficiency for the chapter "Basic Properties of Real Numbers".

Proficiency exam

For the following problems, simplify each of the expressions.

( [link] ) 8 ( 6 3 ) 5 4 + 3 ( 8 ) ( 2 ) ÷ 4 3

40

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( [link] ) 1 8 + 4 0 + 3 3 ( 1 + 4 ) 2 2 ( 2 + 15 )

137 68

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( [link] ) 2 3 4 10 2 4 3 + 5 ( 2 2 + 3 2 ) 11 6

75

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( [link] ) Write the appropriate relation symbol ( > , < ) in place of the * .
5 ( 2 + 11 ) 2 ( 8 3 ) 2

>

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For the following problems, use algebraic notation.

( [link] ) ( x 1 ) times ( 3 x plus 2 ) .

( x 1 ) ( 3 x + 2 )

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( [link] ) A number divided by twelve is less than or equal to the same number plus four.

x 12 ( x + 4 )

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( [link] ) Locate the approximate position of 1.6 on the number line.

A real number line with arrow on each end, labeled from negative three to three in increments of one.

A number line with arrows on each end, labeled from negative five to five in increments of one. There is a closed circle at a point between negative two and negative one, labeled as negative one point six.

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( [link] ) Is 0 a positive number, a negative number, neither, or both?

Zero is neither positive nor negative.

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( [link] ) Draw a portion of the number line and place points at all even integers strictly between 14 and 20.

A number line with arrows on each end, labeled from fourteen to twenty in increments of one. There are closed circles at sixteen, and eighteen.

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( [link] ) Draw a portion of the number line and place points at all real numbers strictly greater than 1 but less than or equal to 4.

A number line with arrows on each end, labeled from negative four to five in increments of two. There is a closed circle at four, and an open circle at negative one. These circles are connected by a black line.

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( [link] ) What whole numbers can replace x so that the following statement is true? 4 x 5 .

0 , 1 , 2 , 3 , 4 , 5

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( [link] ) Is there a largest real number between and including 6 and 10? If so, what is it?

yes; 10

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( [link] ) Use the commutative property of multiplication to write m ( a + 3 ) in an equivalent form.

( a + 3 ) m

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( [link] ) Use the commutative properties to simplify 3 a 4 b 8 c d .

96 a b c d

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( [link] ) Use the commutative properties to simplify 4 ( x 9 ) 2 y ( x 9 ) 3 y .

24 y 2 ( x 9 ) 2

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( [link] ) Simplify 4 squared times x cubed times y to the fifth.

16 x 3 y 5

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( [link] ) Simplify ( 3 ) ( 3 ) ( 3 ) a a b b b b a b b a ( 3 ) a .

81 a 5 b 6

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For the following problems, use the rules of exponents to simplify each of the expressions.

( [link] , [link] ) ( 3 a b 2 ) 2 ( 2 a 3 b ) 3

72 a 11 b 7

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( [link] , [link] ) x 10 y 12 x 2 y 5

x 8 y 7

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( [link] , [link] ) 52 x 7 y 10 ( y x 4 ) 12 ( y + x ) 5 4 y 6 ( y x 4 ) 10 ( y + x )

13 x 7 y 4 ( y x 4 ) 2 ( y + x ) 4

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( [link] , [link] ) ( x n y 3 m z 2 p ) 4

x 4 n y 12 m z 8 p

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( 5 x + 4 ) 0 ( 3 x 2 1 ) 0

1

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x x y Δ x Δ y

The product of x to the power 'delta plus square minus triangle' and y to the power 'triangle minus delta'.

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( [link] , [link] ) What word is used to describe the letter or symbol that represents an unspecified member of a particular collection of two or more numbers that are clearly defined?

a variable

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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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