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Basic Operations with Real Numbers: Proficiency Exam

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

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Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples. This module provides a proficiency exam for the chapter "Basic Operations with Real Numbers".

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

Proficiency Exam

Simplify the expressions for the following problems.

Exercise 1

((Reference)) −{−[(−6)]} −{−[(−6)]}

Solution

−6 −6

Exercise 2

((Reference)) −|−15|−|−15|

Solution

−15 −15

Exercise 3

((Reference)) − [ | −12 |−10 ] 2 − [ | −12 |−10 ] 2

Solution

−4 −4

Exercise 4

((Reference)) −5(−6)+4(−8)−| −5 | −5(−6)+4(−8)−| −5 |

Solution

−7 −7

Exercise 5

((Reference)) 3(−8)−(−2)(−4−5) (−2)(−3) 3(−8)−(−2)(−4−5) (−2)(−3)

Solution

−7 −7

Exercise 6

((Reference)) −| 7 |− (2) 2 + (−2) 2 −| 7 |− (2) 2 + (−2) 2

Solution

−7 −7

Exercise 7

((Reference)) −6(2)(−2) −(−5−3) −6(2)(−2) −(−5−3)

Solution

3

Exercise 8

((Reference)) −3{ [ ( −2−3 ) ][ −2 ] } −3( 4−2 ) −3{ [ ( −2−3 ) ][ −2 ] } −3( 4−2 )

Solution

5

Exercise 9

((Reference)) Ifz=x−usz=x−us, find zz if x=14x=14, u=20u=20, and s=2s=2.

Solution

−3 −3

When simplifying the terms for the following problems, write each so that only positive exponents appear.

Exercise 10

((Reference)) 1 − ( −5 ) −3 1 − ( −5 ) −3

Solution

125

Exercise 11

((Reference)) 5 x 3 y −2 z −4 5 x 3 y −2 z −4

Solution

5 x 3 z 4 y 2 5 x 3 z 4 y 2

Exercise 12

((Reference)) 2 −2 m 6 (n−4) −3 2 −2 m 6 (n−4) −3

Solution

m 6 4 ( n−4 ) 3 m 6 4 ( n−4 ) 3

Exercise 13

((Reference)) 4 a −6 (2 a −5 ) 4 a −6 (2 a −5 )

Solution

8 a 11 8 a 11

Exercise 14

((Reference)) 6 −1 x 3 y −5 x −3 y −5 6 −1 x 3 y −5 x −3 y −5

Solution

1 6 1 6

Exercise 15

((Reference)) (k−6) 2 (k−6) −4 (k−6) 3 (k−6) 2 (k−6) −4 (k−6) 3

Solution

1 ( k−6 ) 5 1 ( k−6 ) 5

Exercise 16

((Reference))(y+1)3(y−3)4(y+1)5(y−3)−8(y+1)3(y−3)4(y+1)5(y−3)−8

Solution

( y−3 ) 12 ( y+1 ) 2 ( y−3 ) 12 ( y+1 ) 2

Exercise 17

((Reference)) ( 3 −6 )( 3 2 )( 3 −10 ) ( 3 −5 )( 3 −9 ) ( 3 −6 )( 3 2 )( 3 −10 ) ( 3 −5 )( 3 −9 )

Solution

1

Exercise 18

((Reference)) (a4)−3(a4)−3

Solution

1 a 12 1 a 12

Exercise 19

((Reference)) [ r 6 s −2 m −5 n 4 ] −4 [ r 6 s −2 m −5 n 4 ] −4

Solution

n 16 s 8 m 20 r 24 n 16 s 8 m 20 r 24

Exercise 20

((Reference)) ( c 0 ) −2 , c≠0 ( c 0 ) −2 , c≠0

Solution

1

Exercise 21

((Reference)) Write 0.000271 0.000271 using scientific notation.

Solution

2.71× 10 −4 2.71× 10 −4

Exercise 22

((Reference)) Write 8.90× 10 5 8.90× 10 5 in standard form.

Solution

890,000 890,000

Exercise 23

((Reference)) Find the value of (3× 10 5 )(2× 10 −2 ) (3× 10 5 )(2× 10 −2 ) .

Solution

6000 6000

Exercise 24

((Reference)) Find the value of (4× 10 −16 ) 2 (4× 10 −16 ) 2 .

Solution

1.6× 10 −31 1.6× 10 −31

Exercise 25

((Reference)) If k k is a negative integer, is −k −k a positive or negative integer?

Solution

a positive integer

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