Worksheet Examples 1 - Prealgebra Review

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Different Number Sets

A mathematician, like a painter or poet, is a maker of patterns. G.H. Hardy (from A Mathmematician’s Appology, London 1941)

Mathematicians are, in fact, all about finding patterns and sorting things into groups of similar things. When you are reading a math text you need to know what set of numbers they are talking about.

Do some research, on line or in the text, about what the different numbers sets listed below are, then on your own paper do the following: (Please do as much of this as you can before the first day of class. You will need to turn this in before you leave class on June 5.)

1.      Give an example of the elements of each set of numbers.

2.      If there is a capital letter used as a shorthand name for the set, identify it

3.      If you can, try to figure out where the name and/or shorthand letter come from. If you are not able to find a reason, come up with your own, just make sure to tell me that it is your thoughts and not fact. Please do not copy and paste, paraphrase what you read and cite your sources.

·         Natural Numbers

·         Whole Numbers

·         Negative Numbers
·         Integers
·         Rational Numbers
·         Irrational Numbers
·         Real Numbers
·         Imaginary Numbers
·         Complex Numbers
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R.1

Factoring, GCF, LCM

Name:                                                             

Please do as much of this as you can before the first day of class. You will need to turn this in before you leave class on June 5. Use pencil only. Work in pen will be graded as incorrect.

Many students find that doing the online homework helps before doing problems from the textbook. You can use any sources to answer these questions as long as you cite your sources. Use your own words as much as possible. 

What is a prime number?

What is a composite number?

Is 1 a prime number or a composite number? Explain.

Why do you think the book limits the definitions of the above to natural numbers?

Do the following problems from the textbook on your own paper and attach to the back.
R.1 (pp 7 & 8): 6, 10, 14, 18

Did you approach the above problems the same way or differently? Were there any tricks that you used? Explain.

Define each of the following.

Greatest Common Factor (GCF)

Lowest Common Multiple (LCM)

When do you use each of them?

Do you have a trick you use to keep the two of them straight?

On your own paper find the GCF and LCM of each of the following:

        i.            12, 24

      ii.            30, 135
    iii.            3, 5, 22

Did you use any tricks or shortcuts for any of the above? Explain.

Do the following problems from the textbook on your own paper and attach to the back. If you find that you are using any tricks or shortcuts please note them in the body of the problem.
R.1 (pp 7 & 8): 20, 28, 32, 36, 44, 52

On your own paper write out your own reasoning and solve #56. That is, are you going to use GCF or LCM and why. Please answer the word problem with a complete sentence.