This Blog exists for the collective benefit of all algebra students. While the posts are specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.
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Friday, September 30, 2011
Unit 1 Review - ARE U READY FOR THE TEST
When you ask a question, please be sure to:
a) identify the page number
b) identify problem number
c) describe any attempts/steps you have tried in an attempt to solve the problem
general question: at what point can i take off the parentheses on a substitution and if there if a problem with parentheses within parentheses should i add brackets instead? Secondly on chapter review on page 70 excercised i am confused as to whether 0.57 repeated would be considered a rational or irrational number? And lastly what does mean when it asks for the subset of a number because in the glossary it says its a set of elements in the given set so wouldnt any two alike numbers be the subsets of each other? Im confused on what they want you to answer in questions like those.. Feel free to answer any question!!
You should leave the parentheses (protective coating...never hurts)on until the end of the problem unless you still need them and you can put brackets just to make the problem a little clearer, but it isn't necessary if they are already there. 0.57 is considered a rational number. If it was 0.5757575894323 (random, made up #) it would be irrational because they do not terminate or repeat. A subset of #'s is the "group" the number belongs to. For example 16 would belong to the subsets natural #'s, whole #'s, integers, and rational #'s because 16 has all of the qualities of those subsets. Hope this helps. -Maggie
Maggie is basically correct... it never hurts to leave the parens for an extra step or so. The bottom line is that you SHOULD leave them until they are no longer providing value... let's look at an example:
Do you see how we kept the parens around while they provided value, and dropped them when no longer needed. Notice that we kept the parens around in Step 3&4 simply for the "cosmetic" purpose of "hugging" the negative... this is mathematical convention (i.e. good mathematical notation).
We will investigate more examples later in the year... but the SHORT ANSWER for now is that repeating decimals (no matter how many digits are involved) are rational numbers.
You SHOULD know that the primary irrational numbers are Pi and any square root of a non-perfect square. If you are a little confused by this, you are in GOOD COMPANY. The concept of irrational numbers baffled advanced mathematicians for centuries before they slowly and grudgingly agreed on the specifics.
As far as a question like: What subsets does -3/2 belong to... the "subsets" are
1) Counting (aka Natural) numbers 2) Whole numbers (zero is born!) 3) Integers (do you have to be so negative?) 4) Rational numbers (decimals, fractions and percents are numbers, too) 5) Irrational numbers (Got Pi?)
-3/2 belongs to Rational -4/2 belongs to Rational, Integers (cuz it can be expressed as -2) 4/2 belongs to Rational Integers, Whole, and Counting (cuz it can be expressed as 2)
For awhile, it may be helpful to memorize some of this stuff, but it will actually start to make sense as you progress as an algebratician!
Anyone else: I'd also like to know if you peeked in got some help, too. It takes a village to teach an algebra class... communication will be the KEY to our SUCCESS!
In #3, the negative is acting as a multiplier, so cousin Pemdas, which do you act on first? A multiplier or an exponent? Does this answer your question?
general question: at what point can i take off the parentheses on a substitution and if there if a problem with parentheses within parentheses should i add brackets instead? Secondly on chapter review on page 70 excercised i am confused as to whether 0.57 repeated would be considered a rational or irrational number? And lastly what does mean when it asks for the subset of a number because in the glossary it says its a set of elements in the given set so wouldnt any two alike numbers be the subsets of each other? Im confused on what they want you to answer in questions like those.. Feel free to answer any question!!
ReplyDeletehopefully, someone else can answer your questions today (that's a challenge) otherwise I'll answer tonite...
ReplyDeleteYou should leave the parentheses (protective coating...never hurts)on until the end of the problem unless you still need them and you can put brackets just to make the problem a little clearer, but it isn't necessary if they are already there.
ReplyDelete0.57 is considered a rational number. If it was 0.5757575894323 (random, made up #) it would be irrational because they do not terminate or repeat.
A subset of #'s is the "group" the number belongs to. For example 16 would belong to the subsets natural #'s, whole #'s, integers, and rational #'s because 16 has all of the qualities of those subsets.
Hope this helps.
-Maggie
Maggie is basically correct... it never hurts to leave the parens for an extra step or so. The bottom line is that you SHOULD leave them until they are no longer providing value... let's look at an example:
ReplyDeleteEvaluate 6x - x^2 - 2x^3 when x=-5
Step1: 6(-5) - (-5)^2 - 2(-5)^3
Step2: -30 - (25) - 2(-125)
Step3: -30 - 25 - (-150)
Step4: -55 - (-150)
Step5: -55 + 150
Step6: 95
Do you see how we kept the parens around while they provided value, and dropped them when no longer needed. Notice that we kept the parens around in Step 3&4 simply for the "cosmetic" purpose of "hugging" the negative... this is mathematical convention (i.e. good mathematical notation).
We will investigate more examples later in the year... but the SHORT ANSWER for now is that repeating decimals (no matter how many digits are involved) are rational numbers.
ReplyDeleteYou SHOULD know that the primary irrational numbers are Pi and any square root of a non-perfect square. If you are a little confused by this, you are in GOOD COMPANY. The concept of irrational numbers baffled advanced mathematicians for centuries before they slowly and grudgingly agreed on the specifics.
Great question!
As far as a question like: What subsets does -3/2 belong to... the "subsets" are
ReplyDelete1) Counting (aka Natural) numbers
2) Whole numbers (zero is born!)
3) Integers (do you have to be so negative?)
4) Rational numbers (decimals, fractions and percents are numbers, too)
5) Irrational numbers (Got Pi?)
-3/2 belongs to Rational
-4/2 belongs to Rational, Integers (cuz it can be expressed as -2)
4/2 belongs to Rational Integers, Whole, and Counting (cuz it can be expressed as 2)
For awhile, it may be helpful to memorize some of this stuff, but it will actually start to make sense as you progress as an algebratician!
Enjoy the ride!
Ca-peesh?
Candace, lmk if this helped.
ReplyDeleteAnyone else: I'd also like to know if you peeked in got some help, too. It takes a village to teach an algebra class... communication will be the KEY to our SUCCESS!
# 3 on the chapter test, when u have -(8) sqaured do u distribute the negative first or use the exponent.
ReplyDelete# 24 on the chapter test is worded funny and has me confuzzled, can u explain it?
ReplyDeleteIn #3, the negative is acting as a multiplier, so cousin Pemdas, which do you act on first? A multiplier or an exponent? Does this answer your question?
ReplyDeleteThe final answer is 8, because -64/-8 = 8
Yup, #24 is confuzzling for sure, so let me assure you there will be nothing that confuzzling on the test.
ReplyDeleteThey are asking you: when is |a-b| = |a| - |b|?
It's an interesting problem to examine, but not when you should be studying for a test.
The answer is: When a>b>0 or a<b<0 or a=b
Don't sweat it... can you do all the other stuff? That's the key!
yep thanks mr. c it helped i got it!!!!!!!!!
ReplyDelete