factor out -1 from both -125 and -8 and cancel it out
Hi All,
I've been touching up on my algebra in preparation for university and have found a knowledge gap due to me never learning a concept.
Could someone please explain to me why -125/-8 became positive? Image below
Thanks in advance
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factor out -1 from both -125 and -8 and cancel it out
B Arts / B Science (Advanced Mathematics), UNSW
Firstly, When you had -125/-8 on LHS the minus and minus cancel out to become positive. Its basically -1/-1 multiplied by 125/8 and when you have two of the same numbers on the numerator and the denominator they yield to = 1.
Now you have 125/8=1/r^3
Multiply 8 to the other side
∴ 125=8/r^3
Multiply r^3 to both sides
∴125*r^3=8
Divide 125 to both sides
∴ r^3=8/125
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I failed so many tests in high school because of that. If i'm thinking in the right way below then my problem was believing that 1/x^y automatically converted into just x^y without any further simplification needed.
So fundamentally when you have r^-3 = -125/-8 you complete the following process
1. As r has a negative coefficient you first convert it into a fraction so that it can become positive
-1/r^-3 = -125/-8
2. As both sides of the equation are negative - the negative exponents cancel out and the equation stays balanced
1/r^3 = 125/8
3. You then need to separate r^3 from the 1 which it is dividing. You do this by multiplying across the 8.
8/r^3 = 125
4. You then need to isolate variable r. As the coefficients 8 and 125 are on different sides of the equation this can be done in 2 operations.
Operation One
8 = 125 * r^3
Operation Two
r^3 = 8/125
5. Now that variable r has been isolated we can find the value by taking the cube root of both sides of the equation.
r = 2/5
Is this the correct way of thinking or is there a concept behind it.
Site Moderator: Business Studies, Community & Family Studies, Information Processes & Technology, Information Technology,University of Technology Sydney, All General Discussion Boards
Bachelor of Commerce (Finance & Banking) @ University of Sydney
Operations @ Big 4 Bank
2016 Preliminary
Maths Extension • English Advanced • Biology • Legal Studies • Physics • PDHPE
2017 HSC
Maths Extension 2 • English Advanced • Biology • Physics • PDHPE
Atar aim: 97
Desired Course: Physiotherapy
Site Moderator: Business Studies, Community & Family Studies, Information Processes & Technology, Information Technology,University of Technology Sydney, All General Discussion Boards
Bachelor of Commerce (Finance & Banking) @ University of Sydney
Operations @ Big 4 Bank
Site Moderator: Business Studies, Community & Family Studies, Information Processes & Technology, Information Technology,University of Technology Sydney, All General Discussion Boards
Bachelor of Commerce (Finance & Banking) @ University of Sydney
Operations @ Big 4 Bank
2016 Preliminary
Maths Extension • English Advanced • Biology • Legal Studies • Physics • PDHPE
2017 HSC
Maths Extension 2 • English Advanced • Biology • Physics • PDHPE
Atar aim: 97
Desired Course: Physiotherapy
I never knew that..... I sat General Math for 2 years and was never told that even once.....
I finally understand basic algebra.
Thanks guys; very much appreciated
Site Moderator: Business Studies, Community & Family Studies, Information Processes & Technology, Information Technology,University of Technology Sydney, All General Discussion Boards
Bachelor of Commerce (Finance & Banking) @ University of Sydney
Operations @ Big 4 Bank
Firstly, you should know that anything divided by itself is 1 so that's one way i.e.
5/5 = 1 and -10/-10 =1
Another way is factorisation i.e.
check the attachement cos i cant latex
Capture.PNG
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CodeCogsEqn.gif
there's three approaches in the link. i'm sure that you undestand atleast one of them
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English Advanced, Mathematics Advanced, Chemistry, Biology, Economics, Business Studies
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If you know a bit of abstract algebra, you can read the top answer here about why (-x)(-y) = xy in any ring (though in that case you may have already thought about this and had it answered before): http://math.stackexchange.com/questi...rs-is-positive .
Let x= 1 dollar coin covered in aceitic acid
Let y= he-mann's shitty sarcasm
-x/-x = -1(x)/-1(x) = x/x = 1
-x/-y = -1(x)/-1(y) = x/y
HSC 2017
English Advanced, Mathematics Advanced, Chemistry, Biology, Economics, Business Studies
Atar goal: 90+
HSC goal: Band 6 all subjects boiii
I'll give you a basic example.
Let x = Matthew587's debt to He-Mann = 2017 apologetic letters typesetted in LaTeX and must include a picture of a golden coin covered in acetic acid.
Let y = 2017 letters sent to He-Mann.
Then, x/y = 2017/2017 = 1.
That is, your debt can be paid in one payment!
Here, we are working with positives. Try incorporating negatives and try to make sense out of it.
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