HSC Stuff > HSC Mathematics Advanced
Year 11 Revision
RuiAce:
--- Quote from: mfjw on July 16, 2016, 06:54:43 pm ---Hi ATAR Notes maths people!
I have a question regarding year 11 revision, below:
Solve:
12p-7q+1=0
8p+7q-11=0
How do I solve this question by using elimination? Also the topic I'm studying for school right now is Simultaneous Equations.
I never know whether the signs are meant to be positive or negative - I always get them mixed up.
Thanks! ~ M.
P.S. I went to your free lectures over the past week and they were extremely helpful!
--- End quote ---
mfjw:
--- Quote from: RuiAce on July 16, 2016, 07:01:31 pm ---
--- End quote ---
Thank you so much! Your explanation was very clear :)
mfjw:
Hi ATAR Notes!
My school teacher hasn't taught me how to express recurring decimals as fractions in simplest form, such as in the question below:
Express as a fraction in simplest form:
0.72 - the recurring dots are on the 7 and the 2, so 0.72727272727272....
RuiAce:
--- Quote from: mfjw on July 17, 2016, 01:47:29 pm ---Hi ATAR Notes!
My school teacher hasn't taught me how to express recurring decimals as fractions in simplest form, such as in the question below:
Express as a fraction in simplest form:
0.72 - the recurring dots are on the 7 and the 2, so 0.72727272727272....
--- End quote ---
jamonwindeyer:
--- Quote from: mfjw on July 17, 2016, 01:47:29 pm ---Hi ATAR Notes!
My school teacher hasn't taught me how to express recurring decimals as fractions in simplest form, such as in the question below:
Express as a fraction in simplest form:
0.72 - the recurring dots are on the 7 and the 2, so 0.72727272727272....
--- End quote ---
Hey!! No worries at all, it's a clever method that works the same every time.
So let us put x equal to the recurring decimal. Then, let us also consider 100x, you'll see why:
What we see here is that the recurring decimals actually line up with each other!! In general, we always consider x, and then x multiplied by 10 once for every recurring decimal. This has two, so we consider 100x. If it were 4, we'd consider 10,000x. That just guarantees the repeats will line up. Now, we subtract the first equation from the second, because everything after the decimal point cancels:
Basically, we've been clever and allowed subtraction to cancel out the recurrence!! From there we just simplify.
Edit: Rui gave a method as I finished typing this, but this sort of explains the methodology behind it ;)
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