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 Post subject: Maths essentialsPosted: Sun Mar 22, 2009 4:45 am

Joined: Sun Mar 22, 2009 4:37 am
Posts: 1
Is there an easier way to explain the answer to questions 6, 7 and 8 on integers at page 4 of the Maths Essentials booklet (draft answer on pages 20 & 21 possibly requires further explanation)?

Would appreciate further explanation?

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 Post subject: Re: Maths essentialsPosted: Sun Mar 22, 2009 6:56 am

Joined: Thu Feb 12, 2009 6:32 pm
Posts: 497
Basically, you have the definition of a "remainder" which comes in to play.
Normally, when we do calculations, we don't deal with remainders, but, for
example, when you divide 10 by 3, you get 3 with a remainder of 1.
(Normally, you'd get 3.3333 or 3 and 1/3)
So, in question 6, for example:
We have q which is 2-digit number that is 4 higher than a multiple of 9.
We also know that q is a multiple of 7.
Multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117,
126, etc. (FYI: You'll notice a pattern in their units digits if you watch
closely: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0,
......)
Multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98,
105, ... (FYI, again, there's a pattern in the units digits: 7, 4, 1, 8,
5, 2, 9, 6, 3, 0, 7, 4, 1, 8, 5, 2, 9, 6, 3, 0, 7, 4.....)
Now, look at the multiples of 7 to see which one(s) are multiples of 7
that are also 4 more than multiples of 9... You'll find 49 first. This is

In #7
i/3 has a remainder of 1, so i/3 is 1 more than a multiple of 3.
i/4 has a remainder of 3, so i/4 is 3 more than a multiple of 3.
Then we learn that it's between 5 and 30.
A. 13 -- when we divide by 3, we get remainder of 1, which works. When we
divide by 4, we also get remainder of 1, so it's not our answer.
B. 15 -- when we divide by 3, we get no remainder, so it's not our answer
either.
C. 16 -- when we divide by 3, we get remainder of 1. When we divide by 4,
we get no remainder. Not our answer.
D. 19 -- when we divide by 3, we get remainder 1. When we divide by 4, we
get remainder 3. This must be our answer.
Check E just in case: 23 -- when we divide by 3, we get remainder 2. Not
You can, of course, go through these much more quickly, by scanning to
first see which ones are 1 higher than multiples of 3, and rule out the
others... I'm just giving you detailed steps to help you understand the
basics behind the process.

#8.
n/m results gives remainder 3.
m is multiple of 4, n<20.
Plug in a value for m. Since we know it's less than 20, and a multiple of
4, I'd just pick 4.
A. 10/4 -- remainder is 2 -- Can't be it.
B. 11/4 -- remainder is 3 -- must be our answer <-----**
C. 13/4 -- remainder is 1 -- can't be it.
D. 17/4 remainder is 1 -- can't be it

Hope this helps -

Valerie, Veritas Help

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