Questions

[jambafan38]

How can you do like 428.571 x 76... or 14.2857 x 348. These are approximatinos granted.

I know it has something with the divisor of the fraction being 7 but i cannot remember.

[SumitG]

You're right, some of these numbers are approximately fractions of 7 scaled by some power of 10; these types of problems do turn up rather often, so just try to look out for:

[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]

If you want to just straight out memorize these, you can just memorize the digits, and note how each fraction is simply a sort of "shift" in them. You can always remember 1/7 and then think about what the appropriate shift might be to get the other fractions. These problems are easily solvable because you can factor out these fractions and powers of 10 from an appropriate number, and then multiply the fractional part by another approximate multiple of that number, so that multiplication overall is made easier. For example, in your problems

1) 428.571 x 76 is approximately (3/7) x 1000 x 76 is approximately (3/7) x 77 x 1000 = 33000
2) 14.2857 x 348 is approximately (1/7) x 100 x 348 is approximately (1/7) x 350 x 100 = 5000

Make sure to remember that these types of problems don't occur with fractions just of denominator 7, there could be other denominators, such as 8, or 9...hope this helps.

[jambafan38]

Thank you!
man i am so rusty! how do you do 232*18?
also, how do i do 245 base9 divided by 7 base 9

[SumitG]

You're welcome!
Hmm...well, with a little practice, you'll be fine again!
For something like 232 x 18, I'd just treat 18 as a single digit. So the same way you'd multiply something like 46 x 9 you'd multiply 232 x 18, except there are more digits to multiply by in 232 than in 46.

245 base 9 divided by 7 base 9 is done the same way as division in base 10 pretty much...
Just like you'd see how many times 7 went into 24 if you were dividing in base 10, you'd see how many times 7 went into 24 in base 9...3. Then you'd take the remainder (1), and pull down the 5, and see how many times 7 went into 15 in base 9...2. So now, your quotient is 32 base 9, which is also 29 base 10.

Another way you could do it is simply to convert everything to base 10 and then convert back to base 9 at the end...I sometimes find that easier.

[jambafan38]

Thanks!

Do you know what the specific tricks are for this year that we need to know?

[SumitG]

I really am not sure what tricks we are required to know this year... I'd say just study your basics, like square memorization, FOIL, stuff like that... If you have a good knowledge of certain theorems (like sum of squares and stuff), then you should be really well prepared for the exam.

If you don't have a trick for some problem, just do a little algebra and you might find some really interesting stuff.

[jambafan38]

7/13 + 6/7

How many groups of 4 can be made using 6 people?

4 sec^2 43 - 4 tan ^2 43

How many positive 3digit integers end with 8

3 4/7 +7/4

25^3-24^3

[jambafan38]

bump

[sqrtneg1]

1) [unparseable or potentially dangerous latex formula]

2) This is merely a combination, so the answer is [unparseable or potentially dangerous latex formula].

3) For an angle [unparseable or potentially dangerous latex formula], we have the trig identity [unparseable or potentially dangerous latex formula]. Dividing through by [unparseable or potentially dangerous latex formula], we can obtain that [unparseable or potentially dangerous latex formula]. Considering the specific case [unparseable or potentially dangerous latex formula], the answer is [unparseable or potentially dangerous latex formula].

4)For the three digit numbers which satisfy the required condition, the ones place has [unparseable or potentially dangerous latex formula] choice ([unparseable or potentially dangerous latex formula]). The tens place then has [unparseable or potentially dangerous latex formula] choices (any of the digits), and the hundreds place has [unparseable or potentially dangerous latex formula] choices (any of the digits except [unparseable or potentially dangerous latex formula]). Thus, the number of possibilities is [unparseable or potentially dangerous latex formula].

5)[unparseable or potentially dangerous latex formula].

6)Note that [unparseable or potentially dangerous latex formula]. For the specific case [unparseable or potentially dangerous latex formula], the answer is [unparseable or potentially dangerous latex formula].

[jambafan38]

Thanks for the help!

I have a couple more questions

12^4 / 6^3 x 3^2

how do you add the 1 + 3 + 8 + 21... 144 with the missing fibonacci numbers

and any quick way to find the first nine terms of a sequence of fibonaccis with 4,6,10,16 without multipling the 7th times 11 and subtracing the 10th digit

1/56 + 1/72 + 1/90 +1/110

[stupidityismygam]

[jambafan38]

thanks thanks! i just seem to be having a lot of trouble with the fractions

7/6 + 7/12 + 7/20

1/6 + 1/10 + 1/15 +1/21

1/15 +1/35 +1/63

,333 base 5 to a base 10 fraction

If A is 20% greater than B and B is 15% greater than C, then a is what percent greater htan C

[bradp]

7/6 + 7/12+7/20

Change 'em to a LCD of 60

1/6+1/10+1/15+1/21

Triangular numbers = 1,3,6,10,15,21...
Sum of X consecutive inverse triangular numbers starting with the nth triangular number (n=3 and X = 4 in this case)

write them out as 2/n(n+1)+2/(n+1)(n+2)+....
common denominator -----> simplify and you should get a nice expression

You can do that for 2,3,4, etc. terms and see that there's a general formula that has n and X in it.



I think 0.xxxx repeating in base n is..... x/(n-1) ?

[AuSmith]

What we want is a general formula for the expression

[unparseable or potentially dangerous latex formula]

Start with just a couple terms:

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]


And so on. You can continue the trend and get the formula, "number of terms divided by the product of the first and last numbers"


[unparseable or potentially dangerous latex formula]