Maths is Fun ( MERGED with Cherry's)

Sarah_Radzi

Originally posted by amorist at Sun 22-Feb-2004 17:23:
Maths is so simple lah bulan. Let me show you some examples:

Kalau nak cari ganda dua number ending with 5, such as 65, 75, etc:

Take 65 x 65 lah:

Last 2 digits will always be 25. First 2  ...

i dah lama cari formal proof utk benda ni .. (actually terpikir nak cari tapi tak cari pun )

u ade tak ?

Originally posted by amorist at 22-2-2004 11:23 PM:
Maths is so simple lah bulan. Let me show you some examples:

Kalau nak cari ganda dua number ending with 5, such as 65, 75, etc:

Take 65 x 65 lah:

Last 2 digits will always be 25. First 2  ...

err...need time to digest this thing...but not tonite...interesting though...
...thanks for the contributions...

mbhcsf

Originally posted by amorist at 2004-2-22 23:23:
Maths is so simple lah bulan. Let me show you some examples:

Kalau nak cari ganda dua number ending with 5, such as 65, 75, etc:

Take 65 x 65 lah:

Last 2 digits will always be 25. First 2  ...

hmm..yer ker i tak perasan pulakk..eh ini mmg fun... tapi kan you boleh buat bende ni sbb you know the rules already ..tapi kan ..ini asah kita tengok ciri- ciri number tu lah kan..hmm ajaq kita fikir lahkan..ini tidak ( ini masalah saya  lah) i see it, i look at it BUT I NEVER OBSERVED...sbb tu tak nampak ciri -ciri ..hmm...dear Mr Sherlock where are you??:bg:

..now i realise it..if u know how..maths is easy..


.

amorist

Originally posted by Sarah_Radzi at 2004-2-22 11:51 PM:
i dah lama cari formal proof utk benda ni .. (actually terpikir nak cari tapi tak cari pun )

u ade tak ?

(10a + 5)(10a +5) = 100a*a +100a + 25
= 100a(a+1) +25

Notice that 100 means placing the answer on the 3rd digit.
So the ending is 25, the third digit is a(a+1)

We can extend this further:

(10a+b)(10a+10-b)= 100a*a + 100a -10ab + 10ab + 10b -b*b
=100a(a+1) + b(10-b)

Jadi, kalau kita ambil 63 x 67 (i.e. b=3), say, then we get
100*6*7 +3*7 = 4200 + 21 = 4221

so, mentally, we can do the following:

76 x 74 = 5624
87 x 83 = 7221
92 x 98 = 9016
and so on.

We can also use algebra to prove that kalau darab number ending with 5, beza 10, (such as 45 x 55) then the last 2 digits will always be 75. The first 2 digits is the smaller number darab (the larger number + 1)

Contoh: 45 x 55 :

First 2 digits is (4 x 6) = 24
Last 2 digits is 75
Answer: 2475

Contoh2: 65 x 75
First 2 digits is (6 x 8) = 48
Last 2 digits is 75
Answer: 4875

and so on.

Sarah_Radzi

ok amorist ... tq ...

ps: pas ni ade soalan math i tanya u terus lah

Hi..guys..another one from me..
..sape kata maths susah..yg penting kena tahu caranyeee..

You may have heard of Einstein's famous equation E = mc2 here it can be said that c is raised to the power 2, or c has order 2 or c is squared (they all mean the same thing!).

Here's an example to show how to use all the features of BODMAS:
Explain the answer that a calculator would give to the calculation 4 + 70/10 x (1 + 2)2 - 1 according to the BODMAS rules.

Brackets gives 4 + 70/10 x (3)2 - 1

Order gives 4 + 70/10 x 9 - 1

Division gives 4 + 7 x 9 - 1

Multiplication gives 4 + 63 - 1

Addition gives 67 - 1

Subtraction gives 66

peace

best.. nyer.. menyesal aku tak pandai math masa sekolah dulu.. sekarang dah 23 tahun.. semua dah past tense.. huhuhu..

That u take any number,
say..
13

and minus the sum of its digits
13 - 1 - 3 = 9

or take 567
and minus the sum of the digits
567 - 5 - 6 - 7 = 549 = 61*9

That is, whenever you take any number and minus the sum of its digits, you always end up with a number that is a multiple of 9? (including 0 for single digit number.)


cheers

mbhcsf

i nak tanya kalau in multiplication concept kan hasil darab tu akan bertambah besar  like 7X 7 = 49

kenapa in PECAHAN..bila kita darab say 1/6 X 1/6 = nombornya jadi lebih kecil..?

apa itu nombot bulat ?
apa itu integer

senarai topik ulangkaji...

peace

dah didarab dengan mende yang lagi kecil dari 1.. dah tentulah jawapannya akan lebih kecil daripada satu..

Penjelasan tak tau ler.. sebab tak panda Matematik masa kat sekolah dulu

mbhcsf

yer tak yer jugak ..tapi..

..aku lak nak kaji...kenapa?...mengapa?...bagaimana?...tak pandai...
...tapi aku suka ngan maths ni...to love maths u must know the formula...
...dah sah aku tak jawab soalan miss mbhcsf ni...
...super mod mana?...tolong jawab...aku pun nak tau jugak!!...

amorist

Originally posted by forgiv at 2004-5-11 10:32 PM:
That is, whenever you take any number and minus the sum of its digits, you always end up with a number that is a multiple of 9? (including 0 for single digit number.)

Let's take a 2-digit number as an example. The number is "ab" (kalau 13, then a=1 and b=3 )

This number, ab, is actually 10a + b
When you subtract the sum of the digits, you subtract a + b

so here's the maths:

10a + b - (a + b)
= 10a + b - a - b = 9a

That's why the answer is always a multiple of 9

amorist

Originally posted by mbhcsf at 2004-5-11 10:44 PM:
kenapa in PECAHAN..bila kita darab say 1/6 X 1/6 = nombornya jadi lebih kecil..?

Macam ni lah senang...

Katalah 1/2 x 1/6

"x" bermaksud "of". So, 1/2 x 1/6 is 1/2 of 1/6
You have 1/6 of something, then you take half of it. Of course, the result will be less than 1/6!!

Originally posted by mbhcsf at 2004-5-11 10:44 PM:
apa itu nombot bulat ?
apa itu integer

Samalah maksudnya tu - any of the natural numbers (+ve and -ve) or zero

mbhcsf

Originally posted by dockers_guy at 2004-5-12 17:57:
..aku lak nak kaji...kenapa?...mengapa?...bagaimana?...tak pandai...
...tapi aku suka ngan maths ni...to love maths u must know the formula...
...dah sah aku tak jawab soalan miss mbhcsf ni...
. ...

salam..dah terjawab ....

Originally posted by amorist at 13-5-2004 12:07 AM:

Let's take a 2-digit number as an example. The number is "ab" (kalau 13, then a=1 and b=3 )

This number, ab, is actually 10a + b
When you subtract the sum of the digits, you subtrac ...

:lol
You are good!


Here's another question.
Do you think there is such a positive integer (are positive integers),
such that when you move the last digit (unit position) to the front,
the new integer you generate will be twice the original number?
:stp:

[ Last edited by forgiv on 13-5-2004 at 11:20 AM ]

amorist

This is the sort of question that computers handle best. Anyway, there are no 2-digit numbers that meet this criteria.

At first sight, i also think this question is too hard to be done by hand.
However, after I gave more thought to this problem,
I find that it is not so tedious after all!

In fact the smallest integer is a 18-digit number(around there) which can be found easily, digit by digit.

In fact, we do not need any advance knowledge of mathematics. A simple multiplication will do.

amorist

You must have a lot of free time on hand!!