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**rida****Real Member**- Registered: 2006-09-25
- Posts: 839

These are a few things I would like to know, take your time in answering them, I'm in no hurry.

1. How do you use binary ?

2. What is hex decimal ?

3.(this is one I would like answered quickly) How do you do long multiplacation with 3 digit numbers ?

4. (answer very quickly) How do you do long division ?

5. (answer by Saturday, I'll need it then) How do you add fractions with different denominators ?

Please note I'm a 9 year old studying advanced mathematics at home.

Dreams don't come true, you gotta make them come true.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Binary is a different system of counting. Instead of the 10 digits we have normally (0123456789), binary only uses two: 0 and 1.

Binary numbers are basically built out of powers of 2.

To take a random example, 13 = 2³ + 2² + 2°. That makes its binary representation 1101.

You can convert binary numbers back into decimal form in the same way.

To take another random example, 10110 would become 2[sup]4[/sup] + 2[sup]2[/sup] + 2[sup]1[/sup] = 16+4+2 = 22.

I probably haven't explained that very well, so very well done if you understood it.

---

Hexadecimal is yet another system in counting. This time there are 16 digits (0123456789ABCDEF).

Hex numbers are built out of powers of 16, multiplied by numbers between 0 and 15.

As yet another random example, let's convert 139 into hexadecimal. There are eight 16's in 139, with a remainder of 11. But in Hex, 11 becomes the digit B. Therefore, 139(dec) = 8B(hex).

And you'd convert from hex to decimal by doing the opposite. Just remember that A=10, B=11, C=12, D=13, E=14, F=15.

And even more well done if you understood that, because I probably explained that even less well.

---

You do long multiplication with 3-digit numbers just by extending the way you do it with 2-digit ones. You split the bottom number up into its digits, multiply the top one by each of them, and then add up the results.

So your working would look like this template:

####

xabc

------

xc

------

xb0

------

xa00

------

+

---

Long division is not very different from normal division, it's just a bit more fiddly.

Basically, you just keep taking away multiples of the divisor (usually tens, hundreds, thousands, etc.) until you're left with a number smaller than it, which will be the remainder. Then you look at how many times you took away the divisor and that will be your answer.

eg.

----------------

29| 83027

--- - 58000 (x2000)

---------

25027

-23200 (x800)

---------

1827

- 1740 (x60)

---------

87

- 87 (x3)

--------- ---------

0 2863

So that means that 83027/29 = 2863.

---

Lastly, you add fractions with different denominators simply by converting them into fractions that have the same denominators.

For example, 1/5+1/9 can't be done directly. However, 1/5 is equivalent to 9/45 and 1/9 is equivalent to 5/45. So therefore 1/5+1/9 = 9/45+5/45 = 14/45.

You can add any two fractions using that method.

Why did the vector cross the road?

It wanted to be normal.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

There is an easier way to multiply which can be used when encountering different kinds of problems.

Now, here is my horrible explanation for doing this 'quick' way;

Now, OK, 2 digits. Easy, hopefully. Multiply the top-right digit by the bottom-right digit (in other words, multiply the units). If the answer is bigger than 9, then record the unit and record the tens value somewhere else (preferably somewhere you can remember). Then, multiply the top-right number by the bottom-left number (and if you had a tens unit that you carried, add that, too). Lastly, multiply the top-left number by the bottom-right number (once again, add any tens that were carried). Done.

You can manipulate this so that you don't have to do long multiplication for things like 1056*7123, as manipulating the method will help you understand how the 'pattern' works. When facing different-digit values, such as 123x4567, then it's best to do 1230x4567 and divide by 10 once you have finished.

Just tried to make it as clear as possible.

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**rida****Real Member**- Registered: 2006-09-25
- Posts: 839

Thanks that really helped but nobody's answered question 5 yet and seriously I will need to know how to do it by Saturday.

Dreams don't come true, you gotta make them come true.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

*Last edited by JaneFairfax (2007-03-20 04:11:51)*

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

rida wrote:

Thanks that really helped but nobody's answered question 5 yet and seriously I will need to know how to do it by Saturday.

Mathsyperson already explained, read the bottom of his post, under the '---'.

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**GK****Member**- Registered: 2007-03-20
- Posts: 6

the answer to number 5 is..

you need to make the 2 denominators the same. for eg.

2/3 + 2/4

u need to find the least common factor (LCF) of 3 and 4..which is 12. so you multiply the 1st one by 4 and the other one by 3. so the fraction will be 8/12 + 6/12 = 14

or if u're allowed to use a calculator, use a TI-83 or a scientific casio (S.V.P.A.M) and the (ab/c) sign will do it

good luck:D

*Last edited by GK (2007-03-20 05:02:28)*

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**lightning****Real Member**- Registered: 2007-02-26
- Posts: 2,060

i can do the long division one say you were doing 14 divided by 7 put a step like this:

_____

__l then put the numers like this :

_____

7l14 how many 7s can go into 1? none so put a tiny 1 beside the 4 this way <--- and put the 0 up above the 1 (not the tiny one) now how many 7s go into 14? 2 so put it like this:

02

7l14

*Last edited by lightning (2007-03-20 05:36:16)*

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