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Guest:

Hi everyone,

I have a problem which is very annoying. I struggle with remembering how to solve addition, subtraction, multiplication and division fractions.
I know how to solve them but I forget which rules apply to which ones, does anyone have an easy way to remember the rules for them?

Every time I do fractions I will work out 5 or 6 questions in a row easy and then get stuck with the next 2 or 3 for ages before I figure out
how to do them again, it will save a lot of time and be very helpful if anyone's got like a SOHCAHTOA for trigonometry.



I like Serena has got some really good ideas there!

I teach this stuff at my home and my favourite teaching aid is 1 or more empty egg carton and some coloured lego blocks.
Egg cartons have 12 eggs in them.
If you want 1/2 a cartoon then you have to divide the box into 2 equal pieces and put lego blocks in 1 of those peices. That means there will be lego in 6 spaces because that is a half of the carton.
Now say you want 1/12 of a carton. That means you have to divide the carton into 12 peices, thats easy because it held 12 eggs to start with. So 1/12 of the carton will be just one eggs worth.
Now, if you want to add 1/2 + 1/12 You can do it with your carton.
Fill up half the carton with red blocks What is 1/2 the same as? the lego should be in 6 of the 12 holes. That is a 1/2 so 1/2 must be equal to 6/12
Now fill up 1/12 of the carton with blue blocks that means think of think of the carton as 12 bits and put a blue block in 1. That's just like 1 egg.
Now if you want 1/2 + 1/12 you can count the eggs 1/2 was 6 eggs that 6/12 add the other 1/12 and you get 7/12

Once you play with the egg cartons for a while you will understand much better and then it will be much easier to do it without the cartons.

Times and divide are actually easier than plus and minus but i think you should get yourself some egg cartons and have a play first with understanding fractions and with + and -

With an egg carton you can 'play' with 1/2 , 1/3, 1/4, 1/6, 1/12 you can also play with 2/3,3/3,2/4,3/4,4/4,2/6,3/6,etc, 2/12, 3/12 etc See if you can work out which ones are equal.
I would love to hear back from you and you can tell me if it helped.
BUT you have to actually DO IT first.

If you want to play with 10th or 5th or with decimals you can have a different carton and just tear the end two bits off so it fits 10 eggs.
Jan 30, 2014
 #3
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Postby Guest » Tue Jan 28, 2014 7:48 pm
Transmission time of 1 TB of data at 1.5 Mbps?
***

To properly calculate this, a clarification is necessary.
(The most glaring error is converting bits to bytes)

In the early years of computing, there was no significant error in using the same prefix for either quantity (2^10 = 1024 and 10^3 = 1000 they are about equal, to two significant figures). Thus, the SI prefixes were utilized indicate nearby binary multiples for these computer-related quantities.
-- This is actually referenced in the preamble to the amendments for IEEE. (You'll have to search for it in the original documents, or search for it on Wiki - a much easier read). As computer power increased and memory and disk size increased the error became significant.

This along with inconsistent use of the symbols to indicate quantities for and definitions of bits and bytes (for example: the unit symbol "Mb", has been widely used for both megabytes and megabits), the clarification of current symbols and the introduction of new symbols for measurement became an imperative.

To unambiguously represent these quantities and unit symbols, the IEEE 1541 sets new recommendations

(Note: IEEE and IEC are not the same entity).

The formality started in 1998 an when amendment was proposed to clarify data and data rates. The amendment was adopted in 1999 by the
International Electrotechnical Commission (IEC) published as Amendment 2 to "IEC 60027-2.

In 2002, a proposal (IEEE 1541-2002) was introduced to explicitly define symbols and value units . This was elevated to a full-use standard by the IEEE Standards Association in 2005, and reaffirmed on 27 March 2008. These standards, among others, included the following:

The upper case "B" is a byte

The lower case "b" is a "bit" and 8 (eight) bits are a "Byte"

The upper case "K" when referring to a binary value is 2^10 = 1024. (Always was and always will be).

"M" is a Million (10^6). (This is a decimal number its use is common in older documents where
Meg was often defined as 1000*1024, but sometimes as 1000000).

"Mi" is 2^20 = 1,048,576. (Mebi is Binary). The modern Meg.

"Gi" is 2^30 = 1,073,741,824 (Gibi is Binary). The modern Gig.

"Ti" 2^40 2^40 =1,099,511,627,776 ("Tibi" is Binary) .

Though these symbols and value units are explicitly defined and have been for 9 years or more, confusion still abounds --This is true even in high-end technical papers exposited by scientists and engineers on the cutting-edge of technology. (Many formal papers often preface the definitions to avoid ambiguity).

********
Now to the question.
Postby Guest » Tue Jan 28, 2014 7:48 pm
Transmission time of 1 TB of data at 1.5 Mbps?

Another preface is necessary here: In "dial-up modem days" (back when bear skins and stone knives were common) depending on the modem protocol (handshake) the "data" was usually 7 bits plus 1 bit for parity (even or odd), plus two bits for control (a start and stop bit). This gave a total through-put of ten bits per unit of data. (A unit of data is a byte). As error correction code was improved the parity bit was abandoned which doubled the unique data that could be transmitted.

The value given is 1.5Mbps this suggests an error correction of 32 bits (8 bytes) per block, where a block is multiple (n) of 1024 bytes. Depending on the protocol the code can self correct via an algorithm (if the errors are not too close together) else request to resend the data block. However the throughput averages 1.5Mbps (including data and error correction)

First convert the b(its) (Mbps - not Mibps) per second to B(ytes) per second. 1.5E6/8 = 187500 bytes per second.

In this case, simply divide 1E12 (TB not TeB) by 187500 B(ytes)/s. 1E12/1.87500E5 = 5,333,333 seconds to port this amount of data. This is 1481.5 hours or 61.7 days. If both are the Binary values it's 64.7 days

(Another note: Most "high-speed data providers give the download speed. The upload speed is about 1/4 this). A T1 type connection would be about 10 times as fast -- unless band width is heavy by other connected devices. Also the up-download speeds are about equal for T1's. There are other protocols which can increase through-put speed by a few percent.

This is my two-bits worth.
~~D~~
Jan 30, 2014
Jan 29, 2014

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