Saturday, June 07, 2008

Bonus: Percentages

Yanni in comment 23 gave an excellent tip for working out percentages, so I have taken the liberty of duplicating it here:

Find 7 % of 300. Sound Difficult?

Percents: First of all you need to understand the word “Percent.” The first part is PER , as in 10 tricks per listverse page. PER = FOR EACH. The second part of the word is CENT, as in 100. Like Century = 100 years. 100 CENTS in 1 dollar… etc. Ok… so PERCENT = For Each 100.

So, it follows that 7 PERCENT of 100, is 7. (7 for each hundred, of only 1 hundred).
8 % of 100 = 8. 35.73% of 100 = 35.73
But how is that useful??

Back to the 7% of 300 question. 7% of the first hundred is 7. 7% of 2nd hundred is also 7, and yep, 7% of the 3rd hundred is also 7. So 7+7+7 = 21.

If 8 % of 100 is 8, it follows that 8% of 50 is half of 8 , or 4.

Break down every number that’s asked into questions of 100, if the number is less then 100, then move the decimal point accordingly.

EXAMPLES:
8%200 = ? 8 + 8 = 16.
8%250 = ? 8 + 8 + 4 = 20.
8%25 = 2.0 (Moving the decimal back).
15%300 = 15+15+15 =45.
15%350 = 15+15+15+7.5 = 52.5

Also it’s usefull to know that you can always flip percents, like 3% of 100 is the same as 100% of 3.

35% of 8 is the same as 8% of 35.

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Squaring Numbers

Find the Equation of a Line Given That You Know Two Points it Passes Through

http://www.webmath.com/equline1.html

vedic maths - develop ur brain into a BUILD-IN calculator

Vedic Maths

Vedic Maths is based on sixteen sutras or principles. These principles are general in nature and can be applied in many ways. In practice many applications of the sutras may be learned and combined to solve actual problems. These tutorials will give examples of simple applications of the sutras, to give a feel for how the Vedic Maths system works.

For detailed tutorials and practice questions go to www.geocities.com/shivam1003/vedic.html

If you are having problems using the tutorials then you could always read the instructions.

Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4 Tutorial 5 Tutorial 6 Tutorial 7

Tutorial 1

Use the formula ALL FROM 9 AND THE LAST FROM 10 to perform instant subtractions.

For example 1000 - 357 = 643

We simply take each figure in 357 from 9 and the last figure from 10. So the answer is 1000 - 357 = 643

And thats all there is to it!

This always works for subtractions from numbers consisting of a 1 followed by noughts: 100; 1000; 10,000 etc.

Similarly 10,000 - 1049 = 8951

For 1000 - 83, in which we have more zeros than figures in the numbers being subtracted, we simply suppose 83 is 083.

So 1000 - 83 becomes 1000 - 083 = 917

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Tutorial 2

Using VERTICALLY AND CROSSWISE you do not need to the multiplication tables beyond 5 X 5.

Suppose you need 8 x 7

8 is 2 below 10 and 7 is 3 below 10. Think of it like this: The answer is 56. The diagram below shows how you get it. You subtract crosswise 8-3 or 7 - 2 to get 5, the first figure of the answer. And you multiply vertically: 2 x 3 to get 6, the last figure of the answer.

That's all you do:

See how far the numbers are below 10, subtract one number's deficiency from the other number, and multiply the deficiencies together.

7 x 6 = 42

Here there is a carry: the 1 in the 12 goes over to make 3 into 4.

Here's how to use VERTICALLY AND CROSSWISE for multiplying numbers close to 100.

Suppose you want to multiply 88 by 98.

Not easy,you might think. But with VERTICALLY AND CROSSWISE you can give the answer immediately, using the same method as above.

Both 88 and 98 are close to 100. 88 is 12 below 100 and 98 is 2 below 100.

You can imagine the sum set out like this:

As before the 86 comes from subtracting crosswise: 88 - 2 = 86 (or 98 - 12 = 86: you can subtract either way, you will always get the same answer). And the 24 in the answer is just 12 x 2: you multiply vertically. So 88 x 98 = 8624

This is so easy it is just mental arithmetic.

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Multiplying numbers just over 100.

	103 x 104 = 10712 The answer is in two parts: 107 and 12, 107 is just 103 + 4 (or 104 + 3), and 12 is just 3 x 4.
	Similarly 107 x 106 = 11342 107 + 6 = 113 and 7 x 6 = 42

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Tutorial 3

The easy way to add and subtract fractions.

Use VERTICALLY AND CROSSWISE to write the answer straight down!

Multiply crosswise and add to get the top of the answer: 2 x 5 = 10 and 1 x 3 = 3. Then 10 + 3 = 13. The bottom of the fraction is just 3 x 5 = 15. You multiply the bottom number together.

So:

Subtracting is just as easy: multiply crosswise as before, but the subtract:

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Tutorial 4

A quick way to square numbers that end in 5 using the formula BY ONE MORE THAN THE ONE BEFORE.

	75² = 5625 75² means 75 x 75. The answer is in two parts: 56 and 25. The last part is always 25. The first part is the first number, 7, multiplied by the number "one more", which is 8: so 7 x 8 = 56
	Similarly 85² = 7225 because 8 x 9 = 72.

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Method for multiplying numbers where the first figures are the same and the last figures add up to 10.

32 x 38 = 1216

Both numbers here start with 3 and the last figures (2 and 8) add up to 10.

So we just multiply 3 by 4 (the next number up) to get 12 for the first part of the answer.

And we multiply the last figures: 2 x 8 = 16 to get the last part of the answer.

Diagrammatically:

And 81 x 89 = 7209

We put 09 since we need two figures as in all the other examples.

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Tutorial 5

An elegant way of multiplying numbers using a simple pattern.

21 x 23 = 483

This is normally called long multiplication but actually the answer can be written straight down using the VERTICALLY AND CROSSWISE formula.

We first put, or imagine, 23 below 21:

There are 3 steps:

a) Multiply vertically on the left: 2 x 2 = 4. This gives the first figure of the answer. b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8 This gives the middle figure. c) Multiply vertically on the right: 1 x 3 = 3 This gives the last figure of the answer.

And thats all there is to it.

	Similarly 61 x 31 = 1891
	6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1

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Multiply any 2-figure numbers together by mere mental arithmetic!

If you want 21 stamps at 26 pence each you can easily find the total price in your head.

There were no carries in the method given above. However, there only involve one small extra step.

21 x 26 = 546

The method is the same as above except that we get a 2-figure number, 14, in the middle step, so the 1 is carried over to the left (4 becomes 5).

So 21 stamps cost £5.46.

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33 x 44 = 1452

There may be more than one carry in a sum:

Vertically on the left we get 12. Crosswise gives us 24, so we carry 2 to the left and mentally get 144.

Then vertically on the right we get 12 and the 1 here is carried over to the 144 to make 1452.


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Any two numbers, no matter how big, can be multiplied in one line by this method.

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Tutorial 6

Multiplying a number by 11.

To multiply any 2-figure number by 11 we just put the total of the two figures between the 2 figures.

26 x 11 = 286

Notice that the outer figures in 286 are the 26 being multiplied.

And the middle figure is just 2 and 6 added up.

So 72 x 11 = 792

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77 x 11 = 847

This involves a carry figure because 7 + 7 = 14 we get 77 x 11 = 7₁47 = 847.

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234 x 11 = 2574

We put the 2 and the 4 at the ends. We add the first pair 2 + 3 = 5. and we add the last pair: 3 + 4 = 7.

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Tutorial 7

Method for diving by 9.

	23 / 9 = 2 remainder 5 The first figure of 23 is 2, and this is the answer. The remainder is just 2 and 3 added up!
	43 / 9 = 4 remainder 7 The first figure 4 is the answer and 4 + 3 = 7 is the remainder - could it be easier?

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134 / 9 = 14 remainder 8

The answer consists of 1,4 and 8. 1 is just the first figure of 134. 4 is the total of the first two figures 1+ 3 = 4, and 8 is the total of all three figures 1+ 3 + 4 = 8.

842 / 9 = 8₁2 remainder 14 = 92 remainder 14

Actually a remainder of 9 or more is not usually permitted because we are trying to find how many 9's there are in 842.

Since the remainder, 14 has one more 9 with 5 left over the final answer will be 93 remainder 5

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Instructions for using the tutorials

Each tutorial has test sections comprising of several questions each. Next to each question is a box (field) into which you can enter the answer to the question. Select the first question in each test with the mouse to start a test. Enter the answer for the question using the numeric keys on the keyboard. To move to the answer field of the next question in the test, press the 'TAB' key. Moving to the next question, will cause the answer you entered to be checked, the following will be displayed depending on how you answered the question :-

Correct Wrong Answer has more than one part (such as fractions and those answers with remainders). Answering remaining parts of the question, will determine whether you answered the question correctly or not.

Discover the elegance of mathematics...

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Saturday, June 07, 2008

Bonus: Percentages

BEATCALC: Beat the Calculator!

Squaring Numbers

Multiplying Numbers

Dividing Numbers

Adding Numbers

Subtracting Numbers

Finding Percentages

Find the Equation of a Line Given That You Know Two Points it Passes Through

vedic maths - develop ur brain into a BUILD-IN calculator

Tutorial 1

Tutorial 2

Tutorial 3

Tutorial 4

Tutorial 5

Tutorial 6

Tutorial 7

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