Friday, August 10, 2012

10 simple mathematical techniques

In many people, mathematics can terrify. This list may improve the general knowledge of mathematical techniques and will accelerate the implementation of mathematical calculations in his mind.



A. Multiply by 11

We all know that when multiplied by 10 is added to the number 0, and did you know that there is a simple way to multiply two-digit number by 11? Here it is:

Take the original number and imagine a space between two characters (in this example, we use the number 52):
5_2

Now add the two numbers and write them down in the middle:
5_ (5 +2) _2

So your answer is 572.

If you add up the numbers in parentheses obtained by two-digit number, just remember the second number and add one to the first number:
9_ (9 +9) _9
(9 +1) _8_9
10_8_9
1089 - It always works.

Two. Quickly squaring

This technique will help to quickly build a square two-digit number that ends in 5. Multiply the first digit of itself over the one, and append at the end of 25. That's it!
252 = (2x (2 +1)) & 25
2 x 3 = 6
625

Three. Multiply by 5

Most people are very easy to remember the multiplication table for 5, but when dealing with large numbers, it becomes harder to do, or not? This technique is incredibly simple.

Take any number, divide by 2 (in other words, divide in half). If the result is a whole number, assign 0 to the end. If not, do not pay attention to the comma at the end, add 5. It always works:
2682 x 5 = (2682/2) & 5 or 0
2682/2 = 1341 (whole number so add 0)
13,410

Let's try another example:
5887 x 5
2943.5 (a fractional number (skip the comma, add 5)
29,435

4. Multiply by 9

It's easy. To multiply any number from 1 to 9 of 9, look at his hands. Fold the thumb, which multiplies the number of matches (eg 9h3 - bend the third finger), count fingers to the thumb bent (in the case 9h3 - a 2), then count after the bent finger (in this case - 7). The answer - 27.

Five. Multiply by 4

This is a very simple method, although evident only for some. The trick is that you just need to multiply by 2 and then multiply by 2 again:
58 x 4 = (58 x 2) + (58 x 2) = (116) + (116) = 232

6. Counting the tip

If you need to leave 15% tip, there is an easy way to do it. Calculate 10% (Divide the number 10), and then add the resulting number to its half and get an answer:
15% = $ 25 (10% from 25) + ((10% of 25) / 2)
$ 2.50 + $ 1.25 = $ 3.75

7. The complex multiplication

If you need to multiply large numbers, and one of them - even, you can simply rearrange them to get the answer:
32 x 125 is the same as:
16 x 250 is the same as:
8 x 500 is the same as:
4 x 1,000 = 4,000

Eight. Divide by 5

In fact, large numbers to divide by 5 is very simple. All that is needed - just multiply by 2 and move the comma: 195/5
Step 1: 195 * 2 = 390
Step 2: Transferring the comma: 39.0 or just 39.

2978/5
Step 1: 2978 * 2 = 5956
Step 2: 595.6

9. Subtraction from 1000

To perform a subtraction in 1000, you can use this simple rule: Subtract from 9 all the numbers except the last. And subtract the last digit of 10: 1000
-648
Step 1: subtract 6 from 9 = 3
Step 2: subtract 4 from 9 = 5
Step 3: subtract 8 from 10 = 2
A: 352

10. Systematic rules of multiplication

Multiply by 5: Multiply by 10 and divide by 2.
Multiply by 6: Sometimes it is easier to multiply by 3, then 2.
Multiply by 9: Multiply by 10 and subtract the original number.
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then - 2.
Multiply by 15: Multiply by 10 and add 5 times the original number, as in the previous example.
Multiply by 16: If you want to multiply 4 times 2. Or multiply by 8, and then by 2.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 18: Multiply by 20 and subtract twice the original number.
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number.
Multiply by 45: Multiply by 50 and subtract 5 times the original number.
Multiply by 90: Multiply by 9, and assign 0.
Multiply by 98: Multiply by 100 and subtract twice the original number.
Multiply by 99: Multiply by 100 and subtract the original number.


Bonus: Interest

How to calculate interest.

Compute 7% of the 300. It seems complicated?

Interest: First you need to understand the meaning of the word "rate» (Percent). The first part of the word - PRO (PER), a 10-point to the page listverse. PER = FOR EVERYONE. The second part - CENTS (CENT), a 100. For example, Century = 100 years. 100 cents in a dollar and so on. So PERCENT FOR EACH = HUNDREDS.

So, it turns out that 7% of the 100 would be 7. (7 for each hundred, one hundred only).
8% of 100 = 8.
35.73% of 100 = 35.73

But how can this be useful?
We return to the puzzles 7% of the 300. 7% of
first hundred is 7. 7% from the second hundred - same as 7, and 7% of the Third Squadron - the same 7. Thus, 7 + 7 + 7 = 21. If 8% of 100 = 8, then 8% of 50 = 4 (half of 8).

Crush each number, if you want to calculate the percentage of 100, if the number is less than 100, just move the comma to the left.

EXAMPLES:
8% of 200 =? 8 + 8 = 16.
8% of 250 =? 8 + 8 + 4 = 20,
8% 25 = 2.0 (left Move the comma).
15% of 300 = 15 +15 +15 = 45,
15% of 350 = 15 15 15 7.5 = 52.5

It is also useful to know that you can always change the number of places: 3% of the 100 - the same thing as 100% from 3. 35% of 8 - the same as 8% of 35.

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