Multiples of 9 Using Finger Trick

Some find it hard to memorize the multiplication table. For multiples of 9, learn this finger trick and you will find that multiplying 9 with any number will be quick and easy.

This trick is done by spreading your fingers as shown in the image, then fold the corresponding finger for the multiplier of 9. Left side of the folded finger will be the tens digit while right side of the folded finger will be the ones digit.

1 x 9 = ?
Folding 1st finger, no finger remains on left side, while 9 fingers remain on the right side. That makes 0 and 9, so 1 x 9 = 9. The answer is obviously 9, this is just for the sake of example.

2 x 9 = ?
Folding 2nd finger, 1 finger remains on left side, while 8 fingers on right side. So 2 x 9 = 18.

3 x 9 = ?
Folding 3rd finger, 2 fingers remain on left side, while 7 fingers on right side. So 3 x 9 = 27.

4 x 9 = ?
Folding 4th finger, 3 fingers remain on left side, while 6 fingers on right side. So 4 x 9 = 36.

5 x 9 = ?
Folding 5th finger, 4 fingers remain on left side, while 5 fingers on right side. So 5 x 9 = 45.

6 x 9 = ?
Folding 6th finger, 5 fingers remain on left side, while 4 fingers on right side. So 6 x 9 = 54.

7 x 9 = ?
Folding 7th finger, 6 fingers remain on left side, while 3 fingers on right side. So 7 x 9 = 63.

8 x 9 = ?
Folding 8th finger, 7 fingers remain on left side, while 2 fingers on right side. So 8 x 9 = 72.

9 x 9 = ?
Folding 9th finger, 8 fingers remain on left side, while 1 finger on right side. So 9 x 9 = 81.

10 x 9 = ?
Folding 10th finger, 9 fingers remain on left side, while no finger on right side. So 10 x 9 = 90.
It's obviously 90. I just show here that this trick is applicable from 1 to 10.

Quick and easy, right?

#Matamata

Multiplying Any Number with 5

Multiplying any number with 5 can be done easily by adding digit "0" after it, then divide it by 2.

Example:
You are buying 5 pieces of something worth 245 Php. How much is the total cost?

245 x 5 = ?

Add "0" to 245, then divide it by 2.
245 x 5 = 2450/2  = 1225 Php


More examples:

14 x 5 = ?
14 x 5 = 140/2 = 70

160 x 5 = ?
160 x 5 = 1600/2 = 800

887 x 5 = ?
887 x 5 = 8870/2 = 4435

1268 x 5 = ?
1268 x 5 = 12680/2 = 6340

#Matamata

Multiplying Special 2-digit Numbers

42 x 48 = ?

Notice that their tens digits are the same, 4. And their ones digits sums up to 10, that is, 2 plus 8 equals 10. For special numbers like these, there is a shortcut to get the product.

To get the answer, first multiply the tens digit by itself plus 1, that is 4 x (4+1) or simply put 4 x 5.
4 x 5 = 20
20 will be the first digits of the answer. To get the remaining two digits, multiply  the ones digits 2 and 8.
2 x 8 = 16
So we have 20 and 16, put them together, we have 2016 as the answer.
42 x 48 = 2016

More examples:


53 x 57 = ?
53 x 57 = 5x6   3x7

53 x 57 = 3021

61 x 69 = ?
61 x 69 = 6x7   1x9

61 x 69 = 4209

26 x 24 = ?
26 x 24 = 2x3   6x4

26 x 24 = 624

35 x 35 = ?
35 x 35 = 3x4   5x5

35 x 35 = 1225

#Matamata

Computing Percent Savings

We love to get discounts whenever we buy something. Know first hand how much you are about to save for a given amount of percent off sale with these mental tricks.

Example, a shirt with a price of 300 Php with a given % sale.

For 10%, moving 1 decimal point, 300 becomes 30.
10% of 300 = 30 Php.

For 5%, that's half of 10% savings.
5% of 300 = 30/2 = 15 Php.

For 15%, add the 10% and 5% savings.
15 % of 300 = 30 + 15 = 45 Php.

For 20%, that's twice of 10% savings.
20% of 300 = 30x2 = 60 Php.

For 25%, add 20% and 5% savings.
25% of 300 = 60 + 15 = 75 Php.
Or take 1/4 of the price. To make it simple, divide by 2 twice.
25% of 300 = 300/2 = 150/2 = 75 Php.

For 30%, that's 3 times of 10%.
30% of 300 = 30x3 = 90 Php.

For 35%, add 30% and 5% savings.
35% of 300 = 90 + 15 = 105 Php.

For 40%, multiply 10% savings with 2 twice.
40% of 300 = 30x2 = 60x2 = 120 Php.

For 45%, add 40% and 5% savings.
45% of 300 = 120 + 15 = 135 Php.

For 50%, that's half of the price.
50% of 300 = 300/2 = 150 Php.

More examples:

10% of 985 = 98.5
15% of 280 = 28 +14 = 42
20% of 740 = 74x2 = 148
25% of 460 =  460/2 =230/2 =115
30% of 1500 = 150x3 = 450
35% of 600 = 60x3 + 30 =210
40% of 240 = 24x2 = 48x2 = 96
45% of 240 = 96 + 12 = 108
50% of 649 = 649/2 = 324.5

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Checking Exact Change

"Count your money before you leave." A friendly reminder when you are paying at the cashier or in vendor's stand. Check the exact change by mastering "All from 9, Last from 10."

Example:
You hand 1000 Php bill for payment of goods worth 648 Php. How much is the exact change? Know the exact change without the aid of calculators.

Just deduct all the digits from 9 and the last non-zero digit from 10.
1000 - 648 = ?
9 - 6 = 3
9 - 4 = 5
10 - 8 = 2
1000 - 648 = 352

Or you can think of it this way:
1000 - 648 = ?
   9  9  10
 - 6  4  8  
   3  5  2   answer

Or simply think of a number that will complete the digits into 9 9 10.
 1000 - 468 = ?
 6 4 8 
 3 5 2 answer

More examples:
 100 -78 = ?
 7 8 
 2 2 answer

 1000 - 385 = ?
 3 8 5 
 6 1 5 answer

 1000 - 740 = ?
   9 10 0           (10 for last non-zero)
- 7  4  0  
  2  6  0   answer

1000 - 407 = ?
   9  9 10
- 4  0  7   
  5  9  3  answer

#Matamata

Subtracting From Left to Right

Subtraction can be done from left to right. You can even start answering while the question is still ongoing.

Example 1

Step 1
  7,896
- 5,2--   (question ongoing)
  2,6--   (answer ongoing)

Step 2
  7,896
- 5,28-   (question ongoing)
  2,61-   (answer ongoing)

Step 3
  7,896
- 5,281   (question done)
  2,615   (answer also done)

Example 2
  8,652
- 5,478   
  3,2(-2)(-6)
  3,174 answer

The answer is done by subtracting digit to digit.
8 - 5 = 3
6 - 4 = 2
5 - 7 = (-2)
2 - 8 = (-6)

3,2(-2)(-6)
From here, apply "All from 9, Last from 10" and subtract 1 from the preceding positive number. Bar above the number indicates negative.
      _ _
3,2 2 6 = 3, 2-1, 9-2, 10-6
3,1 7 4 answer

Example 3
   134
 -  78   
     _ _
  1 4 4   = 1-1, 9-4, 10-4
     5 6 answer

Example 4
  52,485
- 38,347  
   _        _
2 6, 1 4 2   = 2-1, 10-6, 1, 4-1, 10-2
1 4, 1 3 8  answer

Example 5
  654,321
- 345,678   
      _  _ _ _
3 1 1, 3 5 7  =  3, 1-1, 9-1, 9-3, 9-5, 10-7
3 0 8, 6 4 3 answer

"All from 9, last from 10" is applied for negative numbers because these are simply subtracted from base number with zeros.
       _ _
3, 2 2 6  = 3,200 - 26 = 3,174
   _ _
1 4 4  = 100 - 44 = 56
   _        _
2 6, 1 4 2  = 20-6, 1, 40-2 = 141,388
      _  _ _ _
3 1 1, 3 5 7  =  310,000 - 1, 357 = 308,643

#Matamata

Square of Any 2-digit Number

The square of any 2-digit number can be done easily by this trick.

Square the tens digit and the ones digit and put it on both sides. Double the product of the digits and put it in the middle. If the results have no carry over, these become the digits of the answer.

Below are examples of no carry over.

13 x 13 = ?
1*1   2*1*3   3*3
  1       6        9
13 x 13 = 169

12 x 12 = ?
1*1   2*1*2   2*2
  1       4        4
12 x 12 = 144

11 x 11 = ?
1*1   2*1*1   1*1
  1       2        1
11 x 11 = 121

21 x 21 = ?
2*2   2*2*1   1*1
 4        4        1
21 x 21 = 441

41 x 41 = ?
4*4   2*4*1   1*1
 16       8        1
41 x 41 = 1681

70 x 70 = ?
7*7   2*7*0   0*0
 49       0        0
70 x 70 = 4900

When the results are 2-digit numbers, carry the tens digit to the preceding number.
Below are examples with carry over.

62 x 62 = ?
6*6     2*6*2   2*2
 36        24       4
 36+2    4         4
 38        4         4
62 x 62 = 3844

18 x 18 = ?
1*1   2*1*8     8*8
 1         16      64
 1+1     6+6     4
 2         12       4
2+1       2        4
3           2        4
18 x 18 = 324

15 x 15 = ?
1*1     2*1*5    5*5
 1         10       25
 1+1      0+2      5
 2          2          5
15 x 15 = 225

It seems long to write because I am showing here the step by step process. But this trick takes only seconds in the mind.

#Matamata