Mathematics tricks are useful or not?
Let us recall early school days mathematics tricks and see how useful they are and when to apply them. I faced challenge from my kids recently when they said they have got some mathematics tricks and they asked me to help them solving problems using tricks.
I recalled few tricks I knew and learnt from my kids and sharing my understanding about them, may be it will help your kids too to handle difficult mathematics problems.
Sometimes it is easy to get the answer without using trick?
Trick 1: Take an example trick multiplying by 5
If you have to multiply an even number by 5. Find half of the even number and add a zero at the end of half.
64 X 5 = 320
480 X 5 = 2400
6480 X 5 = 32400
Half of 64 or 480 is easy to find without any pen and paper but for complex even numbers like 6588 it is little time taking for a kid in primary school.
Some simple number like 100, 1000, 200, 2000, 900, 1400 etc are all so simple (only first digit is non zero) that just multiplying first number by 5 and adding other zeros at the end is simpler and here is almost no special advantage in using any trick.
1400 X 5 = [14 X 5 ] [add remaining zeros at the end of the result] = 70 00
Some of the tricks have lots of rules/conditions?
Trick 2: Multiplication of two special numbers
Conditions apply :)
a. Both should be two digit numbers (68 X 62)
b. Sum of unit digits should be 10 (22 X 28)
c. Digits at tenth place should be the same (97 X 93)
Step 1
Multiply unit digit numbers:
68 X 62 => ...16
Note: if result is single digit add a zero before it, e.g 9 X 1 = 09
Step 2
Multiply digit at tenth place with number one greater than itself (68 X 62)
6 X 7 => 42
Step 3
Keep this result of Step 2 before result found in Step 1 and you have the answer
68 X 62 = 42 16
Another example
97 X 93 = 90 21
Another example
91 X 99 = 90 09
Sometimes tricks are applicable in very limited situations?
Trick 3: Square of two digit number whose unit digit is 5
Example: Find square of 75
Step 1
Multiply tenth digit by a number which is one more than itself
7 X 8 = 56
Step 2
Add 25 at the end of stage 1 result
56 25
You have got the square of 75 = 5625
Instead of tricks kids should first learn basics?
May be I am wrong and too conservative but I think small kids should learn tables and solve basic mathematics problems without tricks so that basics like tables become easy. Solving mathematics problems helps sharpening their basic skills.
Are tricks going to be used in real life?
If one has to avoid doing straight forward multiplication, instead of tricks he would be using calculator or any spreadsheet software like excel when he will be grown up. That way he will focus on solving other real world problem not complex multiplication.
Straight forward multiplication or other maths stuff is easier than remembering tricks and conditions?
There are many conditions to remember, couple of rules to remember to use the tricks. Better and simpler is to use straight forward techniques. If some one forgets any condition he may write wrong answers or results.
Dependency on certain patterns not necessarily found all the time?
These tricks assume certain patterns in the numbers otherwise they don't work. For example above find square of a two digit number requires 5 to be at the unit place. There are other techniques which will be applicable to other types of numbers too for square but it means for every number there is a different rule and trick to achieve the same thing square. This is not easy to remember and handle.
Take another example: Multiplying a two digit number (say 76) with 11
Step 1
Add up two digits
7 + 6 = 13
Step 2
Insert once' digit of this resulting number in between two digits of the number
7 3 6
And add tens digit of the resulting number to the first digit (tens digit) of the number
7 3 6
1
------
836
This is the result of 76 X 11 = 836
A simpler case
23 X 11
2 + 3 = 5
23 X 11 = 2 5 3
Conclusion
There are many tricks and people love tricks. If you find a pattern which you are able to remember easily some times these tricks can be of good use. It may add fun to subject like mathematics but how much do you use in your work or like when you become adult is something I wanted to check with you. Please let me know in the comments if you would like to teach your kids these mathematics tricks?.