Squaring any 2-digit number
A guest post by Maria Rainier
Shortcut to Squaring Any 2-Digit Number
What do you do when your calculator has been confiscated and the world is depending on you to square a two-digit number within a minute? Don’t panic – just follow three simple steps that require basic addition and multiplication, and you’ll be able to solve the problem in no time. If you practice enough, you’ll even be able to complete each step mentally, rendering scratch paper unnecessary. This will save you time on drills and strengthen your skills so you can tackle other challenges. Eventually, you’ll be able to solve multi-step squaring problems without ever breaking a sweat – or a pencil.
Divisibility Rules for 7 , 11 and 13
A guest post by Dr. Cecily Zacharias from Oklahoma city, The United Sates of America. Currently she is an instructor at Oklahoma City Community College
Rules for divisibility of 7 , 11 and 13
It is equally good for 11 and 13.
Step 1 Divide into groups of three from the right. 245782 245 782
______________________________________________________________-1 1
Step 2. Write 1,-1,1,-1(alternate 1 and -1) in a row above the number 245 782
( start at the right end and go left)
____________________________________________________________-1 1
Step 3. Divide each Group by 7 (or 11 or 13, whatever the divisor is ) 245 782
0 5
* You can avoid step 2, by simply subtracting first remainder from the second. In this case it will be simply, 5 – 0 = 5
Step 4. Multiply the corresponding numbers in the top row and bottom row and add 0x -1 + 5x 1 = 5
** Step 4 can also be avoided.
Step 5. a. If the sum obtained is zero, The number is divisible by 7 (or 11 or 13 )
b. If the sum is positive, then that is the remainder when we divide the number by 7 ( or 11 or 13 )
c. If the sum is negative, then add 7 (or 11 or 13 ) to get the remainder.
The sum is always less than the divisor.
In the example given, the sum is 5 . Which can be verified.
When 245782 is divided by 7 by long division, the quotient is 35111 and remainder is 5.
If we test for divisor 11, the bottom row will be 3 1
The sum of products of the two rows is -2. since it is negative , add 11 .
So the remainder will be 9
Actual division gives the quotient to be 22343 and remainder 9.
It is the same method for dividing by 13 too.
If you want you can simplify the steps 2 ,to 4 as
Find the remainders in each group and alternately add and subtract the remainders starting from the right. Then use step 5.
On behalf of all the QuickerMaths.com users, I am highly grateful for her contribution.
Divisibility Rule of 7, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47
You might have seen divisibility rules of various numbers. But most of them very conveniently skip the ones which are very difficult and a divisibility rule for which is very much required. This post includes the divisibility rule for some such numbers like 7, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.
While reading this you have to be little patient. Read this carefully and try to apply it practically. If you master divisibility rules or tests explained below, I am sure these will come very handy in various examinations including competitive ones.
Quick Multiplication up to 20 x 20
“I’m having trouble above 10x10.”
This was a statement I heard many times while interacting with students preparing for competitive examinations including CAT. This was in response to my appeal to them to memorize tables up to 20x20.
Today I am posting here on QuickerMaths.com, the method which I recommend to my students too.
How to multiply up to 20x20 in your head?
Assumption: You know your multiplication table reasonably well up to 10×10.
I am trying to explain this with an example,
Quick method to evaluate polynomials – Horner’s method
This is a guest post by Nandeesh H.N. of Kolkata
How to find the value of a Polynomial Function?
Horner's method is commonly used to find the roots of a polynomial function. However it can also be used to evaluate the polynomial function for a given value of x.
Suppose, we want to evaluate the polynomial
p(x) = 4x^5 - 3x^4 + 7x^3 + 6x^2 + 3x + 9 at x = 2.41.
The usual method of evaluation is to evaluate each product (such as 4*2.41^5 or 7*2.41^3) separately and then add. The drawback is that to evaluate any power of x, we go through all of the previous powers.
A slightly better method is to make a table of powers of 2.41 and put them in the given polynomial.
Shortcut to Find Square of a Number
Today I will discuss a very simple method of finding square of numbers between 26 to 74 mentally. In the subsequent post we will cover higher numbers. So keep watching this space to learn squaring any number within your mind
Square (also called perfect square) is an integer that is the square of an integer; in other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 3 × 3.
How to find the square of any number?
To apply this method you should know squares of 1 to 25 by heart. You can refer to this table to learn the same.
Quick calculations for extremely large numbers
A guest post by Nandeesh H.N. of Kolkata
Quick calculations with a few logarithms
If you can remember a few logarithms, you can do many calculations quite easily without the aid of calculators or computers.
Try to remember the logarithms of just seven numbers:
Log 2 = 0.30, log 3 = 0.48, log 7 = 0.85, log 11= 1.04, log 13= 1.11, log 17 = 1.23 and log 19=1.28.
The logarithm of a composite number is equal to the sum of the logarithms of its prime factors; you can formulate the following table of logarithms:
Shortcut Method for Multiplication
A guest post by Nandeesh H.N. of Kolkata
Shortcut multiplication for approximate numbers
When applying the rules of multiplication of exact numbers to approximate numbers we waste time and effort in the computation of digits that will be dropped at a later stage. The computation can be made more efficient if we are guided by the following rules:
Herons Method of Finding Roots
A guest post by Nandeesh H.N. of Kolkata
"Dear Vineet,
I am really grateful to you for your blog which makes Mathematics a pleasure. Keep up your good work. As requested by you I am sending a brief note on Heron’s method of finding square root. This method can be easily extended to find any root.
Find Day of the Week on Any Date
Lots of time we are in a situation where we are supposed to know the day on a particular date of the current year. Most of the methods you will come across are not mentally possible for everyone and hence not feasible. So find below a practical Quicker Maths method of finding what day of the week will be on a particular date.
Find the day on any date of current year
I have come across a very simple way to find the day of the week for any date of the current year. This idea is so easy, that most of you will wonder why you didn't think of it yourselves.
All you have to do is........
Who is behind QuickerMaths?
I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths
I believe that if trained properly using powerful tools like Vedic Maths, the immense intellect of human mind can be ignited instantly - find out more
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Recent Comments
watchman was paid for awaking not for sleeping so that he can see dreams.. – 05Feb12
as a night watchman he shouldnt have slept at night to get that dream... – 04Feb12
Can u plz give me clarity in ur solution Kaush sir..... – 04Feb12
thanks for these tricks. Are these from the book "quicker maths by m.tyra" ? – 03Feb12
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