Squaring numbers ending in 1

Here’s a simple trick to square any number that ends in 1.

• Subtract 1 from the number.
• Square the difference. (Squaring of such number is easy as it ends in ‘0’)
• Add the difference twice to its square.
• Add 1.

Example: If the number to be squared is 61  

1.    Subtract 1=> 61 - 1 = 60.

2.    Square the difference => 60 × 60 = 3600.

3.    Add the difference twice to its square => 3600 + 60 + 60 = 3720.

4.    Add 1 => 3720 + 1 = 3721.

So, 61² = 3721

81² =?

1)    81 - 1 = 80 (Subtract 1). 

2)    80² = 6400 (square the difference). 

3)    6400 + 80 + 80 = 6560 (add the difference twice to its square).

4)    6560 + 1 = 6561 (add 1)

So, 81² = 6561

If the number to be squared is a 3-digit number, let’s say 121

1)    121 - 1 = 120 (Subtract 1). 

2)    120² = 14400 (square the difference). 

3)    14400 + 120 + 120 = 14640 (add the difference twice to its square).

4)    14640 + 1 = 14641 (add 1)

So, 121² = 14641

251² =?

1)    251 - 1 = 250  

2)    250² = 62500 

3)    62500 + 250 + 250 = 63000

4)    63000 + 1 = 63001

So, 251² = 63001

Ref. http://faster-maths.blogspot.com/2013/05/squaring-numbers-ending-in-1.html#.UadByNjKWVo

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Divisibility Rules

Dividing by 3

Add up the digits: if the sum is divisible by three, then the number is as well. Examples:
1. 111111: the digits add to 6 so the whole number is divisible by three.
2. 87687687. The digits add up to 57, and 5 plus seven is 12, so the original number is divisible by three.
Why does the 'divisibility by 3' rule work?
Look at a 2 digit number: 10a+b=9a+(a+b). We know that 9a is divisible by 3, so 10a+b will be divisible by 3 if and only if a+b is. Similarly, 100a+10b+c=99a+9b+(a+b+c), and 99a+9b is divisible by 3, so the total will be if a+b+c is.
This explanation also works to prove the divisibility by 9 test. It is originates from modular arithmetic ideas.

  Dividing by 4

Look at the last two digits. If the number formed by its last two digits is divisible by 4, the original number is as well.
Examples:
1. 100 is divisible by 4.
2. 1732782989264864826421834612 is divisible by four also, because 12 is divisible by four.

  Dividing by 5

If the last digit is a five or a zero, then the number is divisible by 5.

  Dividing by 6

Check 3 and 2. If the number is divisible by both 3 and 2, it is divisible by 6 as well.

Another easy way to tell if a [multi-digit] number is divisible by six . . . is to look at its [ones digit]: if it is even, and the sum of the [digits] is a multiple of 3, then the number is divisible by 6.

  Dividing by 7

To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number.
Example: If you had 203, you would double the last digit to get six, and subtract that from 20 to get 14. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven. If you don't know the new number's divisibility, you can apply the rule again.

Another methods is:

To know if a number is a multiple of seven or not, we can use also 
3 coefficients (1 , 2 , 3). We multiply the first number starting 
from the ones place by 1, then the second from the right by 3, 
the third by 2, the fourth by -1, the fifth by -3, the sixth by -2, 
and the seventh by 1, and so forth.

Example: 348967129356876. 

6 + 21 + 16 - 6 - 15 - 6 + 9 + 6 + 2 - 7 - 18 - 18 + 8 + 12 + 6 = 16 
means the number is not multiple of seven.

If the number was 348967129356874, then the number is a multiple 

 of seven because instead of 16, we would find 14 as a result, which is a
  multiple of 7. So the pattern is as follows: for a number onmlkjihgfedcba,
  calculate a + 3b + 2c - d - 3e - 2f + g + 3h +



2i - j - 3k - 2l + m + 3n + 2o.

Example:  348967129356874.

Below each digit let me write its respective figure.

3  4  8  9  6  7  1  2  9  3  5  6  8  7  6 
2  3  1 -2 -3 -1  2  3  1 -2 -3 -1  2  3  1

(3×2) + (4×3) + (8×1) + (9×-2) + (6×-3) + (7×-1) + 
(1×2) + (2×3) + (9×1) + (3×-2) + (5×-3) + (6×-1) + 
(8×2) + (7×3) + (6×1) =  16 -- not a multiple of seven.

  Dividing by 8

Check the last three digits. Since 1000 is divisible by 8, if the last three digits of a number are divisible by 8, then so is the whole number.
Example: 33333888 is divisible by 8; 33333886 isn't. How can you tell whether the last three digits are divisible by 8?
If the first digit is even, the number is divisible by 8 if the last two digits are. If the first digit is odd, subtract 4 from the last two digits; the number will be divisible by 8 if the resulting last two digits are. So, to continue the last example, 33333888 is divisible by 8 because the digit in the hundreds place is an even number, and the last two digits are 88, which is divisible by 8. 33333886 is not divisible by 8 because the digit in the hundreds place is an even number, but the last two digits are 86, which is not divisible by 8.

  Dividing by 9

Add the digits. If that sum is divisible by nine, then the original number is as well. This holds for any power of three.

  Dividing by 10

If the number ends in 0, it is divisible by 10.

  Dividing by 11

Take any number, such as 365167484. Add the first, third, fifth, seventh,.., 

digits.....3 + 5 + 6 + 4 + 4 = 22
Add the second, fourth, sixth, eighth,.., digits.....6 + 1 + 7 + 8 = 22
If the difference, including 0, is divisible by 11, then so is the number.
22 - 22 = 0 so 365167484 is evenly divisible by 11.

  Dividing by 12

Check for divisibility by 3 and 4.

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Number Notations for Maths

Hierarchy of Decimal Numbers

Number	Name	How many
0	zero
1	one
2	two
3	three
4	four
5	five
6	six
7	seven
8	eight
9	nine
10	ten
20	twenty	two tens
30	thirty	three tens
40	forty	four tens
50	fifty	five tens
60	sixty	six tens
70	seventy	seven tens
80	eighty	eight tens
90	ninety	nine tens

Number	Name	How Many
100	one hundred	ten tens
1,000	one thousand	ten hundreds
10,000	ten thousand	ten thousands
100,000	one hundred thousand	one hundred thousands
1,000,000	one million	one thousand thousands

Some people use a comma to mark every 3 digits. It just keeps track of the digits and makes the numbers easier to read.
Beyond a million, the names of the numbers differ depending where you live. The places are grouped by thousands in America and France, by the millions in Great Britain and Germany.

Name	American-French	English-German
million	1,000,000	1,000,000
billion	1,000,000,000 (a thousand millions)	1,000,000,000,000 (a million millions)
trillion	1 with 12 zeros	1 with 18 zeros
quadrillion	1 with 15 zeros	1 with 24 zeros
quintillion	1 with 18 zeros	1 with 30 zeros
sextillion	1 with 21 zeros	1 with 36 zeros
septillion	1 with 24 zeros	1 with 42 zeros
octillion	1 with 27 zeros	1 with 48 zeros
googol	1 with 100 zeros
googolplex	1 with a google of zeros

Fractions
Digits to the right of the decimal point represent the fractional part of the decimal number. Each place value has a value that is one tenth the value to the immediate left of it.

Number	Name	Fraction
.1	tenth	1/10
.01	hundredth	1/100
.001	thousandth	1/1000
.0001	ten thousandth	1/10000
.00001	hundred thousandth	1/100000

Examples:
0.234 = 234/1000 (said - point 2 3 4, or 234 thousandths, or two hundred thirty four thousandths)
4.83 = 4 83/100 (said - 4 point 8 3, or 4 and 83 hundredths)
SI Prefixes

Number Prefix Symbol 10 1 deka- da 10 2 hecto- h 10 3 kilo- k 10 6 mega- M 10 9 giga- G 10 12 tera- T 10 15 peta- P 10 18 exa- E 10 21 zeta- Z 10 24 yotta- Y

Number Prefix Symbol 10 -1 deci- d 10 -2 centi- c 10 -3 milli- m 10 -6 micro- u (greek mu) 10 -9 nano- n 10 -12 pico- p 10 -15 femto- f 10 -18 atto- a 10 -21 zepto- z 10 -24 yocto- y

Roman Numerals

I=1		(I with a bar is not used)
V=5		_ V=5,000
X=10		_ X=10,000
L=50		_ L=50,000
C=100		_ C = 100 000
D=500		_ D=500,000
M=1,000		_ M=1,000,000

Examples:

1 = I 2 = II 3 = III 4 = IV 5 = V 6 = VI 7 = VII 8 = VIII 9 = IX 10 = X

11 = XI 12 = XII 13 = XIII 14 = XIV 15 = XV 16 = XVI 17 = XVII 18 = XVIII 19 = XIX 20 = XX 21 = XXI

25 = XXV 30 = XXX 40 = XL 49 = XLIX 50 = L 51 = LI 60 = LX 70 = LXX 80 = LXXX 90 = XC 99 = XCIX

There is no zero in the roman numeral system.
The numbers are built starting from the largest number on the left, and adding smaller numbers to the right. All the numerals are then added together.
The exception is the subtracted numerals, if a numeral is before a larger numeral, you subtract the first numeral from the second. That is, IX is 10 - 1= 9.
This only works for one small numeral before one larger numeral - for example, IIX is not 8, it is not a recognized roman numeral.
There is no place value in this system - the number III is 3, not 111.
Number Base Systems

Decimal(10)	Binary(2)	Ternary(3)	Octal(8)	Hexadecimal(16)
0	0	0	0	0
1	1	1	1	1
2	10	2	2	2
3	11	10	3	3
4	100	11	4	4
5	101	12	5	5
6	110	20	6	6
7	111	21	7	7
8	1000	22	10	8
9	1001	100	11	9
10	1010	101	12	A
11	1011	102	13	B
12	1100	110	14	C
13	1101	111	15	D
14	1110	112	16	E
15	1111	120	17	F
16	10000	121	20	10
17	10001	122	21	11
18	10010	200	22	12
19	10011	201	23	13
20	10100	202	24	14

Each digit can only count up to the value of one less than the base. In hexadecimal, the letters A - F are used to represent the digits 10 - 15, so they would only use one character.

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Subtraction Tricks

An operation of finding an addend by a sum and another addend: 17 – 6 = 11.  Here 17 is a minuend,  6 – a subtrahend,  11 – the difference.

Math tricks 1: subtracting by oversubtracting
251-85
=(151+100)-85
=151+100-85
=151+15
=166
In this example,251 is break into 151 and 100
Math tricks 2:
subtracting by adding to each number
251-85
=(151+100)-85
=151+100-85
=151+15
=166
In this example,251 is break into 151 and 100
Math tricks 3:
subtracting by subtracting to each number
831-104
=(831-4)-(104-4)
=827-100
=727
In this example,251 is break into 151 and 100

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Easy way to check your answer: Check the answer by working backward
Example:

543 - 295 = 248

Add 248 to 295,and see whether you can get 543 back or not.

248 + 295 = 543

If the answer(eg.248) add with one of the numbers(eg.295) give you another numbers(eg.543),then your aswer is correct.

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Addition Tricks

Addition
-an operation of finding a sum of some numbers: 21 + 5 = 26. Here 21 and 5 – addends,  26 – the sum. If addends are changed by places, a sum is saved the same: 21 + 5 = 26 and 5 + 21 = 26.

Math tricks 1:
Adding by breaking apart a number
Example:
137+85
=(122+15)+85
=122+100
=222
In example here,break 137 to 122 and 15.
Math tricks 2:
Adding by overadding
Example:
247+97
=247+(100-3)
=347-3
=344
In example here,97 was add to 100 first.

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Easy way to check your answer: Estimating the answer by rounding off numbers
Example:

249 159 + 504 = 912

249 rounds off to 250,159 to 160 and 504 to 500,then add up these figures.

250 160 + 500 = 910

The amount that has been estimated is 910,so the answer should be around 910.If your answer is only 800,then you know it is wrong.

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History of Maths

An overview
Mathematics starts with counting. It is not reasonable, however, to suggest that early counting was mathematics. Only when some record of the counting was kept and, therefore, some representation of numbers occurred can mathematics be said to have started.
In Babylonia mathematics developed from 2000 BC. Earlier a place value notation number system had evolved over a lengthy period with a number base of 60. It allowed arbitrarily large numbers and fractions to be represented and so proved to be the foundation of more high powered mathematical development.
Number problems such as that of the Pythagorean triples (a,b,c) with a2+b2 = c2 were studied from at least 1700 BC. Systems of linear equations were studied in the context of solving number problems. Quadratic equations were also studied and these examples led to a type of numerical algebra.
Geometric problems relating to similar figures, area and volume were also studied and values obtained for p.
The Babylonian basis of mathematics was inherited by the Greeks and independent development by the Greeks began from around 450 BC. Zeno of Elea's paradoxes led to the atomic theory of Democritus. A more precise formulation of concepts led to the realisation that the rational numbers did not suffice to measure all lengths. A geometric formulation of irrational numbers arose. Studies of area led to a form of integration.
The theory of conic sections show a high point in pure mathematical study by Apollonius. Further mathematical discoveries were driven by the astronomy, for example the study of trigonometry.
The major Greek progress in mathematics was from 300 BC to 200 AD. After this time progress continued in Islamic countries. Mathematics flourished in particular in Iran, Syria and India. This work did not match the progress made by the Greeks but in addition to the Islamic progress, it did preserve Greek mathematics. From about the 11th Century Adelard of Bath, then later Fibonacci, brought this Islamic mathematics and its knowledge of Greek mathematics back into Europe.
Major progress in mathematics in Europe began again at the beginning of the 16th Century with Pacioli, then Cardan, Tartaglia and Ferrari with the algebraic solution of cubic and quartic equations. Copernicus and Galileo revolutionised the applications of mathematics to the study of the universe.
The progress in algebra had a major psychological effect and enthusiasm for mathematical research, in particular research in algebra, spread from Italy to Stevin in Belgium and Viète in France.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculatory science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry.
Progress towards the calculus continued with Fermat, who, together with Pascal, began the mathematical study of probability. However the calculus was to be the topic of most significance to evolve in the 17th Century.
Newton, building on the work of many earlier mathematicians such as his teacher Barrow, developed the calculus into a tool to push forward the study of nature. His work contained a wealth of new discoveries showing the interaction between mathematics, physics and astronomy. Newton's theory of gravitation and his theory of light take us into the 18th Century.
However we must also mention Leibniz, whose much more rigorous approach to the calculus (although still unsatisfactory) was to set the scene for the mathematical work of the 18th Century rather than that of Newton. Leibniz's influence on the various members of the Bernoulli family was important in seeing the calculus grow in power and variety of application.
The most important mathematician of the 18th Century was Euler who, in addition to work in a wide range of mathematical areas, was to invent two new branches, namely the calculus of variations and differential geometry. Euler was also important in pushing forward with research in number theory begun so effectively by Fermat.
Toward the end of the 18th Century, Lagrange was to begin a rigorous theory of functions and of mechanics. The period around the turn of the century saw Laplace's great work on celestial mechanics as well as major progress in synthetic geometry by Monge and Carnot.
The 19th Century saw rapid progress. Fourier's work on heat was of fundamental importance. In geometry Plücker produced fundamental work on analytic geometry and Steiner in synthetic geometry.
Non-euclidean geometry developed by Lobachevsky and Bolyai led to characterisation of geometry by Riemann. Gauss, thought by some to be the greatest mathematician of all time, studied quadratic reciprocity and integer congruences. His work in differential geometry was to revolutionise the topic. He also contributed in a major way to astronomy and magnetism.
The 19th Century saw the work of Galois on equations and his insight into the path that mathematics would follow in studying fundamental operations. Galois' introduction of the group concept was to herald in a new direction for mathematical research which has continued through the 20th Century.
Cauchy, building on the work of Lagrange on functions, began rigorous analysis and began the study of the theory of functions of a complex variable. This work would continue through Weierstrass and Riemann.
Algebraic geometry was carried forward by Cayley whose work on matrices and linear algebra complemented that by Hamilton and Grassmann. The end of the 19th Century saw Cantor invent set theory almost single handedly while his analysis of the concept of number added to the major work of Dedekind and Weierstrass on irrational numbers
Analysis was driven by the requirements of mathematical physics and astronomy. Lie's work on differential equations led to the study of topological groups and differential topology. Maxwell was to revolutionise the application of analysis to mathematical physics. Statistical mechanics was developed by Maxwell, Boltzmann and Gibbs. It led to ergodic theory.
The study of integral equations was driven by the study of electrostatics and potential theory. Fredholm's work led to Hilbert and the development of functional analysis.

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Division Tricks

An operation of finding one of factors by a product and another factor: 48÷4 = 12. Here  48  is a dividend,  4 – a divisor,  12 – the quotient. At dividing integers a quotient can be not a whole number. Then this quotient can be present as a fraction. If a quotient is a whole number, then it is called that numbers are divisible, i.e. one number is divided without remainder by another. Otherwise, we have a division with remainder. For example, 23 isn’t divided by 4 ; this case can be written as:  23 = 5×4 + 3.  Here 3 is a remainder.

Math tricks 1:
Dividing by grouping
345÷15
=(300÷15)+(45÷15)
=20+3
=23
In example here,separate dividend into two groups:(300÷15)+(45÷15),and add up the answer.
Math tricks 2:
Dividing by augmenting
Example:
418÷11
=(440÷11)-(22÷11)
=40-2
=38
In example here,418 was augmented to 440,that is 418=440-22
Math tricks 3:
Dividing by break apart the divisor
325÷25
=325÷(5×5)
=325÷5÷5
=65÷5
=13
In example here,break 25 to 5 and 5(25=5×5).

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IMPRESS YOUR FRIENDS WITH MENTAL MATH TRICKS

Easy Cal Tricks

Being able to perform arithmetic quickly and mentally can greatly boost your self-esteem, especially if you don't consider yourself to be very good at Math. And, getting comfortable with arithmetic might just motivate you to dive deeper into other things mathematical.
This article presents nine ideas that will hopefully get you to look at arithmetic as a game, one in which you can see patterns among numbers and pick then apply the right trick to quickly doing the calculation.
The tricks in this article all involve multiplication.
Don't be discouraged if the tricks seem difficult at first. Learn one trick at a time. Read the description, explanation, and examples several times for each technique you're learning. Then make up some of your own examples and practice the technique.
As you learn and practice the tricks make sure you check your results by doing multiplication the way you're used to, until the tricks start to become second nature. Checking your results is critically important: the last thing you want to do is learn the tricks incorrectly.

1. Multiplying by 9, or 99, or 999

Multiplying by 9 is really multiplying by 10-1.
So, 9x9 is just 9x(10-1) which is 9x10-9 which is 90-9 or 81.

Let's try a harder example: 46x9 = 46x10-46 = 460-46 = 414.

One more example: 68x9 = 680-68 = 612.

To multiply by 99, you multiply by 100-1.
So, 46x99 = 46x(100-1) = 4600-46 = 4554.

Multiplying by 999 is similar to multiplying by 9 and by 99.
38x999 = 38x(1000-1) = 38000-38 = 37962.

2. Multiplying by 11

To multiply a number by 11 you add pairs of numbers next to each other, except for the numbers on the edges.
Let me illustrate:
To multiply 436 by 11 go from right to left.
First write down the 6 then add 6 to its neighbor on the left, 3, to get 9.
Write down 9 to the left of 6.
Then add 4 to 3 to get 7. Write down 7.
Then, write down the leftmost digit, 4.
So, 436x11 = is 4796.
Let's do another example: 3254x11.
The answer comes from these sums and edge numbers: (3)(3+2)(2+5)(5+4)(4) = 35794.
One more example, this one involving carrying: 4657x11.
Write down the sums and edge numbers: (4)(4+6)(6+5)(5+7)(7).
Going from right to left we write down 7.
Then we notice that 5+7=12.
So we write down 2 and carry the 1.
6+5 = 11, plus the 1 we carried = 12.
So, we write down the 2 and carry the 1.
4+6 = 10, plus the 1 we carried = 11.
So, we write down the 1 and carry the 1.
To the leftmost digit, 4, we add the 1 we carried.
So, 4657x11 = 51227 .

3. Multiplying by 5, 25, or 125

Multiplying by 5 is just multiplying by 10 and then dividing by 2. Note: To multiply by 10 just add a 0 to the end of the number.
12x5 = (12x10)/2 = 120/2 = 60.
Another example: 64x5 = 640/2 = 320.
And, 4286x5 = 42860/2 = 21430.
To multiply by 25 you multiply by 100 (just add two 0's to the end of the number) then divide by 4, since 100 = 25x4. Note: to divide by 4 your can just divide by 2 twice, since 2x2 = 4.
64x25 = 6400/4 = 3200/2 = 1600.
58x25 = 5800/4 = 2900/2 = 1450.
To multiply by 125, you multipy by 1000 then divide by 8 since 8x125 = 1000. Notice that 8 = 2x2x2. So, to divide by 1000 add three 0's to the number and divide by 2 three times.
32x125 = 32000/8 = 16000/4 = 8000/2 = 4000.
48x125 = 48000/8 = 24000/4 = 12000/2 = 6000.

4. Multiplying together two numbers that differ by a small even number

This trick only works if you've memorized or can quickly calculate the squares of numbers. If you're able to memorize some squares and use the tricks described later for some kinds of numbers you'll be able to quickly multiply together many pairs of numbers that differ by 2, or 4, or 6.
Let's say you want to calculate 12x14.
When two numbers differ by two their product is always the square of the number in between them minus 1.
12x14 = (13x13)-1 = 168.
16x18 = (17x17)-1 = 288.
99x101 = (100x100)-1 = 10000-1 = 9999
If two numbers differ by 4 then their product is the square of the number in the middle (the average of the two numbers) minus 4.
11x15 = (13x13)-4 = 169-4 = 165.
13x17 = (15x15)-4 = 225-4 = 221.
If the two numbers differ by 6 then their product is the square of their average minus 9.
12x18 = (15x15)-9 = 216.
17x23 = (20x20)-9 = 391.

5. Squaring 2-digit numbers that end in 5

If a number ends in 5 then its square always ends in 25. To get the rest of the product take the left digit and multiply it by one more than itself.
35x35 ends in 25. We get the rest of the product by multiplying 3 by one more than 3. So, 3x4 = 12 and that's the rest of the product. Thus, 35x35 = 1225.
To calculate 65x65, notice that 6x7 = 42 and write down 4225 as the answer.
85x85: Calculate 8x9 = 72 and write down 7225.

6. Multiplying together 2-digit numbers where the first digits are the same and the last digits sum to 10

Let's say you want to multiply 42 by 48. You notice that the first digit is 4 in both cases. You also notice that the other digits, 2 and 8, sum to 10. You can then use this trick: multiply the first digit by one more than itself to get the first part of the answer and multiply the last digits together to get the second (right) part of the answer.
An illustration is in order:
To calculate 42x48: Multiply 4 by 4+1. So, 4x5 = 20. Write down 20.
Multiply together the last digits: 2x8 = 16. Write down 16.
The product of 42 and 48 is thus 2016.
Notice that for this particular example you could also have noticed that 42 and 48 differ by 6 and have applied technique number 4.
Another example: 64x66. 6x7 = 42. 4x6 = 24. The product is 4224.
A final example: 86x84. 8x9 = 72. 6x4 = 24. The product is 7224

7. Squaring other 2-digit numbers

Let's say you want to square 58. Square each digit and write a partial answer. 5x5 = 25. 8x8 = 64. Write down 2564 to start. Then, multiply the two digits of the number you're squaring together, 5x8=40.
Double this product: 40x2=80, then add a 0 to it, getting 800.
Add 800 to 2564 to get 3364.
This is pretty complicated so let's do more examples.
32x32. The first part of the answer comes from squaring 3 and 2.
3x3=9. 2x2 = 4. Write down 0904. Notice the extra zeros. It's important that every square in the partial product have two digits.
Multiply the digits, 2 and 3, together and double the whole thing. 2x3x2 = 12.
Add a zero to get 120. Add 120 to the partial product, 0904, and we get 1024.
56x56. The partial product comes from 5x5 and 6x6. Write down 2536.
5x6x2 = 60. Add a zero to get 600.
56x56 = 2536+600 = 3136.
One more example: 67x67. Write down 3649 as the partial product.
6x7x2 = 42x2 = 84. Add a zero to get 840.
67x67=3649+840 = 4489.

8. Multiplying by doubling and halving

There are cases when you're multiplying two numbers together and one of the numbers is even. In this case you can divide that number by two and multiply the other number by 2. You can do this over and over until you get to multiplication this is easy for you to do.
Let's say you want to multiply 14 by 16. You can do this:
14x16 = 28x8 = 56x4 = 112x2 = 224.
Another example: 12x15 = 6x30 = 6x3 with a 0 at the end so it's 180.
48x17 = 24x34 = 12x68 = 6x136 = 3x272 = 816. (Being able to calculate that 3x27 = 81 in your head is very helpful for this problem.)

9. Multiplying by a power of 2

To multiply a number by 2, 4, 8, 16, 32, or some other power of 2 just keep doubling the product as many times as necessary. If you want to multiply by 16 then double the number 4 times since 16 = 2x2x2x2.
15x16: 15x2 = 30. 30x2 = 60. 60x2 = 120. 120x2 = 240.
23x8: 23x2 = 46. 46x2 = 92. 92x2 = 184.
54x8: 54x2 = 108. 108x2 = 216. 216x2 = 432.

Practice these tricks and you'll get good at solving many different kinds of arithmetic problems in your head, or at least quickly on paper. Half the fun is identifying which trick to use. Sometimes more than one trick will apply and you'll get to choose which one is easiest for a particular problem.
Multiplication can be a great sport! Enjoy.

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