How to square any number that ends in 5
Squaring a number means to mulitply the number by itself. It's the opposite of taking the square root of a number. Some are easy to do if you know a few tricks. The answer will always end in 25 so you can ignore the 5 part of the number and concentrate on the other digit. Multiply the first digit by itself and then add the digit to the answer. A few examples will clear things up.
Note: For these examples ^2 means to raise to the power of 2 or squared.
Examples
45^2 -> Since the answer always ends in 25 ignore the 5 and work with the 4. Multiply 4 by itself:
4 * 4 = 16
Add 4 to the answer:
16 + 4 = 20 This is our intermediate answer. (If you think of a better word than "intermediate" write me)
Add 25 to the end to get the final answer:
Therefore 45 squared = 2025
35^2 -> Again we'll ignore the 5 and work with the 3. Multiply 3 by itself:
3 * 3 = 9
Add 3 to the answer:
9 + 3 = 12
Add 25 at the end to get the final answer:
1225
105^2 -> Multiply 10 by itself then add 10:
(10 * 10) + 10
100 + 10
110
Now add 25 at the end:
11025
15^2 -> Multiply 1 by itself and add one to the result:
(1 * 1) + 1 = 2
Add 25 on the end:
225
How To Multiply Any Number by 11
To Multiply any number by 11, multiply the number by 10 and add the original number to the result.
Examples
25 * 11 -> Multiply 25 by 10:
25 * 10 = 250 (Remember to multiply any number by ten means just adding a zero to the end of the number)
Now add 25 to the 250
250 + 25 = 275
What we just did was this:
25 * 11 = (25 * 10) + ( 25 * 1) We are breaking the 11 down to 10 and 1 just as we were doing with the
examples above.
43 * 11 -> (43 * 10 ) + 43
430 + 43
473
178 * 11 -> Break the problem down as before:
(178 * 10 ) + 178
1780 + 178
1780 + 100 + 78
1880 + 78
Round 1880 up to 1900 because it's easier to add someting to 100:
1900 + 78 = 1978
Because we added 20 when we rounded up to get 1900 we must subract that same amount to
get our final answer: 1978 - 20 = 1958
How To Multiply Any Number by 5
To multiply a number by 5, multiply by 10 instead and then half the result. Multiplying any number by 10
simply means to add a zero to the end of the number so there is really nothing to do. Afterwards you simply
divide the result by 2. Let's do an example and I'll explain further.
Examples
88 * 5 -> Double the 5 to 10 instead. We now have:
88 * 10 = 880
Now half the the result to get the answer. In other words divide the result by 2:
440
Because we doubled the 5 to 10(in other words we multiplied 5 by 2) we must half the
result by 2 to get the final answer. I you check the addition you'll see I have what I call
"My Little Rule". It states that whatever you do at the beginning you must do the opposite
at the end and by the same amount.
73 * 5 -> Double the 5 and make it 10:
73 * 10 = 730
Now divide 730 by 2:
365
A "quick and dirty" way to divide any number by 2 is to split the number into two halves. For
example in this example 730 is the same as 700 and 30. Now divide 30 by 2 to get 15 and
700 by 2 to get 350. Add 350 and 15 to get 365.
68 * 5 -> Double 5 to get 2:
68 * 10 = 680
Divide 680 by 2:
680 = 600 + 80
Divide 600 by 2 and 80 by 2:
600 / 2 = 300
80 / 2 = 40
Add the two numbers:
300 + 40 = 340
How to multiply any number by 9
Multiplying by 9 is similar to multiplying by 11. The difference is that instead of adding n * 1 after multiply
by 10 we will be subtracting n * 1.
Examples
43 * 9 -> Break the problem down to (43 * 10) - (43 * 1)
43 * 10 = 430
43 * 1 = 43
Subtract two results:
430 - 43 = 387
62 * 9 -> Break the problem down to (62 * 10) - (62 * 1)
62 * 10 = 620
62 * 1 = 62
Subtract the two results:
620 - 62 = 558
Another way to do this example is to use the method in the "Multiplication" section.
Change the problem to (60 * 9) + (2 * 9)
60 * 9 = 540 (6 * 9 = 54 and put a zero on the end)
9 * 2 = 18
Now add the two results:
540 + 18 = 558
