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Multiplication

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Multiplication
-To multiply one number  n ( a multiplicand ) by another m ( a multiplier ) means to repeat a multiplicand  n  as an addend m times. The result of  multiplying is called a product. The operation of multiplication is written as: n x m or n · m . For example, 12 x 4 = 12 + 12 + 12 + 12 = 48. In our case 12 x 4 = 48 or 12 · 4 = 48. Here 12 is a multiplicand, 4 – a multiplier, 48 – a product. If a multiplicand n  and a multiplier  m  are changed by places, their product is saved the same:  12 · 4 = 12 + 12 + 12 + 12 = = 48  and   4 ·12 = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 48. Therefore, a multiplicand and a multiplier are called usually factors or multipliers.

Math tricks 1:

Multiplying by break apart a number

Example:

125×32

=125×(4×8)

=500×8

=4000

In example here,break 32 to 8×4.

Math tricks 2:

Multiplying any number by 11

Example: to multiply 54321 by 11.

11 × 54321
= 5 4+5 4+3 3+2 2+1 1
= 597531

The pattern is simply adding the digit to whatever comes before it.

But you must work from right to left. The reason is that if the numbers, when added together, sum to more than 9, then you have something to carry over.

Let's look at another example...

11 × 9527136

We know that 6 will be the last number in the answer. So the answer now is

???????6.
Calculate the tens place: 6+3=9, so now we know that the product has the form
??????96.
3+1=4, so now we know that the product has the form
?????496.
1+7=8, so
????8496.
7+2=9, so
???98496.
2+5=7, so
??798496.
5+9=14.
Here's where carrying digits comes in: we fill in the hundred thousands place with the ones digit of the sum 5+9, and our product has the form
?4798496.
We will carry the extra 10 over to the next (and final) place.

9+0=9, but we need to add the one carried from the previous sum: 9+0+1=10.

So the product is 104798496.

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