Multiplication by 2

Multiplication by 2 is the simplest of the arithmetic tasks. Yet, it could be carried out in a number of ways. If you multiply by 2 in your head then it is often more convenient to multiply left-to-right and not right-to-left as we are all conditioned to do by the long multiplication algorithm. For example

 1375×2 = (1000 + 300 + 70 + 5)×2 = 2000 + 600 + 140 + 10 = 2750.

and also

 7205×2 = (7000 + 200 + 5)×2 = 14000 + 400 + 10 = 14410.

Note how useful here was the distributive law.

In the two examples above, we split a 4-digit number into four (decimal) pieces. There was no obligation to do so. For example, 1684×2 may be computed as

 1684×2 = (1000 + 600 + 80 + 4)×2 = 2000 + 1200 + 160 + 8 = 3368.

But here is another valid way:

 1684×2 = (1500 + 100 + 50 + 34)×2 = 3000 + 200 + 100 + 68 = 3368. • Multiplication by 9, 99, 999, (Multiply + Subtract) etc.
• Squaring 2-Digit Numbers
• Division by 5
• Multiplication by 5
• Multiplication by 9, 99, 999, etc. (Something Special)
• Product of 10a + b and 10a + c where b + c = 10
• Product of numbers close to 100
• Product of two one-digit numbers greater than 5
• Product of 2-digit numbers
• Squaring Numbers in Range 26-50
• Squaring Numbers in Range 51-100
• Squares of Numbers That End in 5
• Squares Can Be Computed Squentially
• How to Compute Fast Any Square
• Adding a Long List of Numbers
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