You have seen in multiplying by eleven that we added the neighbor. For multiplying by six we also use the neighbor but this time we only use "half" the neighbor.
If you haven't read the definition of the "half" please read before going on.
The Rule For Multiplying By Six
- Add 5 to the number only if it is odd; Add “half” the neighbor.
Lets go through a couple of examples in detail just to make sure we know what the rule means.
An Example - Multiplying 345 By 6
For our first example we will look at 345 x 6.
We add our red square to include the last digit in the multiplicand. We have 5, which is an odd number so we add 5 to it giving us a sum of 10, half of zero is zero so our sum remains unchanged. We write down the zero and carry the one. We put a little dot above the zero to show the carry.
We move the red square one digit to the left. We now have 4 plus 1 from the carry is 5, plus "half" of 5 is 2, giving us a total of 7, which we write.
We move the red square one digit to the left. We have 3, plus 5 because it is odd, giving us 8, then we add half of 4 which is 2, giving us a total of 10. We write the zero and put a dot just above it to show the carry.
We move the red square one digit to the left. Now we have zero, to which we add 1 from the carry and then we add half of 3, which is 1, giving us a total of 2. We write the 2 down and we have our answer of 2070.
An Example - Multiplying 789 By 6
We will look at another example, 789 x 6.
We put our red square in our starting position over the last digit of the multiplicand. We have 9, which is odd so we add 5 giving us 14. The neighbor is zero so half of that is still zero leaving our total as 14. We write the 4 and put a dot to show that we are carrying the one.
We move our red square one step to the left. Now we have 8 plus the 1 carried over, plus half of 9 which is 4, giving us a total of 13. We write the 3 and then put a dot to show we carry the 1.
Moving our red square we now have 7, which is odd so we add 5 giving us 12. We now add the 1 carried over, for a total of 13 to which we add half of 8 which is 4. So we have a total of 17, so we write down the 7 and carry the one, putting a dot above the 7.
Moving the red square to the left we now have zero, to which we add the one carried over, then we add half of 7 which is 3 giving us a total of 4. We write down the 4 giving as an answer of 4734.
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