When multiplying by seven we are following a similar rule to multiplying by twelve where we double the number but for seven we only add "half" the neighbor.
The Rule for Multiplying by Seven
- Double the number and add 5 if the number is odd, and add “half” the neighbor
To explain this rule we will look at our multiplicand 3456 using our red box.The digit we are now focusing on is the 5 and its neighbor is the 6. Following the rule we first double the 5 to give us 10, now as 5 is odd we also add another 5 giving us 15. Then we add "half" the 6 which is 3 giving us a total of 18.
Lets have a look at a complete example in more detail.
An Example - Multiplying 2734 By 7
For this example we will look at the following multiplication:
Placing our red box we have 4 in the box. We double the 4 to get 8, we have no neighbor to add so our first digit to write is 8.
Moving our box to the left by one digit.
We have 3 which we double to get 6 and then we add 5 because 3 is odd, giving us 11. Half of 4, the neighbor, is two so adding this we get 13. We write down the 3 and carry the 1.To show we are carrying one I will put a small 1 above the digit in the product we just wrote down.
As we move the box we now have 7, doubling this gives 14, adding 5 because 7 is odd now gives us 19. Adding 1 which is "half" of 3 we now have 20. Finally carrying the 1 we have a total of 21.We write down the 1 and carry the 2, so I will write a small 2 above the 1 we just wrote down.
We have 2 which doubled is 4. Now we add 3 which is "half" of 7 giving us a total of 7 to which we add the 2 carried over for a total of 9.We write down 9.
The number is zero, doubled is still zero. Adding "half" of 2 is 1 which is the last digit of our answer.Writing down the 1 we have the answer 19138.
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