Multiply by SevenWhen 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

  1. 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 Red BoxThe 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:Multiplying by Seven Example 1 Setup

Step 1
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.Multiplying by Seven Example 1 Step 1

Step 2
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.Multiplying by Seven Example 1 Step 2To show we are carrying one I will put a small 1 above the digit in the product we just wrote down.

Step 3
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.TS_M7_E1_Step3We write down the 1 and carry the 2, so I will write a small 2 above the 1 we just wrote down.

Step 4
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.Multiplying by Seven Example 1 Step 4We write down 9.

Last Step
The number is zero, doubled is still zero. Adding "half" of 2 is 1 which is the last digit of our answer.Multiplying by Seven Example 1 Last StepWriting down the 1 we have the answer 19138.

If you have any comments or questions please leave a comment below.