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:

**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.

**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.To 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.We 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.We 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.Writing down the 1 we have the answer 19138.

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

nikhil says

September 1, 2017 at 11:14 pmhow we can solve 337×7

Tony says

September 2, 2017 at 5:45 pmHi Nikhil,

To solve that you would use the following:

d c b a

0 3 3 7 x 7

——-

2 3 5 9

a) Double 7, then add 5 since 7 is odd. This gives 19, write 9 and carry 1.

b) Double 3, then add 5 since 3 is odd, add “half” of 7 which is 3, add carry of 1. This gives 15, write 5 and carry 1.

c) Double 3, then add 5 since 3 is odd, add “half” of 3 which is 1, add carry of 1. This gives 13, write 3 and carry 1.

d) Take “half” of 3 which is 1, add carry of 1. Which gives 2 and final answer of 2359.

I ignored doubling the zero in d)