Multiplying by five is similar multiplying by eleven except we only add "half" the neighbor. When adding "half" the neighbor we also add 5 if the number is odd.

## The Rule for Multiplying By Five

*Use “half” the neighbor, plus 5 if the number is odd.*

When multiplying by five we only look at the current digit to see if it is odd or even. If it is if even we start with zero, if odd we start with 5, then we add "half" of the neighbor.

## An Example - Multiplying 7346 by Five

We setup or calculation in our normal way.

**Step 1**

We put our red box over the last digit, we have 6, which is even so we start with zero. The neighbor is also zero so our first sum is zero, so we put down zero.

**Step 2**

Moving to the left we have 4, which is even so we start with zero. The neighbor is 6 so half is 3. We write the 3 down.

**Step 3**

Moving left to the next digit we have 3, which is odd, so we start with 5. The neighbor is 4 so half of this is 2. Adding the 2 to the 5 we have 7, so we write this down.

**Step 4**

Moving left again we now have 7, which is odd, so we start with 5. The neighbor is 3 and half is 1 so 5 plus 1 gives us 6 so we write 6 as the next digit of the answer.

**Final Step**

Moving to the end we have zero, which is not considered odd, so we start with zero. The neighbor is 7 and half this is 3, so we write down the 3 giving us our answer of 36730.

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

Sara says

2293*5 first number is odd should I not add 5

Tony says

Yes, for multiplying by five, you add “half” the neighbor and add 5 if the number is odd. The first number, 3, has no neighbor but is odd so you add 5.

Urvashi says

This is so useful and amazing, I wish I’d known about Trachtenberg earlier!

I’ll definitely be sharing this with my peers at school ❤️️

Thanks!