# Always a Multiple?

Think of a two-digit number.

For example, Alison chose 42 and added 24 to get 66.

Try a few examples.
Can you explain why your answer is always a multiple of 11?

Alison and Charlie came up with their own explanations:

If you can't play the videos, you can read a description below.

Alison arranged multilink to show four tens and two units for 42, and two tens and four units for 24.
She then put the four units with the four tens, and the two units with the two tens, giving six lots of eleven.

Charlie imagined a two-digit number $ab$, where $a$ represents the number in the tens column, and $b$ respresents the number in the units. This can be written as $10a+b$. Similarly, $ba$ can be written as $10b+a$.

Charlie added these together to get $11a+11b$, which he wrote as $11(a+b)$.

Here are some similar number tricks.
Can you use Charlie's or Alison's representation to explain how they work?

• Take any two-digit number. Reverse the digits, and subtract your answer from your original number. What do you notice?

• Take any three-digit number. Reverse the digits, and subtract your answer from your original number. What do you notice?

• Take any five-digit number. Reverse the digits, and subtract your answer from your original number. What do you notice?

Can you make up some number tricks of your own?

### THIS QUESTION

This is incredibly cool and fun to try out. I highly recommend.

### This Question

This is really cool, I highly recommend it.

### Really cool, easy to

Really cool, easy to understand

### COOL

it is good and fun and easy to understand

### it is always a multiple of 11

it is always a multiple of 11 because the reversed digits even it out, eg. 5+6 equals 11, and 60+50 equals 110

### maths

Hey i love the videos