# how to add up quickly

Numbers

## Why?

The traditional method of adding numbers relies on remembering too much. We will see a method where you don't need to add much beyond 11. The method takes a little practice, but once you master it it becomes easier and less prone to error. There might not be a big advantage for small numbers or only a few numbers, but for several columns and a long list, it is very good.

## First - a rediculously simple example.

Let's add 6 + 5. Of course, we know instantly it is 11, but let's use the complete method to help gain insight on how it works:

` 6`
``` 5
--
00
1
--
11

I will re-state this as letters to allow us to talk about each in turn.

a
b
--
0c
d
--
ef
```

This is the method used: a+b = 11 so we write 1 in position d. There are none left over when 11 is taken from 11, so we set c to zero. Put 0 in front of c as a reminder for the next step.

f = c + d = 0 + 1

e = 0 + 0 + d = 1

If you did not follow it - don't worry. Paradoxically, a more complex example will help, and this simple example will then later help you understand how it works.

## A more complex example

` 8`
` 3`
` 2`
` 6`
` 7`
``` 1
```
`--`
`0x`
` y`
`--`
```pq

```

Here is the method: 8+3 = exactly 11, so y becomes 1

2+6+7+1=16 which is 5 more than 11, so y becomes 2. x is the remainder 5. q=x+y and p=0+0+y.

` 8`
` 3`
` 2`
` 6`
` 7`
``` 1
```
`--`
`05`
` 2`
`--`
```27

```

## A two column example

87 ( Do First column )

67 → 7+7 = 14 which is 3 more than 11 so d becomes 1 and

56 → 3+6 = 9 keep going

78 → 9+8 = 17 which is 6 more than 11 so d becomes 2 and b=6

---

0ab

cd

---

efg

87 ( Do Second column )

67 → 8+6 = 14 which is 3 more than 11 so c becomes 1 and

56 → 3+5 = 8 keep going

78 → 8+7 = 15 which is 4 more than 11 so c becomes 2 and a=4

---

0ab

cd

---

efg

g = b + d = 6 + 2 =8

f = a + c + d = 4 + 2 + 2 = 8

e = 0 + 0 + c = 2

## But it looks complicated!

It's less familiar - so it seems complicated. When you add long lists of numbers, then it becomes very efficient. Scan the column, and look for pairs and tripples of numbers which add to 11, and just cross them out. Take note of how many pairs and triples you find. In contrast, the normal method means you need to deal with an ever increasing value. It gets harder and more prone to error as the number grows.

## One last thing to notice.

Sometimes, you end up with a total of 10. What do you do with this? It's a double digit and yet not 11 or more so it seems like an edge-case. Here is an example:

` 6 The 6 and 5 add to 11 So y = 1`
``` 5
9
1 The 9 and 1 make you end up with x=10
```
```--
0x
y
--
ab

```

When you get 10, write it as "tick zero" like this: '0. This allows you to squeeze it into one column.

```b = '0 + y = '0 + 1 = 11
a = 0 + 0 + y + the one carried from b = 0+0+1+1 = 2

```