# Subtraction of natural numbers

**Subtraction** is also one of the four basic arithmetic operations (the others being: addition, multiplication and division).

## The basic concept of subtraction

In addition you add (objects) members to a group, while in subtraction you “take them away”. When you doing that, you’re making the starting group of objects smaller.

For example, *let’s say you have five candies to start with. If you eat two of them, you are left with three uneaten candies.*

### Elements of subtraction

The number that’s being subtracted from is called the **minuend**, while the number subtracted from the minuend is the **subtrahend**. The result of the subtraction is called the **difference** and the sign for subtraction is “-“. The basic principle behind subtraction is this:

### How to subtract natural numbers?

The most popular method of performing subtraction with multiple digit numbers relies on doing several subtractions using the more manageable, single digit numbers that form the multiple digit numbers in question.

You begin by subtracting the digit with smallest **positional value** (the one on the far right) of the subtrahend from the digit with the same positional value (again, the one on the far right) of the *minuend*. The number you got as a result from that subtraction (the difference) will have the same positional value as the *minuend* and *subtrahend* did. Then you move to the digits with the next greatest positional value (one digit to the left) and repeat. You do that until you run out of digits. Like this:

### Examines:

**Examine 1.**

The subtraction in the previous example should look like this:

-> $7$ is lower than $8$, so we can’t subtract. “Borrow” the $1$ from the tens digit. Now we have $17$ and now we can subtract.

->$17 – 8 = 9$. Write down $9$.

-> We borrowed $1$ from the ‘tens’ digit so it is now $8$ instead of $9$. $8 – 8 = 0$. Write down $0$.

-> $2 – 1 = 1$.

-> The final result is number $109$.

**Examine 2.**

$\ 948 – 652 – 121 = 296 – 121 = 175$

The process of subtracting three three-digit numbers can be divided into two subtractions of two three digit numbers. In our example the process of subtracting should look like this:

-> $8 – 2 = 6$.

-> $4$ is lower than $5$ so we can’t subtract. Borrow the $1$ from the ‘hundreds’ digit. Now we have $14$ and we can subtract. $14 – 5 = 9$. Write down number $9$.

-> Now the hundreds digit is $8$ because we borrowed $1$ for the previous subtraction. $8 – 6 = 2$. Write down number $2$.

-> Now we need to subtract number $296$ with $121$. $6 – 1 = 5$. Write down $5$.

-> $9 – 2 = 7$. Write down $7$.

-> $2 – 1 = 1$. Write down $1$.

-> The final result is number $175$