# What is Subtraction?

If addition is about putting things together, subtraction is about**taking things away**. It could be as simple as eating two (2) apples from a pile of six (6) apples. You would wind up with four (4) apples left over. It could also be as complex as figuring out the number of organisms that die each year in a specific ecosystem.

Terms that tell you subtraction is happening:

Take some away.

Subtract an amount.

Lose some.

This minus that.

Give up some.

# Setting up the Problems

The big symbol you will learn in subtraction is the**minus**sign. It's a little dash (-) that goes between the two numbers in the problem. The order of the values in a subtraction problem is very, very important. In addition, you could move the numbers around and get the same answer. If you move numbers in a subtraction problem, the answer will be wrong. You cannot reorder numbers when you subtract.

**Examples:**

3 + 9 = 12

9 + 3 = 12 (You can reorder in addition and get the same sum.)

9 - 3 = 6

3 - 9 = -6 (See how the answer is a negative number? If you put the numbers in the wrong order on a test you will get the wrong answer.)

10 - 5 - 3 = 2

3 - 10 - 5 = -12

5 - 3 - 10 = -8 (Don't rearrange the numbers in your subtraction problems!)

The numbers in a subtraction problem also have special names. You don't need to memorize them, just know that they have special names. The first value is the

**minuend**. The second value (the one you are subtracting) is called the

**subtrahend**. The answer in a subtraction problem is called the

**difference**. Actually, you probably should remember that the answer to a subtraction problem is called the difference.

**Example:**

Problem: 9 - 3 = 6

Minuend: 9

Subtrahend: 3

Difference: 6

# Subtracting Single-Digits

We'll start easy and have you work with single-digit numbers that are less than 10. Since you are just starting out, you can do these problems with your fingers if you get stuck. The idea is simple. You start with a specific number of objects and you take a few away. If you start with four balls (4) and take away two balls (2) how many are left? 4 - 2 leaves you with two (2) balls left. Here are some examples...1 - 1 = 0

2 - 1 = 1

2 - 2 = 0

5 - 1 = 4

5 - 2 = 3

5 - 3 = 2

5 - 4 = 1

5 - 5 = 0

9 - 1 = 8

9 - 2 = 7

9 - 3 = 6

9 - 4 = 5

9 - 5 = 4

9 - 6 = 3

9 - 7 = 2

9 - 8 = 1

9 - 9 = 0

You will want to continue looking at the next couple of pages. We have some more complicated problems and we will go into the idea of borrowing and regrouping. You need to borrow when you subtract a larger number from a smaller one. That will happen all of the time when you start working with two-digit numbers.

- Overview
- Operations
- Addition
**Subtraction****1 to 10**- 1 to 20
- Borrowing
- Borrowing-2
- 2-Digit Numbers
- 3-Digit Numbers
- Multiple Values
- Integers
- Integers-2
- Workbooks
- Multiplication
- Division
- Activities

# Useful Reference Materials

**Wikipedia:**

*https://en.wikipedia.org/wiki/Arithmetic*

**Encyclopædia Britannica:**

*http://www.britannica.com/topic/arithmetic*

**Encyclopedia.com:**

*http://www.encyclopedia.com/topic/arithmetic.aspx*