Lesson Objectives
• Demonstrate the ability to construct a number line for the whole numbers
• Learn about the subtraction operation with whole numbers.
• Learn how to label the parts of a subtraction problem as subtrahend, minuend, and difference
• Learn how to subtract two whole numbers using a number line.

## Subtracting Whole Numbers

What is Subtraction? Subtraction is the mathematical operation of taking away and is normally accompanied by "-" (the subtraction symbol). The main idea is to find out how much is left after one amount is taken away from another. Subtraction is the opposite operation of addition. The subtraction operation is usually the second operation we learn in elementary school, after mastering addition. Let's think about the subtraction concept using an example. Suppose we started out with 6 boxes: Now, let's suppose we wanted to take away or subtract away 2 boxes. How many boxes would be left? We could simply cross out 2 boxes and count what remains: We can see from our picture above that we have 4 boxes remaining. This example can be translated into the subtraction problem: 6 - 2 = 4.
There are three parts to a subtraction problem:
• Minuend - the starting amount or leftmost number
• Subtrahend - the amount being taken or subtracted away from the minuend. This will be the number that comes after the subtraction symbol
• Difference - the result of the subtraction operation. We start with the minuend and subtract away the subtrahend, the result is the difference
So using our example, we would label the 6 as the minuend. This was the starting number of boxes. The 2 would be our subtrahend. This was the number of boxes that we removed or subtracted away. The 4 would be the difference. This is the result of subtracting 2 away from 6. Notice how working backward will give us a related addition problem:
4 + 2 = 6. In other words, the difference added to the subtrahend will give us our minuend back. This should make perfect sense. If we start with an amount such as 6 and we take away an amount such as 2, the result is 4. If we reverse the process and start with 4, and then add back the 2 that was taken away, we will end up with 6 again.
When we first learn to subtract, we utilize counting and related addition problems, until we can memorize the single-digit subtraction facts. Once these are known, we can use the process of vertical subtraction to subtract with numbers that are as large as we would like.

## Subtracting Whole Numbers using a Number Line

Recall that we learned how to perform addition with whole numbers using a number line. The same can be done for subtraction. Again this process may seem trivial now, but it will help tremendously when we encounter the addition and subtraction of integers. Before we dive into number line subtraction, let's recall that addition is commutative:
3 + 4 = 7
4 + 3 = 7
Changing the order of the addends does not change the sum. This is not true with subtraction.
7 - 4 = 3
4 - 7 ≠ 3
The main point to understand is that the order matters when we subtract, so there is no commutative property for subtraction.

### Subtracting on a Number Line

• On the number line, start at the leftmost number of the subtraction problem (the minuend)
• Move to the left by the number of units being subtracted away (subtrahend)
Recall that numbers increase moving to the right. Notice how with number line addition we moved right, as the addition of two non-zero whole numbers results in a larger number. The opposite is now true for subtraction. This operation is taking away, so the subtraction of one non-zero whole number from another will result in a smaller number. This means we will move left on the number line. Let's take a look at a few examples:
Example 1: Subtract 9 - 5, using the number line
• Start out at the number 9, the leftmost number of the subtraction problem
• Move to the left by 5, the number of units being subtracted away
• We end up at 4, which is our answer
• 9 - 5 = 4
Example 2: Subtract 15 - 8, using the number line
• Start out at the number 15, the leftmost number of the subtraction problem
• Move to the left by 8, the number of units being subtracted away
• We end up at 7, which is our answer
• 15 - 8 = 7