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## What is sub

**sub is the short form of subtraction.**

**What Is Subtraction?**

**Subtraction**

subtraction in mathematics means you are taking something away from a group or number of things. When you subtract, what is left in the group becomes less. An example of a subtraction problem is the following: 5 – 3 = 2.

Notice that there are three parts to the subtraction problem shown. The part you start with is called the **minuend**. The part being taken away is called the **subtrahend**. The part that is left after subtraction is called the **difference**. In the problem 5 – 3 = 2, the number 5 is the minuend, the number 3 is the subtrahend, and the number 2 is the difference.

## Addition vs. Subtraction

Addition and subtraction are closely linked. Although addition is the opposite of subtraction, it is also true that every addition problem can be rewritten as a subtraction problem. For example, the problem 3 + 2 = 5 can be rewritten as the subtraction problem 5 – 3 = 2 or 5 – 2 = 3. Notice that the sum 5 in the addition problem became the minuend and the other numbers became the subtrahend and the difference.

In addition, you probably learned something like the following: if 3 + 2 = 5, then 2 + 3 = 5. In other words, you can change the order of the numbers you add and get the same answer. This cannot be done in subtraction. For example, 5 – 3 and 3 – 5 do not equal the same value.

## Methods of Subtraction

There are various methods of subtraction. One method is to use a diagram showing what you start with, what you are taking away, and what you are left with.

For example, the problem 5 – 3 might be described with this diagram:

Another method to describe and aid in subtraction is to use a number line.

To indicate the problem 5 – 3, an arrow is drawn starting at the number 5, moving three units in the direction of the smaller numbers, and ending on the final difference 2.

When subtracting numbers with two or more digits, it’s important to write the numbers one on top of the other so that the same place values are lined up, as shown in the problem 37 – 25.

You then subtract, starting with the digits farthest to the right. So, in this problem, you would start with 7 – 5 and place the difference, 2, below the numbers. Then, you would subtract 3 – 2 and place the difference, 1, below those numbers. This gives you the solution 37 – 25 = 12.

When subtracting numbers with two or more digits in this fashion, you may find that the minuend is not big enough to subtract the subtrahend. In this case, you will have to borrow from the nearest non-zero minuend to the left. To **borrow**, you take one from the nearest minuend and count that as ten to add to the other minuend to the right. This will make a number large enough to subtract from.

Many times, we are given a name for the things we are subtracting. For example, 10 puppies – 4 puppies = 6 puppies. In this example, notice that all three parts of the subtraction problem had the same unit, which was puppies. If a unit is given in a subtraction problem, then all the parts of the problem must have the same unit.

Additional Activities

**Extra Practice – Subtraction Word Problems**

In the following practice problems, students will interpret real-world situations described in word problems and find the answer using subtraction.

## Practice Problems

1. You have $30.00 and want to buy a sweater priced at $23.75. How much change will you receive?

2. There are 5,280 feet in a mile. You have walked 2,300 feet. How many more feet must you walk in order to walk one mile?

3. You have a dozen eggs and a recipe which requires 4 eggs. How many eggs are left after you make the recipe?

## Solutions

1. To find the change, we must subtract the cost of the sweater from the $30.00. To calculate $30.00 – $23.75 we will need to use some borrowing:

The change will be $6.25.

2. To find how many feet are left to walk, we need to subtract 2,300 from 5,280.

If you walk 2,980 more feet, you will have walked one mile.

3. There are 12 eggs in one dozen. To find how many eggs are left, we need to perform the subtraction 12 – 4. Imagining on a number line, we move 4 spots to the left of 12 to get 8. There will be 8 eggs left.

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