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PSAT Prep: Help and Review18 chapters | 194 lessons

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Lesson Transcript

Instructor:
*Betty Bundly*

Betty has a master's degree in mathematics and 10 years experience teaching college mathematics.

In this lesson, we will learn about subtraction, which is the opposite of addition. We'll learn ways to picture simple subtraction problems, how to calculate the problems that are not so simple, and how to recognize subtraction in everyday situations.

**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 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.

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.

The answer to a subtraction problem can easily be checked using addition. For example, 37 - 25 = 12. To check this answer, add the subtrahend 25 and the difference 12. If your subtraction was correct, this sum will equal the original minuend 37. If we were to add 25 + 12, the answer would be 37, and this tells us that we subtracted correctly.

If you are not sure whether a problem calls for subtraction, certain words or phrases used in the problem may help. Besides the words minus, difference, or take away, other phrases often used to indicate subtraction are how much more, how many are left, and how many more. Also, whenever you need to know how much a value has increased or decreased, subtraction is often involved. Consider the following examples.

- You buy $13.42 worth of groceries and give the cashier $15.00. How much change should you receive? To find the change in a money transaction, you must subtract. $15.00 - $13.42 = $1.58.
- You are taking a trip and must travel 500 miles. If you have traveled 150 miles so far, how many more miles do you have to travel? The phrase 'how many more' means that you must subtract to get your answer. 500 miles - 150 miles = 350 miles.
- You have $46 saved in the bank. Your friend has $63 saved in the bank. How much more money has your friend saved? The phrase 'how much more' indicates subtraction. $63 - $46 = $17.
- If you are 66 inches tall and your sister is 61 inches tall, what is the difference in your heights? The key word here is 'difference'. 66 inches - 61 inches = 5 inches.
- The price of gas dropped from $3.89 per gallon to $3.55 per gallon. How much did the price change? In this problem, you are trying to find out how much the cost of a gallon of gas changed. $3.89 - $3.55 = $0.34.

**Subtraction** is a common mathematical operation that means you are taking away from some group or objects. The amount remaining after subtraction will be less. The three parts of any subtraction problem are the **minuend**, the part you start with; the **subtrahend**, the part being taken away; and the **difference**, the part left over.

Diagrams may be used to aid in simple subtraction problems. For two digit problems, you must line up equal place values and subtract from right to left. You may also have to borrow. In word problems, certain phrases are often used which indicate subtraction. Subtraction is also indicated anytime you need to know how much a value has changed.

Following this lesson, you should be able to:

- Define subtraction
- Describe the three parts of a subtraction problem
- Explain how to write and solve subtraction problems
- Recall everyday examples of subtraction and key words used in subtraction problems

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PSAT Prep: Help and Review18 chapters | 194 lessons

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