Place Value Strategies for Solving Multi-Digit Arithmetic

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  • 0:03 Place Value Strategies
  • 0:44 For Adding
  • 1:56 For Subtracting
  • 3:11 For Multiplying
  • 3:55 For Dividing
  • 5:35 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, you'll learn some strategies based on place values that will make solving math problems easier and faster. You'll see how these strategies work for addition, subtraction, multiplication, and division.

Place Value Strategies

When it comes to solving basic math problems, there are many strategies that you can use. In this lesson, you'll learn how to use the place value strategies. The place value strategies are math strategies that use place values, like tens and hundreds, to help you solve basic math problems.

In this lesson, we will look at two types of place value strategies that you can use. You can use what is called compensation, where you regroup your numbers, or you can use expanded notation, where you break up your number into its place value parts.

Let's take a closer look at how you can use these place value strategies to help you when adding, subtracting, multiplying, and dividing.

For Adding

When you are adding, you can use either compensation or expanded notation.


First, let's talk about compensation. Let's look at how you can use compensation for the problem 27 + 13. When you use compensation, you regroup your numbers to make numbers that are easier to work with:

13 - 3 = 10

27 + 3 = 30

For this problem, you can regroup by taking 3 from the 13 and adding it to the 27 to make 30. So your problem is now 30 + 10. Isn't 30 + 10 a much easier problem to do than 27 + 13? Yes. 30 + 10 = 40 and 27 + 13 is also equal to 40.

Expanded Notation

To use expanded notation for the same problem, you break down your numbers into their place value parts, and then you add the parts separately.

27 = 20 + 7

13 = 10 + 3

27 becomes 20 + 7 and 13 becomes 10 + 3. You then add all your parts together. So:

20 + 10 + 7 + 3 = 30 + 10 = 40

For Subtracting

For subtracting, you can use compensation and expanded notation as well.


Compensation for subtraction problems is a bit different than for addition problems. For subtraction problems, you can regroup by adding the same number to all of the numbers in your problem. As you know, it is always easier to subtract if the number you are subtracting, or taking away, is a nice rounded number. So, say you are evaluating the problem 68 - 24. You would want to get the number you are subtracting (24) to end with a 0:

24 + 6 = 30

68 + 6 = 74

So, by adding 6 to each number, you will now have 74 - 30. Well, that's easy:

74 - 30 = 44

Expanded Notation

With expanded notation, you expand only the number you are subtracting, and then you subtract those parts from the number you are subtracting from. For example, for the problem 68 - 24, you are subtracting 24 from 68. So, you expand your 24 and then subtract those parts from 68:

24 = 20 + 4

68 - 20 = 48

48 - 4 = 44

For Multiplying

When you multiply, expanded notation will work. For example, when multiplying 35 * 12, you can do something like this:

place value strategies

Here, you expanded both your numbers and then you made sure that you multiplied all these parts with each other:

35 = 30 + 5

12 = 10 + 2

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