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Math for Kids23 chapters | 325 lessons

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Instructor:
*Nola Bridgens*

Nola has taught elementary school and tutored for four years. She has a bachelor's degree in Elementary Education, a master's degree in Marketing, and is a certified teacher.

In this lesson, you will learn the pattern of dividing, multiplying, and subtracting that makes up the expanded notation method for division. You will then use this method to solve some problems.

Picture yourself blowing up a balloon. What happens when you blow air in? It expands - it gets bigger. Now look at this: 300 + 40 + 7. You remember what this is, right? It is the number 347 written in expanded notation - just a bigger form of the same number. Did you know that there is an **expanded notation method for division** which uses expanded notation to solve long division problems? Let's see how!

As we just reviewed, expanded notation keeps a number's place value and helps us visualize exactly what the numbers represent. Solving long division problems with expanded notation is just a repeated series of steps that involves dividing, multiplying, and subtracting. As with all division problems, it is important that you know your multiplication facts very well, as it is a major part of the long division process.

Remember this pattern: 'Divide, Multiply, Subtract' (÷) (x) (-) and you will do just fine. Let's think about this pattern as we go through the first example.

Step 1: (÷)

How many times can 2 go into 86?

We know that 2 can go into 8 four times, so it can go into 86 at least 40 times

Step 2: (x)

Multiply the answer (40) by the divisor (2) and write the answer under the dividend.

Step 3: (-)

Subtract your answer (80) from the dividend (86) and the answer is 6.

Now we repeat the (÷) (x) (-) pattern.

Step 4: (÷)

How many times can 2 go into 6?

6 ÷ 2 = 3

Step 5: (x)

Multiply the answer (3) by the divisor (2) and write the answer under the second number of the dividend.

Step 6: (-)

Subtract your answer (6) from the second number of the dividend (6) and the answer is 0.

When you have no more numbers to divide into, you are finished. You then find the final answer by adding the numbers above the division sign. In this problem, you add 40 + 3 and the answer is 43.

Let's take our 'Divide, Multiply, Subtract' pattern and try a division problem with a three digit dividend.

Step 1: (÷)

How many times can 3 go into 600?

We know 3 goes into 6 twice, so it will go into 642 at least 200 times

Step 2: (x)

Multiply the answer (200) by the divisor (3) and write the answer under the dividend.

Step 3: (-)

Subtract your answer (600) from the dividend (642) and the answer is 42.

Now we repeat the 'Divide, Multiply, Subtract' pattern.

Step 4: (÷)

How many times can 3 go into 42?

We know 3 will go into 4 one time, so it will go into 42 at least 10 times

Step 5: (x)

Multiply the answer (10) by the divisor (3) and write the answer under the dividend.

Step 6: (-)

Subtract your answer (30) from the remaining numbers of the dividend (42) and the answer is 12.

Now we repeat the 'Divide, Multiply, Subtract' pattern again.

Step 7: (÷)

How many times can 3 go into 12?

12 ÷ 3 = 4

Step 8: (x)

Multiply the answer (4) by the divisor (3) and write the answer under the 12.

Step 9: (-)

Subtract your answer (12) from the remaining numbers (12) and the answer is 0.

When you have no more numbers to divide into, you are finished and the final answer can be found by adding the numbers above the division sign. In this problem, you add 200 + 10 + 4 and the answer is 214.

The **expanded notation method for division** is just a repetition of dividing, multiplying, and subtracting for each number in the dividend. Using expanded notation in long division shows place value and helps us remember what the numbers represent.

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Math for Kids23 chapters | 325 lessons

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