Long Division: How to Solve

Contributor: Meghan Vestal. Lesson ID: 11808

Do you kind of know how to divide numbers, but dividing into long numbers seems too hard? Learn and practice five easy steps to dividing into numerous numbers, and long division won't take so long!

categories

Elementary

subject
Math
learning style
Visual
personality style
Lion, Beaver
Grade Level
Intermediate (3-5)
Lesson Type
Dig Deeper

Lesson Plan - Get It!

Audio:

Mrs. Smith bought a bag of candy. There are 108 pieces of candy in the bag. What can Mrs. Smith do to make sure she distributes the candy evenly to the nine students in her class?

To make sure each student in Mrs. Smith's class is given the same amount of candy, Mrs. Smith would need to divide the candy among the nine students.

Because 108 is a big number, how can Mrs. Smith break it into equal parts? Giving each student a piece of candy, one at a time, until there was none left would take a long time. Is there a process Mrs. Smith can use that would save time and ensure each student is given the same amount? Share your ideas with your teacher or parent.

To determine the answer to this problem, Mrs. Smith needs to perform long division. Long division is a series of steps used to divide large numbers. There are five steps for solving a problem using long division:

  1. Divide
  2. Multiply
  3. Subtract
  4. Check
  5. Bring down

You can remember the order of these steps by remembering the saying, "Does MacDonald's Serve Cheese Burgers."

Let's see what each of those steps looks like by solving the problem from the beginning of the lesson.

Before you start solving, you need to set up your problem correctly. The number being divided into equal parts (108) should be on the inside of the division sign. This is called the dividend. The number of parts it is being broken into (9) should be on the outside of the division sign. This is called the divisor. The answer, which you will write on top of the division sign, is called the quotient.

After you have your problem set up, you can begin solving.

The first step is to divide. You do not want to divide 9 into the entire dividend to start. You want to divide the 9 into one digit at a time. Part of the reason for this is because when you are going through the steps of solving a long division problem, you can only write one digit above the division sign at a time. For this problem, if you divided 9 into 108, you would have to write more than one digit above the line. The 9 cannot be divided into 1, so you will start by dividing it into 10. How many times does 9 go into 10? Tell your teacher or parent.

The 9 goes into 10 one time. Write a 1 above the 0:

The next step is to multiply. Multiply the number you just wrote on top of the division sign (1) by the divisor (9). Write the product (9) below the 10:

The third step is to subtract. You will need to subtract the product (9) from 10. Set up a subtraction problem and write the difference below the line. Remember, you are subtracting from 10 because that is what you divided into:

The fourth step is check. This step helps you make sure you are solving correctly and lets you know if there is anything you need to go back and fix. To check the problem, look at the difference you got when you subtracted. Compare the difference to the divisor. If the difference is less than the divisor, you are solving correctly. If the difference is equal to or greater than the divisor, go back to the first step (divide) and try resolving the problem. Since 1 is less than 9, you are safe to continue solving this problem.

The final step is to bring down. Bring down the next number in the dividend (8) and write it next to the difference (1):

Even though you have gone through all of the steps, you are not finished solving!

You must continue solving until there are no more numbers left in the dividend to bring down. Now, you must repeat the process again, starting with the first step (divide). What number do you think you should divide into next? Tell your teacher or parent.

You may have thought you should divide into 8 since that is the next number in the dividend, but this is not correct. You should divide into the number at the bottom of the problem; the difference combined with the number you brought down (18). Divide 9 into 18 and write the answer above the division sign. The 9 goes into 18 two times. Write a 2 above the division sign at the top of the problem:

What is the second step in solving a long division problem? Tell your teacher or parent.

You should multiply next. Multiply the number you just wrote (2) by the divisor (9). Write the product (18) below the 18:

The third step is to subtract. Like before, set up a subtraction problem and write the difference (0) below the line:

The fourth step is check. Zero (0) is less than 9, so it okay to continue solving the problem.

The final step is to bring down. There are no numbers left in the dividend to bring down. This means you are finished solving. The number written above the division sign is your final quotient. Mrs. Smith can give each of her nine students twelve pieces of candy.

There are many steps to long division, so it can help to see multiple examples. Watch this clip from Math Antics - Long Division to learn more about solving problems using long division:

 

When you are finished watching the video, tell your teacher or parent why you think it is important to be able to solve long division problems.

Then, move on to the Got It? section to practice solving your own long division problems.

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