Long Division: Tips and Tricks

Lesson Plan - Get It!

Audio:

If you said the next step that needs to be performed is divide, you are correct!

Long division consists of a series of steps you must repeat until you finish solving the problem.

• Since you know the next step in the problem is to divide, do you know what number you need to divide into?

This step in the long division process is a step students frequently make mistakes with because they want to divide into the dividend.

In reality, the solver is supposed to divide into the number at the opposite end of the problem — the number that has been subtracted and brought down (15).

In this lesson, you will review some of the most common mistakes students make when solving long division problems, and learn some strategies to help you avoid making those mistakes.

Long division consists of a lot of steps.

• Do you remember all five steps?

If you need a refresher, return to the first Related Lesson in our Long Division series, found in the right-hand sidebar.

Often, when students go to solve long division problems, they forget steps or get the steps mixed up.

One of the simplest things you can do to help you remember all the steps is write them down the side of your paper before you start solving. You can even just write the first letter in each step to help you save time.

Look at the example below.

The solver has the problem set up and has abbreviated the list of steps written to the side of the problem - divide, multiply, subtract, check, bring down. Also, remember this makes the acronym Does McDonald's Sell Cheese Burgers.

If you struggle with setting up your problem and lining up the numbers correctly, try writing the problem on graph paper.

Write one digit in each box. This will help you line everything up evenly:

Another common mistake students make when solving long division problems has to do with the times tables.

Knowing your times tables is essential to solving division problems, but if you are uncertain of the multiples for the divisor, write them out before you start solving.

Look at the example below. The solver has set up the problem, listed the steps, and listed the multiples for the divisor (3):

If you have the multiples listed, you can use them to help you when you start solving.

In the example below, the solver is on the multiplication step. Since he or she has the multiples listed, he or she just has to count to the fourth number down on the list because three is being multiplied by four.

The solver can quickly identify that 3 x 4 = 12:

The fourth and final trick you can use to help you solve can be used with the divide step.

In the example from the beginning of the lesson (also shown below), the solver was uncertain what number into which to divide.

An easy way to help you remember what number to divide into is to highlight the number at the bottom of the problem immediately after you bring the next number down. This will draw your eyes to that number, and will help you remember that is the number you need to divide into:

Earlier you predicted that the next step for this problem was to divide. You were correct!

Instead of finding how many times 3 goes into 13, like the first step, you are finding how many times 3 goes into 15. Use the list of multiples of 3 to find this answer.

Good job!

• What is the next step to solve this problem?

Use the abbreviated steps on the left to help you.

• Are you following along on your own piece of paper?

Complete the next steps. You should now have a quotient without any remainder.

However, do not forget to bring up the decimal into your answer.

• Do these tips and tricks help remedy any problems you are having with long division?
• Can you think of any other tips or tricks to help you solve long division problems?

Once you are comfortable, move on to the Got It? section to practice solving a few problems using these strategies.