T.J. is currently a grade 5 teacher and Vice-Principal. He has a master's degree in Educational Administration and is working toward an Ed.D. in Educational Leadership.
What Is Long Division?
Alex was in the middle of building a small house and he lost track of time. Suddenly, it was getting dark. With no shelter, he was afraid of wild animals and other intruders. But he did have one hope: he had a pile of bricks (56 blocks, to be exact) and in a last-ditch effort, he was going to build a shelter.
To do it, Alex would need to take the 56 blocks and turn them into four walls. How would he figure out how many blocks would go into each wall? He would use long division, the method of finding the answer to complex division problems by writing out each step of the process.
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Setting Up the Problems
When using long division, we write out equations using a long division bracket. The dividend (the number being divided) goes inside the bracket, while the divisor (the number by which the dividend is being divided) goes to the left of the bracket. Alex's problem would look like this, with the dividend (56) inside the brackets and the divisor (4) outside the bracket :
Once you begin to solve the problem, the quotient, the answer to the division problem, will be placed on top of the bracket.
There are four main steps to solving a long division problem:
- Drop down the last digit
Let's work through these steps with Alex's long division problem.
Start by looking at the digit that's in the largest place value of the dividend, which is always the first digit (in this case, it's 5). You'll find how many times the divisor goes into the largest place digit. So, in this case, you need to find how many times 4 goes into 5. The quotient is 1, and that goes above the bracket over the first digit of the dividend:
Next, multiply the divisor outside of the bracket by the quotient on top of the bracket. In Alex's case, that would be 4 x 1, which equals 4. Place the answer (4) beneath the first digit of the dividend:
Now, subtract the multiplication answer found in the last step from the first digit of the dividend. In this case, it would be 5 - 4, which equals 1.
5. Drop down the next digit
So far, only one digit in the dividend has been divided, so the other digit still needs to be divided. To do that, bring it down and add it to the leftover 1:
Finish up by dividing this number by the divisor: 16 / 4 = 4. Place this answer to the right of the quotient above the bracket, which will give you your final answer: 14.
Sometimes, the divisor will not fit perfectly into a dividend, like it did in our last problem. In these cases, division problems create remainders, or leftover numbers. Let's look at an example, and you'll see the steps are mostly the same. Say that Alex wants to make 4 walls from 38 blocks:
When trying to divide the first digit in the dividend, you will notice that it is smaller than the divisor. So, the whole number needs to be divided: How many times can 4 go into 38 without going over? (Feel free to use your multiplication chart for help.) The answer is 9:
Next, multiply the quotient (9) by the divisor (4) to get 36. The 36 goes under the dividend:
Subtract that number from the dividend:
You'll notice there's 2 left over. This is called a remainder. When you have a remainder, you write the quotient out like this:
So, in this case, each wall would have 9 blocks and there would be 2 left over.
Long division is the method of finding the answer to complex division problems by writing out each step of the process. For long division problems, remember to follow the divide, multiply, subtract, and drop down process until each digit in the dividend has been divided. The quotient is the answer to the division problem. Sometimes the divisor will not fit perfectly into a dividend. These leftover numbers are called remainders.
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Long Division Steps: Lesson for Kids
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