Division in Math (2024)

• Division is an opposite game – If you multiply numbers, you can “undo” them using division. It’s multiplication’s opposite function!
• There’s a few signs to look for – There are three main symbols for division.
• You won’t always get “even Stevens” – Sometimes, you’ll have a little left over. That leftover number is known as the “remainder.”

• Key takeaways
• What is division?
• Common symbols and terminology
• Properties of division
• How to divide in 6 easy steps
• What is long division?
• Working with remainders
• Let’s practice together!
• Practice problems
• FAQs

Division is one of the most important math skills you’ll practice, helping you to undo multiplication problems or break off parts of a “whole.” We know it looks complicated, but it really isn’t! You just need to know what signs to look for that tell you when division is needed.

Like addition and subtraction, division uses a few special terms and symbols. Knowing these can help you to work out your problems quickly and correctly.

We know it sounds complicated right now —but with a little practice and this handy guide, you’ll be flying through your math homework in no time!

It can also be written horizontally: 10 ÷ 2, as 10/2 , or using a division bar: 2 ⟌ 10.

No matter how you see it, though, the use for it is always the same. You’re breaking down a number or quantity into smaller pieces.

Let’s take a look at some key terms that’ll help you build your division skills.

Division is a simple mathematical operation, but there are still a few terms to know to help you find the correct solution.

Here are the terms you need to know to solve division equations with ease:

➗ — This is known as a division sign, and it tells you that a number needs to be broken down into multiple pieces.

⟌ — This is the division bar, and it also means to divide. On the outside of the bar, you’ll see the number determining how many pieces are needed from the whole (the divisor), and the dividend on the inside, which is what you’ll be dividing. The answer goes on the top of the bar.

∕ —This is known as the division slash. Generally, the divisor comes first, and the dividend will appear second.

Knowing these terms will help you to know what numbers you’re dividing and how you should set up and read your equations. There are four main terms to know as you work through your arithmetic operations.

• Divisor – The divisor is the number that is determining how many pieces are needed from the whole. For example: in 15 ÷ 3, three would be the divisor. It’s also the number located outside of the bracket when you see a division bar.
• Dividend – The dividend is the number that’s being divided, and it’s found inside the division bar.
• Quotient – The quotient is your answer, which goes after the equals (=) sign or on the top of the division bar.
• Remainder – In some cases, you’ll have a remainder —which means that the divisor can’t be equally divided into the dividend. The remainder is written to the side of your equation next to the division bar.

15 3

We know that the problem above can feel overwhelming —so we want to take this moment to remind you that what we’re doing is breaking down a number into smaller numbers (or smaller groups of numbers).

First things first, we have to prepare the equation. Feel free to keep it horizontal, write it vertically, or use a division bar if you’d like. Use whatever method you feel comfortable with.

Remember: The dividend (15) belongs inside the division bar if you choose to use that method.

As we begin to divide, we need to start from the first digit from the left (in this case, 1) and ask ourselves: Does the divisor (3) go into 1 at least once?

The answer here is “no,” so we will then evaluate the first AND second integer (making 15) as a dividend.

We ask again: Does the divisor (3) go into 15 at least once?

Now, the answer is “yes” —we just have to count how many times 3 can go into 15, starting our division process.*

*NOTE: You can do this by using basic arithmetic operations (such as multiplication) to “undo” the problem (i.e., 3 x ? = 15) or counting by threes until you reach 15.

In our case, 3 goes into 15 a total of five times.

Now, we have to check our work. We have to ask ourselves: What is 5 x 3? Does it equal our dividend? If it does, you’re golden —you’ve done it!

Do the multiplication, and then subtract your product to ensure that there’s no other steps remaining (like you’d see in the case of a remainder).

In our example, 15 – 15 = 0…so no remainder or further action is needed.

In other problems, if you did have a three or four digit dividend, you might need to bring down the next digit in the dividend, and determine if your divisor divides that number cleanly.

You would then repeat the division process, putting your answer over the third or “next” place above the division bar as part of the quotient.

Next, yo would repeat step 4 to determine if more steps in the division process are needed.

In our example, we don’t have to do this, so we will leave it as is. Good work!

• We know that our divisor is going to be 6, and our dividend (the number being divided) is 20. We identify them, and we put them into a division bar, like this:
  • 6 ⟌ 20
• We ask: “How many times can 6 go into 2?”
• 6 is greater than 2, so we will not be able to put a number over the 2. We then consider, “How many times can 6 go into 20?”
• Well, this is a bit of a challenge! 6 does not go into 20 evenly. 6 x 3= 18, and 6 x 4= 24. So, 6 can go into 20 three times, but it won’t go evenly.
• So, we add the 3 over the 0, above the division bar.
• We put the product of 6 x 3 (our divisor x our quotient) under the dividend and subtract to determine if the a remainder in our difference.
• There is a remainder of 2. We write our quotient as: 3R2.

• We know that our divisor is going to be 1, and our dividend (the number being divided) is 5. We identify them, and we put them properly into a division bar.
• We ask: “How many times can 1 go into 5?”
• Instead of working the problem counting or using multiplication, we remember the Division By 1 Property.
• We put 5 at the top of our division bar, since any integer that is divided by 1 will always be itself.
• There is no remainder for these types of Division By 1 Property problems. We can move on to the next problem.

• We know that our divisor is going to be 2, and our dividend (the number being divided) is 0. We identify them, and we put them properly into a division bar.
• We ask, “How many times can 2 go into 0?”
• Instead of working the problem counting or using multiplication, we remember the Division Of 0 By (Any) Number Property.
• We put 0 at the top of our division bar, since any integer that attempts to divide 0 as a dividend will always result in a quotient of zero.
• There is no remainder for these types of Division Of 0 By (Any) Number Property problems. We move on to the next problem.

You’ve done great so far —and you’re well on your way to mastering the art of division. Don’t be afraid to keep trying and make mistakes.

Practice makes perfect, so we’ve given you a few more problems to practice as you work to perfect your skills. Remember: You can always scroll up to walk through the tutorials and refresh yourself on the terms, placement, and properties you’ll need to solve these correctly.

By the end of this session, we’re confident that you’ll be ready to claim that A+ on your next math test. You can do it!

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