Division isn’t just a math problem to solve—it’s a life skill we use all the time! Think about splitting a pizza with your family or figuring out how many days your $10 allowance will last if you spend $2 a day.
Each time you’re dividing, you’re working out how many pieces, items, or days fit into what you’ve got.
Today, we’ll show you how we break it down with simple definitions, easy examples, practice exercises, and answers to the questions students and parents often ask.
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Division is one of the four basic mathematical operations, alongside addition, subtraction, and multiplication.
At Mathnasium, we like to say that division is counting “how many of these are there inside of that.” In other words, it’s how we figure out how many times one number can fit into another.
For example, if we want to divide 10 by 2, we’re asking: “How many 2s are inside 10?”
We can count by twos: 2, 4, 6, 8, 10.
That’s five twos—so the answer is 5 or 10 ÷ 2 = 5.
Now, how about dividing 12 by 2?
Let’s do a bit of mental math.
Picture 12 lemons in your mind. Now, imagine grouping them into sets of 2.
You’d get: 2, 4, 6, 8, 10, 12—counting up by twos.
That’s 6 groups. So, there are 6 twos inside of 12.
We can also think of division as the inverse of multiplication. That means it works in the opposite direction.
While multiplication combines equal groups to find a total, division takes a total and breaks it into equal groups.
That’s why knowing our multiplication facts can help us divide, or figure out how many of “these” are inside of “that.”
Let’s try that with an example.
Dividing 36 by 6 is the same as asking: How many 6s are inside 36?
To solve this, we can think about what we know from multiplication.
Since 6 × 6 = 36, we know that there are six 6s inside 36.
Division may look a little different depending on how it's written, but each format represents the same idea.
Let’s say we’re dividing 15 by 5.
We can write this in three common ways:
Each of these asks the same question:
How many 5s are there inside of 15?
And the answer is 3!
At Mathnasium, we help students get comfortable recognizing and using all these formats so they can solve division problems with confidence, no matter how they're written!
When numbers divide evenly, like 15 ÷ 5 = 3, we have three key components:
When numbers don't divide evenly, like 16 ÷ 5 = 3 with a leftover of 1, we have four main components:
Sometimes, division problems are simple enough that we can solve them using mental math, counting equal groups, or thinking through our multiplication facts.
But what happens when the numbers are too big, or when they don’t divide evenly?
That’s where long division comes in.
Long division is a method, typically used for bigger numbers, that breaks division down into simpler steps to follow.
In other words, when we can’t work out a division task in our head, we use long division to help us figure it out—one step at a time.
There are four main steps to long division:
Divide: Look at the first digit (or group of digits) of the number you're dividing. Ask: how many times does the divisor fit into it?
Multiply: Multiply your answer by the divisor.
Subtract: Subtract the result from the number you just divided into.
Bring down: Bring down the next digit and repeat the steps.
We keep going until there are no more digits left to bring down.
This may sound like a lot—but it’s actually pretty simple once you see it in action.
Let’s see how this works with an example. We’ll divide 85 by 3.
Before we go into the steps, we place 85 (the dividend) under the division bar and 3 (the divisor) outside to the left like so:
Now, we can follow the steps.
Step 1: Divide
Check how many times 3 (the divisor) goes into 8 (the first digit of the dividend) without going over.
Since 3 × 2 = 6, we see that 2 whole 3s fit into 8.
Write 2 above the 8.
Step 2: Multiply & Subtract
Find the product of 3 (the divisor) and 2 (the new quotient) and subtract it from 8.
Step 3: Bring Down
Now bring down the next digit in the dividend, which is 5, to make 25.
Step 4: Divide Again
Check how many times 3 fits into 25.
3 × 8 = 24, so 3 goes into 25 8 times.
Write 8 above the 5.
Step 5: Multiply & Subtract Again
Find the product of 3 (the divisor) and 8 (the second digit of the quotient) and subtract it from 25.
Since there are no more digits to bring down, 1 is our remainder.
The remainder must always be less than the divisor and can be written as R1 or as a fraction where we put the remainder over the divisor \(\Large\frac{1}{3}\).
So, our final answer is:
85 ÷ 3 = 28 R1 or 28 \(\Large\frac{1}{3}\).
And that’s how we perform long division!
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Ready to practice what you’ve learned? Try these division tasks yourself.
How many 9s are inside 45?
How many 8s are inside 64?
6 times (what number) is closest to 38 without going over?
7 times (what number) is closest to 60 without going over?
How many 6s are inside 44? Is there a remainder?
Using long division, divide 113 by 9.
Division is a topic that follows students throughout their math journey—from early elementary all the way into algebra and beyond. Naturally, students (and parents!) have questions.
Here are some of the most common ones we hear at Mathnasium of Rolling Hills Estates, along with our answers to help bring clarity and confidence to division!
At Mathnasium, we define division as counting how many of “these” are inside of “that”.
But if you try to divide by zero, you're asking:
"How many zeros fit inside this number?"
And that question doesn’t make sense, because no matter how many times you add zero, you’ll never reach the number you're dividing.
Zero can't fit into anything, not even once.
That’s why division by zero is undefined.
Division is repeated subtraction, just like multiplication is repeated addition.
For example, to solve 12 ÷ 3, you could subtract 3 from 12 over and over:
12 − 3 = 9
9 − 3 = 6
6 − 3 = 3
3 − 3 = 0
You subtracted 3 a total of 4 times, so the answer is 4.
It depends on the problem! If you just want to know how many full groups you can make, you write the remainder. If you want the exact amount, you can write it as a decimal or a fraction.
Not always! If you divide by a number smaller than 1 (like a decimal), your answer gets bigger. But when dividing by whole numbers greater than 1, yes—the result is usually smaller.
Mathnasium of Rolling Hills Estates is a math-only learning center for K-12 students in Rolling Hills Estates, CA.
Using a proprietary teaching approach called the Mathnasium Method™, our specially trained math tutors offer face-to-face instruction in an engaging and fun group environment to help students master any math class and topic, including division, typically taught throughout elementary, middle, and high school math.
At Mathnasium, students begin their journey with a diagnostic assessment that helps us identify their specific strengths and knowledge gaps. Guided by these assessment-driven insights, we design personalized learning plans to place them on the best path to math mastery.
Whether your student is looking to catch up, keep up, or get ahead in their math class, schedule an assessment, and enroll at Mathnasium of Rolling Hills Estates today!
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If you’ve given our exercises a try, check your answers below.
There are 5 nines inside of 45.
There are 8 eights inside of 64.
6 times 6 is closest to 38 without going over.
7 times 8 is closest to 60 without going over.
There are 7 sixes inside of 44, with a remainder of 2.
113 ÷ 9 = 12 R5
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