Learn more about this important division term, and discover ways to find the quotient using simple subtraction methods.
Author
Taylor Hartley
Expert Reviewer
Jill Padfield
Last updated: August 24, 2023
Learn more about this important division term, and discover ways to find the quotient using simple subtraction methods.
Author
Taylor Hartley
Expert Reviewer
Jill Padfield
Published: August 24, 2023
Learn more about this important division term, and discover ways to find the quotient using simple subtraction methods.
Author
Taylor Hartley
Expert Reviewer
Jill Padfield
Last updated: August 24, 2023
Key takeaways
Knowing how to find the quotient is a foundational math concept. It’s very simple — we divide one number by another, and the result is the quotient. Let’s dig in to learn more about the quotient, the forms it can take, and how to find it using subtraction skills.
When we divide one number by another number, we get the quotient. The quotient can be a whole number or integer, or, if the first number is not completely divisible, it can be a decimal. Some division problems even give a quotient with a remainder. There are a couple of different ways to find the quotient, too — let’s dive in to explore this concept with examples.
The quotient in math is the number we get when we divide one number by another. For example, let’s take a look at the simple equation 6 ÷ 3 = 2. When we divide, we see that the result is 2.. So, 2 is the quotient. As a refresher, when talking about division, 6 is the dividend and 3 is the divisor.
A quotient can come in a variety of forms, such as whole numbers and decimals. Let’s look at a couple of examples!
When a number is perfectly divisible by another, the quotient is a whole number. For example, 24 ÷ 6 = 4. In this case, 24 is completely divisible by 6 and the whole number 4 is our quotient.
When a number is not perfectly divisible by another number, the quotient is a decimal. For example, 16 ÷ 5 = 3.2. These types of division problems leave a remainder (R). This remainder is another way to find the quotient. You may also write this equation like:
16 ÷ 5 = 3 R 1 (quotient = 3 and remainder = 1)
To find the quotient, you must divide two numbers. You can use repeated subtraction or long division — it’s up to you! Let’s break down each method.
Remember how to subtract? Some find subtraction easier and less overwhelming than division, and it can be helpful to think of division as a repeated subtraction problem. To find the quotient through repeated subtraction, subtract the divisor from the dividend until you get a 0 or until subtraction is no longer possible. Here, the number of times we subtract is the quotient.
Let’s do an example problem together!
Find the quotient of 40 ÷ 10 using repeated subtraction.
We subtracted 10 four times to get 0, so the 4 is the quotient.
When finding the quotient in math using long division, we simplify the problem by dividing large numbers into groups or parts. To divide a number using this method, let’s draw a division house. Here, we write the divisor outside the division house, and the dividend inside the house. The quotient is written on top.
Here’s an example of what that looks like:
DMSBR is a helpful acronym to remember long division steps. DMSBR: divide, multiply, subtract, bring down, repeat. Want to have some fun memorizing it? Come up with your own words for each letter in the acronym!
Let’s do an example together with the steps written out:
When using long division, not every divisor will divide equally. Oftentimes, you will have a leftover bit that can’t be divided any more. This is called your remainder, which is represented with an R hence the R in DMSBR.
Let’s take a look at an example of a long division problem that has a quotient with a remainder:
Find the quotient of 75 ÷ 4 using long division.
1. Find the quotient: 18 ÷ 6
Divide 18 by 6 to get 3. We know that a quotient is the number you get when you divide one number by another. So, the quotient is 3.
2. What is the quotient in this equation? 86 ÷ 2
Divide 86 by 2 to get 43. We know that a quotient is the number you get when you divide one number by another. So, the quotient is 43.
3. True or false. Quotients can be whole numbers or decimals.
True. Quotients can be whole numbers or decimals. Quotients can be decimals when a number is not completely divisible by another number.
Ready to give it a go?
Now that we know what a quotient is and how to find it, we’re ready to do a few more practice problems to put our new skills to the test! Work through the following problems on your own. Feel free to look back at the practice problems above if you get stuck, or if you need a quick reminder on how to find the quotient.
Click to reveal the answer.
The quotient is 6.
Divide, multiply, subtract, bring down, repeat.
The answer is 12.
The answer is 17 R 10
The quotient is 6.
How did we get here?
Divide, multiply, subtract, bring down, repeat.
How did we get here?
The answer is 12.
How did we get here?
The answer is 17 R 10
How did we get here?
Brian can make 6 glasses of lemonade.
How did we get here?
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We understand that diving into new information can sometimes be overwhelming, and questions often arise. That’s why we’ve meticulously crafted these FAQs, based on real questions from students and parents. We’ve got you covered!
In math, the quotient is the result of dividing two numbers whereas the product is the result of multiplying two numbers.
When practicing your division skills, it’s important to know the terms. The most important are dividend, divisor, quotient, and remainder.
The quotient in math is the number we get when we divide one number by another. In perfect division, a quotient is a whole number with no remainder. But sometimes, a number can’t be perfectly divided, and there is a leftover number. This number is the remainder, and can often be expressed as a decimal number.
A helpful tip is to remember that the dividend equals the divisor multiplied by the quotient plus the remainder.
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Taylor Hartley
Taylor Hartley is an author and an English teacher based in Charlotte, North Carolina. When she's not writing, you can find her on the rowing machine or lost in a good novel.
Jill Padfield
Jill Padfield has 7 years of experience teaching high school mathematics, ranging from Alegra 1 to AP Calculas. She is currently working as a Business Analyst, working to improve services for Veterans while earning a masters degree in business administration.
Taylor Hartley
Taylor Hartley is an author and an English teacher based in Charlotte, North Carolina. When she's not writing, you can find her on the rowing machine or lost in a good novel.
Jill Padfield
Jill Padfield has 7 years of experience teaching high school mathematics, ranging from Alegra 1 to AP Calculas. She is currently working as a Business Analyst, working to improve services for Veterans while earning a masters degree in business administration.
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