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How to Do Division
Last Updated: February 10, 2023 References
This article was co-authored by Grace Imson, MA and by wikiHow staff writer, Christopher M. Osborne, PhD . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been viewed 279,098 times.
Division is one of the 4 major operations in arithmetic, alongside addition, subtraction, and multiplication. In addition to whole numbers, you can divide decimals, fractions, or exponents. You can do long division or, if one of the numbers is a single digit, short division. Start by mastering long division, though, because it is the key to the entire operation.
- Sample problem #1 (beginner): 65 ÷ 5 . Place the 5 outside the division bar, and the 65 inside it. It should look like 5厂65 , but with the 65 underneath the horizontal line.
- Sample problem #2 (intermediate): 136 ÷ 3 . Place the 3 outside the division bar, and the 136 inside it. It should look like 3厂136 , but with the 136 underneath the horizontal line.
- In sample problem #1 ( 5厂65 ), 5 is the divisor and 6 is the first digit of the dividend (65). 5 goes into 6 one time, so place a 1 on the top of the divisor bar, aligned above the 6.
- In sample problem #2 ( 3厂136 ), 3 (the divisor) does not go into 1 (the first digit of the dividend) and result in a whole number. In this case, write a 0 above the division bar, aligned above the 1.
- In sample problem #1 ( 5厂65 ), multiply the number above the bar (1) by the divisor (5), which results in 1 x 5 = 5 , and place the answer (5) just below the 6 in 65.
- In sample problem #2 ( 3厂136 ), there is a zero above the division bar, so when you multiply this by 3 (the divisor), your result is zero. Write a zero on a new line just below the 1 in 136.
- In sample problem #1 ( 5厂65 ), subtract the 5 (the multiplication result in the new row) from the 6 right above it (the first digit of the dividend): 6 - 5 = 1 . Place the result (1) in another new row right below the 5.
- In sample problem #2 ( 3厂136 ), subtract 0 (the multiplication result in the new row) from the 1 right above it (the first digit in the dividend). Place the result (1) in another new row right below the 0.
- In sample problem #1 ( 5厂65 ), drop the 5 from 65 down so that it’s beside the 1 that you got from subtracting 5 from 6. This gives you 15 in this row.
- In sample problem #2 ( 3厂136 ), carry down the 3 from 136 and place it beside the 1, giving you 13.
- To continue 5厂65 , divide 5 (the dividend) into the new number (15), and write the result (3, since 15 ÷ 5 = 3 ) to the right of the 1 above the division bar. Then, multiply this 3 above the bar by 5 (the dividend) and write the result (15, since 3 x 5 = 15 ) below the 15 under the division bar. Finally, subtract 15 from 15 and write 0 in a new bottom row.
- Sample problem #1 is now complete, since there are no more digits in the divisor to carry down. Your answer (13) is above the division bar.
- For 3厂136 : Determine how many times 3 goes into 13, and write the answer (4) to the right of the 0 above the division bar. Then, multiply 4 by 3 and write the answer (12) below the 13. Finally, subtract 12 from 13 and write the answer (1) below the 12.
- For 3厂136 : Continue the process for another round. Drop down the 6 from 136, making 16 in the bottom row. Divide 3 into 16, and write the result (5) above the division line. Multiply 5 by 3, and write the result (15) in a new bottom row. Subtract 15 from 16, and write the result (1) in a new bottom row.
- Because there are no more digits to carry down in the dividend, you’re done with the problem and the 1 on the bottom line is the remainder (the amount left over). Write it above the division bar with an “r.” in front of it, so that your final answer reads “45 r.1”.
- In order to do short division , your divisor can't have more than one digit.
- Sample problem: 518 ÷ 4 . In this case, the 4 will be outside the division bar, and the 518 inside it.
- In the sample problem, 4 (the divisor) goes into 5 (the first digit of the dividend) 1 time, with a remainder of 1 ( 5 ÷ 4 = 1 r.1 ). Place the quotient, 1, above the long division bar. Place a small, superscript 1 beside the 5, to remind yourself that you had a remainder of 1.
- The 518 under the bar should now look like this: 5 1 18.
- In the sample problem, the number formed by the remainder and the second number of the dividend is 11. The divisor, 4, goes into 11 twice, leaving a remainder of 3 ( 11 ÷ 4 = 2 r.3 ). Write the 2 above the division line (giving you 12) and the 3 as a superscript number beside the 1 in 518.
- The original dividend, 518, should now look like this: 5 1 1 3 8.
- In the sample problem, the next (and final) dividend number is 38—the remainder 3 from the previous step, and the number 8 as the last term of the dividend. The divisor, 4, goes into 38 nine times with a remainder of 2 ( 38 ÷ 4 = 9 r.2 ), because 4 x 9 = 36 , which is 2 short of 38. Write this final remainder (2) above the division bar to complete your answer.
- Therefore, your final answer above the division bar is 129 r.2.
- Your problem might be, for example, 3/4 ÷ 5/8 . For convenience, use horizontal instead of diagonal lines to separate the numerator (top number) and denominator (bottom number) of each fraction.
- In the sample problem, reverse 5/8 so the 8 is on top and the 5 is on the bottom.
- For example: 3/4 x 8/5 .
- In this case, the numerators are 3 and 8, and 3 x 8 = 24 .
- The denominators are 4 and 5 in the sample problem, and 4 x 5 = 20 .
- In the sample problem, then, 3/4 x 8/5 = 24/20 .
- 24: 1, 2, 3, 4 , 6, 8, 12, 24
- 20: 1, 2, 4 , 5, 10, 20
- 24/20 = 6/5 . Therefore, 3/4 ÷ 5/8 = 6/5
- In the sample problem, 5 goes into 6 one time with a remainder of 1. Therefore, the new whole number is 1, the new numerator is 1, and the denominator remains 5.
- As a result, 6/5 = 1 1/5 .
- As a beginner, start with a sample problem in which both numbers with exponents already have the same base—for instance, 3 8 ÷ 3 5 .
- In the sample problem: 8 - 5 = 3 .
- Therefore: 3 8 ÷ 3 5 = 3 3 .
- For the example 65.5 ÷ 0.5 , 0.5 goes outside the division bar, and 65.5 goes inside it.
- In the sample problem, you only need to move the decimal point over one spot for both the divisor and dividend. So, 0.5 becomes 5, and 65.5 becomes 655.
- If, however, the sample problem used 0.5 and 65.55, you’d need to move the decimal point 2 places in 65.55, making it 6555. As a result, you’d also have to move the decimal point in 0.5 2 places. To do this, you’d add a zero to the end and make it 50.
- In the sample problem, the decimal in 655 would appear after the last 5 (as 655.0). So, write the decimal point above the division line right above where that decimal point in 655 would appear.
- Divide 5 into the hundredths digit, 6. You get 1 with a remainder of 1. Place 1 in the hundredths place on top of the long division bar, and subtract 5 from 6 below the number six.
- Your remainder, 1, is left over. Carry the first five in 655 down to create the number 15. Divide 5 into 15 to get 3. Place the three above the long division bar, next to the 1.
- Carry down the last 5. Divide 5 into 5 to get 1, and place the 1 on top of the long division bar. There is no remainder, since 5 goes into 5 evenly.
- The answer is the number above the long division bar (131), so 655 ÷ 5 = 131 . If you pull out a calculator, you’ll see that this is also the answer to the original division problem, 65.5 ÷ 0.5 .
Practice Problems and Answers
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- ↑ https://www.mathsisfun.com/long_division.html
- ↑ https://www.k5learning.com/blog/step-step-guide-long-division
- ↑ https://www.bbc.co.uk/bitesize/topics/znmtsbk/articles/zqpddp3
- ↑ http://www.mathsisfun.com/fractions_division.html
- ↑ https://www.ck12.org/arithmetic/divide-fractions/lesson/Quotients-of-Fractions-MSM6/?referrer=concept_details
- ↑ http://www.mathsisfun.com/algebra/variables-exponents-multiply.html
- ↑ https://www.mathsisfun.com/dividing-decimals.html
- ↑ https://www.bbc.co.uk/bitesize/topics/zh7xpv4/articles/zwdc4xs
About This Article
To do simple division, think about how many times one number can go into another number. For example, 6 ÷ 2 is 3, because 3 goes into 6 two times. For larger numbers, it's helpful to spend time reviewing the multiplication tables. To do long division, write the number you want to divide under the division bar, and place the number you want to divide by outside of the bar. For example, if you want to calculate 72 ÷ 3, place 72 under the division bar and 3 outside of it. Then, calculate how many times 3 goes into the first number under the division bar. In this case, you’re calculating how many times 3 goes into 7. The answer is 2, with 1 left over. Write the number 2 above the bar, and the remainder – in this case, 1 – below the 7. Then, if there are any numbers left under the division bar, bring them down to the same row as the remainder. So in this case, you’d write a 2 beside the 1 to get 12. Then, repeat the process: how many times does 3 go into 12? In this example, 3 goes into 12 four times, so you’d write 4 on the line above the problem, beside the other numbers. Therefore, 72 ÷ 3 = 24. If you want to learn how to divide fractions, keep reading the article! Did this summary help you? Yes No
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How to Solve Division Problems
Parts of a division problem.
What Is a Remainder in Math?
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5 Fun Division Word Problems | Practice Multiple Ways of Solving | Free Printable
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Division Word Problems
Are your children ready to conquer division? These interactive, division problem-solving worksheets will help children solve division word problems in five different ways.
He has done it numerous times. Sharing a group of toys with his siblings, or even sharing a bag of M&M’s. In those situations, he instinctively knows how to do division problems.
When we hit the division problem in his math book, he wasn’t quite as sure what to do.
I wanted this little man of mine to be able to relate division to what he has done over and over while creating strategies for solving division problems.
These word problems with five steps were what we came up with. These simple division worksheets are perfect for 3rd grade division word problems.
How to Solve Division Word Problems
Step 1: division word problem solving by grouping.
The first step is the way we normally teach children to solve division problems . The students grab the amounts of objects that need to be divided up and then place them in the correct amount of groups. It is very hands-on and a visual way for our children to understand what is happening when we are dividing .
Step 2: Solving Division Word Problems by Repeated Subtraction
To solve a word problem using repeated subtraction, students start with the number being divided up or the dividend. Now they subtract the divisor or the number that tells how many groups are needed from the dividend over and over until they reach zero. The number of times they subtracted is the answer.
Step 3: Division Word Problem Solving with Arrays
Chances are if you taught multiplication in a hands-on way, you taught it using arrays. You can create an array when you place objects, pictures, or numbers in equal columns and equal rows.
With multiplication, you would take a problem like 4 x 5, and make 4 rows with 5 in each column. You would end up with 20 objects, which of course is the answer to the multiplication problem.
Division is a little different. If the problem is 18 ÷ 3, The student creates three rows. They then keep placing one object in each row until they have used 18 objects.
They now have an array that is a 3 by 6. The answer to the division problem is 6.
Want to know how to use arrays to divide when the numbers are larger? Check out this POST !
Step 4: Number Line to Solve Division Word Problems
Number lines have become an important tool in helping children solve problems. The beginning of this video by Ramy Melhem clearly shows how to divide using a number line, and the little frog hopping is a great visual for our little ones.
Step 5: Create an Equation
The final step is very easy after all the work above. The students simply figure out what number was divided up, and place it in the first box.
They then look at how many groups they created, and that is the number that goes into the second box. Finally, they figure out how many objects were in each group and that is the answer or quotient.
That number goes in the last box.
By throwing in markers and painting with q-tips these sheets were fun for my little man, and I could see his understanding of division grow.
We moved on to these cut-and-paste division assessments, and his thinking was challenged even more. Through all this practice he is on his way to mastering simple division problems, and your kiddos can master it too.
Get This Cut and Paste Division Assessment at my TpT Store .
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Division Word Problems Printable
These free division math problems will help your students learn how to solve division problems 5 different ways. You can download this printable by clicking on the download button.
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Division Tips and Tricks
- Divide by 1 - Anytime you divide by 1, the answer is the same as the dividend.
- Divide by 2 - If the last digit in the number is even, then the entire number is divisible by 2. Remember that divide by 2 is the same as cutting something in half.
- Divide by 4 - If the last two digits divide by 4, then the entire number is divisible by 4. For example, we know that 14237732 can be divided evenly by 4 because 32 ÷ 4 = 8.
- Divide by 5 - If the number ends in a 5 or a 0, it is divisible by 5.
- Divide by 6 - If the rules for divide by 2 and divide by 3 above are true, then the number is divisible by 6.
- Divide by 9 - Similar to the divide by 3 rule, if the sum of all the digits is divisible by 9, then the entire number is divisible by 9. For example, we know that 18332145 is divisible by 9 because 1+8+3+3+2+1+4+5 = 27 and 27 ÷ 9 = 3.
- Divide by 10 - If the number ends in a 0, then it is divisible by 10.
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Steps to Long Division Problems (With Examples)
- DESCRIPTION parts of long division problem
- SOURCE Created by Beth Wiggins for YourDictionary
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Math can be tricky. Make it simple by breaking a difficult topic like division into easy-to-follow long division steps. That's just what long division is. It’s a way to break the division of large numbers into simple steps. Learn the steps through several long division examples.
What Is Long Division?
Dividing 543,439 by 31 would be challenging to do in your head. So, rather than focusing all your brainpower on division, you can use a long division method, which breaks the numbers into steps. These steps allow you to take one part of the number at a time, making the math so easy even a fourth grader can do it.
Terms Used in Long Division
Before you learn how to complete long division, it’s essential to get familiar with a few vital math terms . You may see a division problem written in different ways, such as using a ÷ or a / to indicate "divided by."
- dividend - the number that needs dividing
- divisor - the number you are dividing by
- quotient - the answer
- remainder - the leftover amount when dividend doesn't divide equally
Therefore, in the equation 1327 / 25 = 53 R2, 1327 is the dividend, 25 is the divisor, 53 is the quotient, and 2 is the remainder. Alright, now that you’ve got the basics, it’s time to dive right into how to divide.
Simple Long Division Steps
Typically, long division is broken down into five different steps. Explore each separate step using the equation:
1579 / 6 = x.
Step 1: Divide
Long division is all about breaking an equation into different parts. Therefore, rather than looking at the whole equation, you look at the first number of the dividend, which in the equation 1579 / 6 is the number 1. Ask yourself: how many 6s are in 1? Since 1 is less than 6, your answer would be 0.
- DESCRIPTION long division example Step 1 divide
- PERMISSION Owned by YourDictionary, Copyright YourDictionary
Step 2: Multiply
Now that you know that 6 will go into 1 zero times, then you need to multiply (6 * 0 = 0). Place the zero under the 1 in the equation.
- DESCRIPTION long division example step 2 multiply
Step 3: Subtract
Now it is time for you to subtract the numbers from one another (1 - 0 =1). You will write the difference under the line in your equation.
- DESCRIPTION long division example step 3 subtract
Step 4: Bring the Number Down
Once the subtraction is done, you bring the next number in the equation down. In our dividend, you would need to bring the 5 down.
- DESCRIPTION long division example step 4 bring number down
Step 5: Repeat
Once you understand steps 1-4, you just need to repeat the division, multiplication, subtraction, and bringing the number down until there aren’t any more numbers for your to bring down. So for our equation, you find out that 1579 / 6 = 263 R1.
- DESCRIPTION long division example step 5 repeat
Long Division Examples
Now that you know how to do a long division problem, it's time to try a few examples yourself. You'll need to write these down using the standard formatting for a division problem.
- 1204 / 4 4 goes into 1 zero times 1 - 0 = 1, 2 drops down 4 goes into 12 three times (first number in the answer is 3) 12 - 12 = 0, 0 drops down 4 goes into 0 zero times (second number in the answer is 0) 0 - 0 = 0, 4 drops down 4 goes into 4 one time (third number in the answer is 1), answer is 301 Check your answer: 301 * 4 = 1204
- 3024 / 24 24 goes into 3 zero times 3 - 0 = 3, 0 drops down 24 goes into 30 one time (first number in the answer is 1) 30 - 24 = 6, 2 drops down to make 62 24 goes into 62 two times (second number in the answer is 2) 62 - 48 = 14, 4 drops down to make 144 24 goes into 144 six times (last number is 6), answer is 126 Check your answer 24 * 126 = 3024
- 675 / 5 5 goes into 6 one time (first number in the answer is 1) 6 - 5 = 1, 7 drops down 5 goes into 17 three times (second number in the answer is 3) 17 - 15 = 2, 5 drops down 5 goes into 25 five times (last number in the answer is 5), answer is 135 Check your answer 5 * 135 = 675
- 679 / 5 5 goes into 6 one time (first number in the answer is 1) 6 - 5 = 1, 7 drops down 5 goes into 17 three times (second number in the answer is 3) 17 - 15 = 2, 9 drops down 5 goes into 29 five times (last number in the answer is 5) you have a remainder of 4, answer is 135 R4 Check your work (5 * 135) + 4 = 679
Why Do Some Equations Have a Remainder
Not every divisor you have in long division will divide equally. Therefore, most of the time, you have a leftover bit that can’t be divided by the number any further. This is called your remainder. It’s represented in a math equation with an R. Once you advance a bit further into rational numbers , you’ll see how the remainder fits in!
How to Divide Decimals Using Long Division
When dividing decimals in long division, you use the same five steps you did for the long division example problem. However, you need to bring the decimal from the divisor up into the same position in the quotient.
Keep Long Division Steps Simple
Long division isn’t hard since it is breaking a big number into several smaller numbers. However, it can get a bit tricky the bigger the numbers get. As long as you follow your basic five steps, you are well on your way to becoming a long division master. If long division was easy as cake, then you might want to venture into the deep waters of quadratic equations . It might make you wish for the simplicity of long division.
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Long Division is a method for dividing large numbers, which breaks the division problem into multiple steps following a sequence. Just like the regular division problems, the dividend is divided by the divisor which gives a result known as the quotient, and sometimes it gives a remainder too. Let us learn how to divide using the long division method , along with long division examples with answers, which include the long division steps in this article.
What is Long Division Method?
Long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division . Observe the following long division method to see how to divide step by step and check the divisor, the dividend, the quotient, and the remainder.
The above example also showed us how to do 2 digit by 1 digit division.
Parts of Long Division
While performing long division, we need to know the important parts of long division. The basic parts of long division can be listed as follows:
The following table describes the parts of long division with reference to the example shown above.
How to do Long Division?
Division is one of the four basic mathematical operations, the other three being addition , subtraction , and multiplication . In arithmetic, long division is a standard division algorithm for dividing large numbers, breaking down a division problem into a series of easier steps. Let us learn about the steps that are followed in long division.
Long Division Steps
In order to perform division, we need to understand a few steps. The divisor is separated from the dividend by a right parenthesis 〈)〉 or vertical bar 〈|〉 and the dividend is separated from the quotient by a vinculum (an overbar). Now, let us follow the long division steps given below to understand the process.
- Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.
- Step 2: Then divide it by the divisor and write the answer on top as the quotient.
- Step 3: Subtract the result from the digit and write the difference below.
- Step 4: Bring down the next digit of the dividend (if present).
- Step 5: Repeat the same process.
Let us have a look at the examples given below for a better understanding of the concept. While performing long division, we may come across problems when there is no remainder, while some questions have remainders. So, first, let us learn division in which we get remainders.
Division with Remainders
Case 1: When the first digit of the dividend is equal to or greater than the divisor.
Example: Divide 435 ÷ 4
Solution: The steps of this long division are given below:
- Step 1: Here, the first digit of the dividend is 4 and it is equal to the divisor. So, 4 ÷ 4 = 1. So, 1 is written on top as the first digit of the quotient.
- Step 2: Subtract 4 - 4 = 0. Bring the second digit of the dividend down and place it beside 0.
- Step 3: Now, 3 < 4. Hence, we write 0 as the quotient and bring down the next digit of the dividend and place it beside 3.
- Step 4: So, we have 35 as the new dividend. We can see that 35 > 4 but 35 is not divisible by 4, so we look for the number just less than 35 in the table of 4 . We know that 4 × 8 = 32 which is less than 35 so, we go for it.
- Step 5: Write 8 in the quotient. Subtract: 35 - 32 = 3.
- Step 6: Now, 3 < 4. Thus, 3 is the remainder and 108 is the quotient.
Case 2: When the first digit of the dividend is less than the divisor.
Example: Divide 735 ÷ 9
Solution: Let us divide this using the following steps.
- Step 1: Since the first digit of the dividend is less than the divisor, put zero as the quotient and bring down the next digit of the dividend. Now consider the first 2 digits to proceed with the division.
- Step 2: 73 is not divisible by 9 but we know that 9 × 8 = 72 so, we go for it.
- Step 3: Write 8 in the quotient and subtract 73 - 72 = 1.
- Step 4: Bring down 5. The number to be considered now is 15.
- Step 5: Since 15 is not divisible by 9 but we know that 9 × 1 = 9, so, we take 9.
- Step 6: Subtract: 15 - 9 = 6. Write 1 in the quotient.
- Step 7: Now, 6 < 9. Thus, remainder = 6 and quotient = 81.
Case 3: This is a case of long division without a remainder.
Division without Remainder
Example: Divide 900 ÷ 5
Solution: Let us see how to divide step by step.
- Step 1: We will consider the first digit of the dividend and divide it by 5. Here it will be 9 ÷ 5.
- Step 2: Now, 9 is not divisible by 5 but 5 × 1 = 5, so, write 1 as the first digit in the quotient.
- Step 3: Write 5 below 9 and subtract 9 - 5 = 4.
- Step 4: Since 4 < 5, we will bring down 0 from the dividend to make it 40.
- Step 5: 40 is divisible by 5 and we know that 5 × 8 = 40, so, write 8 in the quotient.
- Step 6: Write 40 below 40 and subtract 40 - 40 = 0.
- Step 7: Bring down the next 0 from the dividend. Since 5 × 0 = 0, we write 0 as the remaining quotient.
- Step 9: Therefore, the quotient = 180 and there is no remainder left after the division, that is, remainder = 0.
Long division problems also include problems related to long division by a 2 digit number, long division polynomials and long division with decimals. Let us get an an idea about these in the following sections.
Long Division by a 2 Digit Number
Long division by a 2 digit number means dividing a number by a 2-digit number . For long division by a 2 digit number , we consider both the digits of the divisor and check for the divisibility of the first two digits of the dividend.
For example, if we need to divide 7248 by 24, we can do it using the long division steps. Let us see how to divide step by step.
- Step 1: Since it is a long division by a 2 digit number, we will check for the divisibility of the first two digits of the dividend. The first 2 digits of the dividend are 72 and it is greater than the divisor, so, we will proceed with the division.
- Step 2: Using the multiplication table of 24, we know that 24 × 3 = 72. So we write 3 in the quotient and 72 below the dividend to subtract these. Subtract 72 - 72 = 0.
- Step 3: Bring down the next number from the dividend, that is, 4. The number to be considered now is 4.
- Step 4: Since 4 is smaller than 24, we will put 0 as the next quotient, since 24 × 0 = 0 and write 0 below 4 to subtract 4 - 0 = 4
- Step 5: Bring down the next number from the dividend, that is, 8 and place it next to this 4. The number to be considered now is 48.
- Step 6: Using the multiplication table of 24, we know that 24 × 2 = 48. So we write 2 in the quotient and 48 below the dividend to subtract these. Subtract 48 - 48 = 0. Thus, remainder = 0 and quotient = 302. This means, 7248 ÷ 24 = 302.
- Long Division of Polynomials
When there are no common factors between the numerator and the denominator , or if you can't find the factors, you can use the long division process to simplify the expression. For more details about long division polynomials, visit the Dividing Polynomials page.
Long Division with Decimals
Long division with decimals can be easily done just like the normal division. We just need to keep in mind the decimals and keep copying them as they come. For more details about long division with decimals, visit the Dividing Decimals page.
How to Divide Decimals by Whole Numbers?
When we need to divide decimals by whole numbers, we follow the same procedure of long division and place the decimal in the quotient whenever it comes. Let us understand this with the help of an example.
Example: Divide 36.9 ÷ 3
- Step 1: Here, the first digit of the dividend is 3 and it is equal to the divisor. So, 3 ÷ 3 = 1. So, 1 is written on top as the first digit of the quotient and we write the product 3 below the dividend 3.
- Step 2: Subtract 3 - 3 = 0. Bring the second digit of the dividend down and place it beside 0, that is, 6
- Step 3: Using the multiplication table of 3, we know that 3 × 2 = 6. So we write 2 in the quotient and 6 below the dividend to subtract these. Subtract 6 - 6 = 0.
- Step 4 : Now comes the decimal point in the dividend. So, place a decimal in the quotient after 12 and continue with the normal division.
- Step 5: Bring down the next number from the dividend, that is, 9. The number to be considered now is 9.
- Step 6: Using the multiplication table of 3, we know that 3 × 3 = 9. So we write 3 in the quotient and 9 below the dividend to subtract these. Subtract 9 - 9 = 0. Thus, remainder = 0 and quotient = 12.3. This means, 36.9 ÷ 3 = 12.3
Long Division Tips and Tricks:
Given below are a few important tips and tricks that would help you while working with long division:
- The remainder is always smaller than the divisor.
- For division, the divisor cannot be 0.
- The division is repeated subtraction, so we can check our quotient by repeated subtractions as well.
- We can verify the quotient and the remainder of the division using the division formula : Dividend = (Divisor × Quotient) + Remainder.
- If the remainder is 0, then we can check our quotient by multiplying it with the divisor. If the product is equal to the dividend, then the quotient is correct.
☛ Related Articles
- Long Division Formula
- Long Division with Remainders Worksheets
- Long Division Without Remainders Worksheets
- Long Division with 2-digit Divisors Worksheets
- Long Division Calculator
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Long Division Examples with Answers
Example 1: Ron planted 75 trees equally in 3 rows. Use long division to find out how many trees did he plant in each row?
The total number of trees planted by Ron = 75. The number of rows = 3. To find the number of trees in each row, we need to divide 75 by 3 because there is an equal number of trees in each of the three rows. Let us also observe how to do 2 digit by 1 digit division here.
Therefore, the number of trees in each row = 25 trees.
Example 2: $4000 needs to be distributed among 25 men for the work completed by them at a construction site. Calculate the amount given to each man.
The total amount is $4000. The number of men at work = 25. We need to calculate the amount given to each man. To do so, we have to divide 4000 by 25 using the long division method. Let us see how to work with long division by a 2 digit number and also see how to do long division step by step.
Each man will be given $160. Therefore, $160 is the amount given to each man.
Example 3: State true or false with respect to long division.
a.) In the case of long division of numbers, the remainder is always smaller than the divisor.
b.) We can verify the quotient and the remainder of the division using the division formula: Dividend = (Divisor × Quotient) + Remainder.
a.) True, in the case of long division of numbers, the remainder is always smaller than the divisor.
b.) True, we can verify the quotient and the remainder of the division using the division formula: Dividend = (Divisor × Quotient) + Remainder.
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Practice Questions on Long Division
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FAQs on Long Division
What is long division in math.
Long division is a process to divide large numbers in a convenient way. The number which is divided into smaller groups is known as a dividend, the number by which we divide it is called the divisor, the value received after doing the division is the quotient, and the number left after the division is called the remainder.
The following steps explain the process of long division. This procedure is explained with examples above on this page.
- Write the dividend and the divisor in their respective positions.
- Take the first digit of the dividend from the left.
- If this digit is greater than or equal to the divisor, then divide it by the divisor and write the answer on top as the quotient.
- Write the product below the dividend and subtract the result from the dividend to get the difference. If this difference is less than the divisor, and there are no numbers left in the dividend, then this is considered to be the remainder and the division is done. However, if there are more digits in the dividend to be carried down, we continue with the same process until there are no more digits left in the dividend.
What are the Steps of Long Division?
Given below are the 5 main steps of long division. For example, let us see how we divide 52 by 2.
- Step 1: Consider the first digit of the dividend which is 5 in this example. Here, 5 > 2. We know that 5 is not divisible by 2.
- Step 2: We know that 2 × 2 = 4, so, we write 2 as the quotient.
- Step 3: 5 - 4 = 1 and 1 < 2 (After writing the product 4 below the dividend, we subtract them).
- Step 4: 1 < 2, so we bring down 2 from the dividend and we get 12 as the new dividend now.
- Step 5: Repeat the process till the time you get a remainder less than the divisor. 12 is divisible by 2 as 2 × 6 = 12, so we write 6 in the quotient, and 12 - 12 = 0 (remainder).
Therefore, the quotient is 26 and the remainder is 0.
How to do Long Division with 2 Digits?
For long division with 2 digits, we consider both the digits of the divisor and check for the divisibility of the first two digits of the dividend. If the first 2 digits of the dividend are less than the divisor, then consider the first three digits of the dividend. Proceed with the division in the same way as we divide regular numbers. This procedure is explained with examples above on this page under the heading of 'Long Division by a 2 Digit Number'.
What is the Long Division of Polynomials?
In algebra , the long division of polynomials is an algorithm to divide a polynomial by another polynomial of the same or the lower degree. For example, (4x 2 - 5x - 21) is a polynomial that can be divided by (x - 3) following some defined rules, which will result in 4x + 7 as the quotient.
How to do Long Division with Decimals?
The long division with decimals is performed in the same way as the normal division. This procedure is explained with examples above on this page under the heading of 'How to Divide Decimals by Whole Numbers'? For more details, visit the page about dividing decimals . The basic steps of long division with decimals are given below.
- Write the division in the standard form.
- Start by dividing the whole number part by the divisor.
- Place the decimal point in the quotient above the decimal point of the dividend.
- Bring down the digits on the tenths place, i.e., the digit after the decimal.
- Divide and bring down the other digit in sequence.
- Divide until all the digits of the dividend are over and a number less than the divisor or 0 is obtained in the remainder.
How to Divide
Introduction: How to Divide
Division is a core life skill. Calculating the fraction someone is owed or should receive — for instance when splitting a check or dividing the costs of a trip — is a mathematical challenge you are likely to encounter on an almost daily basis.
Long division sounds scary, but it’s not. This instructable will teach you how to find the answer to a division problem, also known as the quotient. It will also teach you how to solve division problems that have remainders. You won’t need a calculator, and you will be able to show your work. You’ll not only be able to complete any worksheet for school, you’ll always be prepared and confident when you have to split a check three ways.
Step 1: Things You'll Need
There are three different "methods" that I will be teaching you. To learn all of the methods you will need a pencil and lots of paper. You may also want to have a calculator to double-check your answers.
Step 2: Simple Division
The first method is simple division. Your answer will come out as a whole number.
1) Setup the division problem (84/7). 2) Divide 8 by 7 to get 1. Place this on top of the 8 and the division sign. 3) Multiply 1 and 7 to get 7. Place this under the 8. 4) Subtract 7 from 8 to get 1. 5) Carry down the 4. 6) Divide 14 by 7 to get 2. Place this on top of the 4 and the division sign. 7) Multiply 2 by 7 to get 14. 8) Subtract 14 from 14 to get 0.
The answer is 12!
Step 3: Simple Division With Remainder
This is the same as simple division except we add in the remainder.
1) Setup the division problem (10/3). 2) Divide 10 and 3 to get 3. Place this on top the 0 and the division sign. 3) Multiply 3 by 3 to get 9. Place this under the 10. 4) Subtract 9 from 10 to get 1. That is the remainder.
The answer is 3 r 1!
Step 4: Long Division With Decimal
This is similar to dividing with a remainder except you go a step further and have a decimal.
1) Setup the division problem (127/4). 2) Divide 12 and 4 to get 3. Put this on top of the 12 and the division sign. 3) Multiply 3 and 4 to get 12. Place this under the 12. 4) Subtract 12 and 12 to get 0. 5) Carry down the 7. 6) Divide 7 and 4 to get 1. Put this on top of the 7 and the division sign. 7) Multiply 4 and 1 to get 4. Place this under the 7. 8) Subtract 7 and 4 to get 3. 9) Add a 0 and a decimal point. Carry down as before. Dividing to a decimal, you can add as many zeroes as the problem requires. 10) Divide 30 and 4 to get 7. 11) Multiply 4 and 7 to get 28. Place this under the 30. 12) Subtract 30 and 28 to 2. 13) Add another 0 and a decimal point. Carry down as before. 14) Divide 20 by 4 to get 5. 15) Multiply 4 and 5 to get 20. The remainder is 0, therefore you have completed the division problem.
The answer is 31.75!
Step 5: Divide With More Than One Digit
Last method! Dividing when the divisor is more than one digit, like 63. 1) Setup the division problem (2856/84). 2) Divide 285 by 84 to get 3. Place this on top of the 5 and the division sign. 3) Multiply the 3 and 84 to get 252. Place this under the 285. 4) Subtract 285 and 252 to get 33. 5) Carry down the 6. 6) Divide 336 by 84 to get 4. Place this on top of the 6 and the division sign. 7) Multiply 4 and 84 to get 336. 8) Subtract 336 and 336 to get 0. The answer is 34!
Step 6: Conclusion
Now you know how to divide! Remember that you can't divide by zero. Thanks for reading! Please feel free to leave a comment if you have any questions or anything.
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10 months ago
2) Simple division 4 subtract 7 by 8 to get 1. carry down 4 HOW THE HECK DID YOU EVEN GET FOUR HOW DID YOU GET FOUR FROM THAT
Reply 27 days ago
lol fr it be like that sometimes
27 days ago
i dont understand can someone ls help meh!
11 years ago on Step 2
thank u i couldnt do it and now i can have my test friday let u know how i get on yhank u
hope you pass even tho this comment is from 11 years ago still waiting for update.
3 years ago
and how do you do 13 ÷ 3? it goes on forever
Reply 10 months ago
the answer is 4 and remainder 1
2 years ago
Pls solve the division
Reply 1 year ago
the answer for that is 6.95
I don't know how to divide or long divide
can someone teach me how to divide and long division
14 years ago on Introduction
What's with that brown paper? Recycled paper bag paper or something?
Reply 2 years ago
how many eggs are there
Reply 3 years ago
In this video, I'll show you a different way to solve division problems called "Short Division".Support Super Easy Math with a donation:
Complete list of Math Videos organized by State Standardshttp://www.moomoomathblog.com/2017/12/6th-grade-math-unit-1-math-videos.
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