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- Division Symbol
- Division Calculator
- Division Calculator With Remainder
- Long Division Calculator
- Division Game
- Division Worksheets
- A 30s gangster movie about how to divide and conquer-and deal with the remainders! Tim and Moby walk you through a little practical math, quotients and all.
- A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals.
Calculator Use
Divide two numbers, a dividend and a divisor, and find the answer as a quotient with a remainder. Learn how to solve long division with remainders, or practice your own long division problems and use this calculator to check your answers.
Long division with remainders is one of two methods of doing long division by hand. It is somewhat easier than solving a division problem by finding a quotient answer with a decimal. If you need to do long division with decimals use our Long Division with Decimals Calculator.
What Are the Parts of Division
For the division sentence 487 ÷ 32 = 15 R 7
- 487 is the dividend
- 32 is the divisor
- 15 is the quotient part of the answer
- 7 is the remainder part of the answer
How to do Long Division With Remainders
From the example above let's divide 487 by 32 showing the work.
Put 487, the dividend, on the inside of the bracket. The dividend is the number you're dividing.
Put 32, the divisor, on the outside of the bracket. The divisor is the number you're dividing by.
4 divided by 32 is 0, with a remainder of 4. You can ignore the remainder for now.
This is the beginning of the quotient answer.
Next, multiply 0 by the divisor 32 and insert the result 0 below the first number of the dividend inside the bracket.
0 * 32 = 0
4 - 0 = 4
48 ÷ 32 = 1
Note that you could skip all of the previous steps with zeros and jump straight to this step. You just need to realize how many digits in the dividend you need to skip over to get your first non-zero value in the quotient answer. In this case you could divide 32 into 48 straight away.
1 * 32 = 32
48 - 32 = 16
167 ÷ 32 is 5 with a remainder of 7
Division Symbol
5 * 32 = 160
167 - 160 = 7
So, 487 ÷ 32 = 15 with a remainder of 7
For longer dividends, you would continue repeating the division and multiplication steps until you bring down every digit from the divdend and solve the problem.
Further Reading
At Ask Dr. Math you can find Instructions for Long Division for simple and more advanced long division problems.
Math is Fun also provides a step-by-step process for long division with Long Division with Remainders.
Cite this content, page or calculator as:
Furey, Edward 'Long Division Calculator with Remainders'; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators
Welcome to the division worksheets page at Math-Drills.com! Please give us your undivided attention while we introduce this page. Our worksheets for division help you to teach students the very important concept of division. If students have a good recall of multiplication facts, the division facts should be a breeze to teach. If you want your students to experience success in learning division, please make sure they know their multiplication facts to 81, how to multiply by 0 and how to multiply by 10. If they don't know these things, this is going to take a lot longer.
On this page you will find many Division Worksheets including division facts and long division with and without remainders. We start off with some division facts which as you know are just the multiplication facts expressed in a different way. The main difference is that you can't divide by 0 and get a real number. If you really want your students to impress, say at their dinner table when their parents ask them what they learned today, you can teach them that division by zero is undefined.
The rest of the page is devoted to long division which for some reason is disliked among some members of the population. Long division is most difficult when students don't know their multiplication facts, so make sure they know them first. Oh, we already said that. What about a long division algorithm... maybe the one you or your parents or your grandparents learned? We adamantly say, yes! The reason that you and your ancestors used it is because it is an efficient and beautiful algorithm that will allow you to solve some of the most difficult division problems that even base ten blocks couldn't touch. It works equally well for decimals and whole numbers. Long division really isn't that hard.
Most Popular Division Worksheets this Week
Division Facts Worksheets
Division facts worksheets including division tables, division facts and worksheets with individual division facts.
Manipulatives can help students 'get' the concept of division. For example, students could regroup base ten blocks into units, then divide the units into piles. For example, 81 ÷ 9 would end up being 9 piles of 9 units.
Division is essentially asing the question, 'How many _____'s are in _____?' For the question, 81 ÷ 9, the prompt would sound like, 'How many 9's are in 81?' This prompt will benefit students in later math studies when there are more complex concepts such as dividing decimals or fractions. 'How many thirds are in four?' or even better, How many third cups are in four cups?' If necessary, get out the measuring cups.
Horizontal Division facts worksheets with focus numbers
Division facts worksheets with combinations of focus numbers
Long Division Worksheets
Long division worksheets for practicing various long division strategies including questions with no remainders, remainders and decimal quotients.
Need an easier way to divide large numbers? Try this method using powers of ten. To successfully use this method, students need to be able to multiply by powers of ten and to subtract. Students subtract the dividend multiplied by decreasing powers of ten until they have zero or a remainder. Example: 1458 ÷ 54. Note 54 × 1 = 54, 54 × 10 = 540 (nothing greater is needed). 1458 - 540 - 540 = 378. Note that 540 was subtracted twice, so the number of times that 54 'goes into' 1458 so far is 20 times. Continuing, 378 - 54 - 54 - 54 - 54 - 54 - 54 - 54 = 0. Since 54 was subtracted seven times, the quotient increases by seven for a total of 27. In other words, 54 'goes into' 1458, 27 times.
We might also mention that this method can be even more sophisticated by using multiples of powers of ten. In the above example, using 54 × 5 = 270 would have helped to get to the quotient quicker.
European Long division worksheets with no remainders
Have you ever thought that you could help a student understand things better and get a more precise answer while still using remainders? It's quite easy really. Remainders are usually given out of context, including on the answer keys below. A remainder is really a numerator in a fractional quotient. For example 19 ÷ 3 is 6 with a remainder of 1 which is more precisely 6 1/3. Using fractional quotients means your students will always find the exact answer to all long division questions, and in many cases the answer will actually be more precise (e.g. compare 6 1/3 with 6.3333....).
European long division worksheets with decimal quotients
Long Division with Remainders worksheets with the steps shown on the answer key
We thought it might be helpful to include some long division worksheets with the steps shown. The answer keys for these division worksheets use the standard algorithm that you might learn if you went to an English speaking school. Learning this algorithm by itself is sometimes not enough as it may not lead to a good conceptual understanding. One tool that helps students learn the standard algorithm and develop an understanding of division is a set of base ten blocks. By teaching students division with base ten blocks first then progressing to the standard algorithm, students will gain a conceptual understanding plus have the use of an efficient algorithm for long division. Students who have both of these things will naturally experience more success in their future mathematical studies.
Long Division on a Grid
Long division with grid assistance and NO remainders worksheets
Some students find it difficult to get everything lined up when completing a long division algorithm, so these worksheets include a grid and wider spacing of the digits to help students get things in the right place. The answer keys include the typical steps that students would record while completing each problem; however, slight variations in implementation may occur. For example, some people don't bother with the subtraction signs,some might show steps subtracting zero, etc.
Long division with grid assistance and SOME remainders worksheets
Divisibility Rules
Worksheets for practicing divisibility rules including a variety of small and large numbers and focusing on various divisors.
Divisibility by 2, 5 and 10
A number is divisible by 2 if the final digit (the digit in the ones place) is even. Numbers ending in 0, 2, 4, 6, or 8 therefore are divisible by 2. A number is divisible by 5 if the final digit is a 0 or a 5. A number is divisible by 10 if the final digit is a 0.
Division Calculator
Divisibility by 3, 6 and 9
Division Calculator With Remainder
A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 285 is divisible by 3 because 2 + 8 + 5 = 15 is divisible by 3. A number is divisible by 6 if it is divisible by both 3 and 2 (see above rules). A number is divisible by 9 if the sum of its digits is divisible by 9. For examples, 285 is not divisible by 9 because 2 + 8 + 5 = 15 is not divisible by 9.
Long Division Calculator
Divisibility by 4, 7 and 8
A number is divisible by 4 if the last two digits of the number are divisible by 4. For 7, there are a couple of strategies to use. Please see Divisibility Tricks for Learning Math for more information. A number is divisible by 8 if the last three digits are divisible by 8. This is the standard rule which can be a little sketchy for larger numbers, like who knows if 680 is divisible by 8? Because of this, we offer our Math-Drills.com solution which requires a little arithmetic, but can be accomplished quite easily with a little practice. As you know 8 is 2 to the third power, so we thought if you could divide the last three digits of a number by 2 three times, it would be divisible by 8. 680 ÷ 2 ÷ 2 ÷ 2 = 340 ÷ 2 ÷ 2 = 170 ÷ 2 = 85. We have a winner! 680 is indeed divisible by 8.
Division Game
Dividing in Other Base Number Systems
Division Worksheets
Dividing numbers in number systems other than decimal numbers including binary, quaternary, octal, duodecimal and hexadecimal numbers.