# Long Division Calculator (2024)

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Division is one of the basic arithmetic operations, the others being multiplication (the inverse of division), addition, and subtraction. The arithmetic operations are ways that numbers can be combined in order to make new numbers. Division can be thought of as the number of times a given number goes into another number. For example, 2 goes into 8 4 times, so 8 divided by 4 equals 2.

Division can be denoted in a few different ways. Using the example above:

8 &div; 4 = 2

8/4 = 2

 8 4
= 2

In order to more effectively discuss division, it is important to understand the different parts of a division problem.

### Components of division

Generally, a division problem has three main parts: the dividend, divisor, and quotient. The number being divided is the dividend, the number that divides the dividend is the divisor, and the quotient is the result:

One way to think of the dividend is that it is the total number of objects available. The divisor is the desired number of groups of objects, and the quotient is the number of objects within each group. Thus, assuming that there are 8 people and the intent is to divide them into 4 groups, division indicates that each group would consist of 2 people. In this case, the number of people can be divided evenly between each group, but this is not always the case. There are two ways to divide numbers when the result won't be even. One way is to divide with a remainder, meaning that the division problem is carried out such that the quotient is an integer, and the leftover number is a remainder. For example, 9 cannot be evenly divided by 4. Instead, knowing that 8 &div; 4 = 2, this can be used to determine that 9 &div; 4 = 2 R1. In other words, 9 divided by 4 equals 2, with a remainder of 1. Long division can be used either to find a quotient with a remainder, or to find an exact decimal value.

### How to perform long division?

To perform long division, first identify the dividend and divisor. To divide 100 by 7, where 100 is the dividend and 7 is the divisor, set up the long division problem by writing the dividend under a radicand, with the divisor to the left (divisorvdividend), then use the steps described below:

1. Starting from left to right, divide the first digit in the dividend by the divisor. If the first digit cannot be divided by the divisor, write a 0 above the first digit of the divisor. 7 cannot be divided into 1, so:

2. Continue the problem by dividing the divisor into the number formed by the combination of the previous and subsequent digit of the dividend. In this case, the next number formed is 10, which 7 can be divided into once, so write a 1 above the 2nd digit of the dividend, and a 7 below.

3. Subtract, then bring down the following digit in the original dividend to determine the new dividend.

4. Determine the number of times the divisor goes into the new dividend; in this case, the number of times 7 goes into 30. Write this value above the radicand and write the product of the divisor and this value below, then subtract. 7 goes into 30 a total of 4 times, and the product of 7 and 4 is 28.

This is the stopping point if the goal is to find a quotient with a remainder. In this case, the quotient is 014 or 14, and the remainder is 2. Thus, the solution to the division problem is:

100 &div; 7 = 14 R2

To continue the long division problem to find an exact value, continue the same process above, adding a decimal point after the quotient, and adding 0s to form new dividends until an exact solution is found, or until the quotient to a desired number of decimal places is determined.

1. Add a decimal point after the quotient and a 0 to the new dividend, and continue the same process as above.

2. Continue this process to the desired number of decimal places. In some cases, long division will reveal that a problem has a solution that is a repeating decimal. In other cases, the problem may result in a terminating decimal or a non-terminating decimal. 100 &div; 7 results in a non-terminating decimal eventually, or it can closely be estimated by the mixed number
14
 2 7
= 14.285714285714.

## FAQs

### What is the trick for long division? ›

Long Division Tips and Tricks:

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.

How accurate is long division? ›

Long division is often more accurate than shorthand division, because the steps are written out plainly in front of us. This allows us to track our division through a step-by-step process, and continue dividing until we discover an exact remainder.

How do you show your work for long division? ›

On a piece of paper, write the dividend (number being divided) on the right, under the division symbol, and the divisor (number doing the division) to the left on the outside. The quotient (answer) will eventually go on top, right above the dividend.

Why is long division so hard for me? ›

Long division is tricky because there are so many steps, and students must complete them in exactly the right order. In addition, many students aren't fluent in multiplication facts. Therefore, they must stop to look up facts on a multiplication chart.

Is 85 * 87 * 89 * 91 * 95 * 96 is divided by 100? ›

Now divide 96 by 4, and it too gets divided fully. So the full product (85 × 87 × 89 × 91 × 95 × 96) is fully divisible by 100 (which is 5x5x4). So the remainder will be zero.

What is the strategy of long division? ›

The steps of long division are set up in a similar way as the partial quotients method, but a memorable process is used to get to the answer. First you divide, then you multiply, then you subtract, and then you bring the next digit down. This process is repeated until you have reached a solution.

What is the 7 trick for division? ›

To determine whether a number is divisible by 7, you have to remove the last digit of the number, double it, and then subtract it from the remaining number. If the remainder is zero or a multiple of 7, then the number is divisible by 7. If the remainder is not zero or a multiple of 7, the number is not divisible by 7.

What grade level is long division? ›

Moving into 5th grade, your child will calculate whole number quotients with four-digit dividends and two-digit divisors. It is typical to begin using the standard algorithm, or long division, in 5th grade.

What age should you know long division? ›

Long division is introduced in Year 6. It is important that children understand the concept of division before this method is taught as this formal method is quite an abstract process. The long division method is usually used to divide by larger numbers than the short division method.

Do schools still teach long division? ›

When do children learn about long division in school? Long division, or the standard algorithm, does not appear in the Common Core standards until 6th grade, although some other states, such as Texas (TEKS), introduce the standard algorithm in 5th grade.

### How do you make long division fun? ›

5 Fun ways to practice long division
1. Visuals around the class. Visual aids give students a reference and help them learn terminology, concepts, and rules. ...
2. The herding game. ...
3. Pizza. ...
4. Magic Square Puzzles. ...
5. Word problems.
Jul 23, 2019

How can you check the correctness of a division answer that has no remainder? ›

(Step 1) multiply the quotient by the divisor and then add the remainder. If the result of Step 1 is equal to the dividend, then your answer to the division problem was correct.

How to recheck division? ›

To check your work, multiply the quotient (answer) by the divisor (number of groups you are dividing into), then add in the remainder. If your work was correct, you will get the dividend, or the total or largest number in the problem. So 3 (divisor) * 3 (quotient) = 9 +1 (remainder) = 10.

What is the division checking formula? ›

Dividend = Divisor x Quotient + Remainder

This is also called the division formula to check whether the answer is correct or not.

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