Long Division Calculator (2024)

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Long Division Calculator (1)

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 ÷ 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 ÷ 4 = 2, this can be used to determine that 9 ÷ 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.

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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:

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  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:

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  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.

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

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  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.

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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 ÷ 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.

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  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 ÷ 7 results in a non-terminating decimal eventually, or it can closely be estimated by the mixed number
    14
    2
    7
    = 14.285714285714.
Long Division Calculator (2024)

FAQs

Why is long division different from calculator? ›

Long division is a versatile method for handling complex divisions without using a calculator. It is the preferred method when dividing by a number with two or more digits, particularly if the division is not exact. It can be used to calculate a remainder or give an answer to a paticular number of decimal places.

Why is long division so hard for me? ›

The standard algorithm for long division is difficult. There's no doubt about it. 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.

How can you always check your answer to a division problem? ›

Solving simple division problems is closely linked to multiplication. In fact, to check your work, you'll have to multiply the quotient by the divisor to see if it equals the dividend. If it doesn't, you've solved incorrectly.

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.

What are the 5 steps of long division? ›

What are the 5 steps of long division? Divide, multiply, subtract, bring the next digit down and repeat the previous steps.

What is the 4 method of long division? ›

Long division method: How to do long division. Long division is laid out in the same way as short division: dividend (the number being divided) under the 'bus stop', divisor (number the dividend is being divided by) to the left of the 'bus stop'; quotient (answer) on top, with each place value aligned with the dividend ...

What is the division formula? ›

The division formula is used for splitting a number into equal parts. Symbols that we use to indicate division are (÷) and (/). Thus, “p divided by q” can be written as: (p÷q) or (p/q).

What is the algorithm for long division? ›

The standard algorithm for long division is a series of steps repeated in this order: divide, multiply, subtract, bring down. With the standard algorithm, we solve division problems one place value at a time.

What grade is long division? ›

It is typical to begin using the standard algorithm, or long division, in 5th grade.

How to find out the answer of division? ›

The formula to calculate the division of two numbers is: Dividend ÷ Divisor = Quotient + Remainder. The remainder is the leftover number in the division operation. If 46 is divided by 5, we get the quotient as 9 and the remainder 1.

How to check your answer in division with remainder? ›

When a math problem has a remainder, it just means that there is a number left over after the division is done. To check your answer, just multiply your quotient and divisor and add your remainder. Your total should match the number you started with.

How do you write a long division answer? ›

Long division is laid out in the same way as short division: The dividend (the number being divided) goes under the 'bus stop' or 'house' (or whatever nickname you refer to it as), the divisor (number the dividend is being divided by) goes to the left of the 'bus stop,' and the quotient (answer) goes on top, with each ...

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