Long Division Calculator (2024)

home / math / long division calculator

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.

Long Division Calculator (3)

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:

Long Division Calculator (4)

  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:

    Long Division Calculator (5)

  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.

    Long Division Calculator (6)

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

    Long Division Calculator (7)

  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.

    Long Division Calculator (8)

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.

    Long Division Calculator (9)

  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

How do you find the answer in long division? ›

How to Do Long Division in Simple Steps
  1. Set up the problem. Write the dividend (845) under the division bar and the divisor (3) outside the bar.
  2. Divide. ...
  3. Multiply. ...
  4. Subtract. ...
  5. Bring down the next digit. ...
  6. Repeat the steps. ...
  7. The final answer with a remainder. ...
  8. Convert the remainder to decimal form.
Feb 6, 2024

Can you use a calculator for long division? ›

Calculator Use

It is a little 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.

How do you find out if your answer in 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.

How to calculate long division without a calculator? ›

Long Division Steps
  1. Step 1: Take the first digit of the dividend from the left. ...
  2. Step 2: Then divide it by the divisor and write the answer on top as the quotient.
  3. Step 3: Subtract the result from the digit and write the difference below.
  4. Step 4: Bring down the next digit of the dividend (if present).

What is the formula to check answer in division? ›

The formula Dividend = (Divisor x Quotient) + Remainder is correct.

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 are you supposed to learn long division? ›

Long division, also known as the standard algorithm for division, is introduced in 5th grade. It is important that children understand the concept of division before this method is taught as this formal method is quite an abstract process.

Is long division hard? ›

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 do you find 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.

What are the 5 steps of long division? ›

Long division can also be used to divide decimal numbers into equal groups. It follows the same steps as that of long division, namely, – divide, multiply, subtract, bring down and repeat or find the remainder.

What is the general formula for long division? ›

Algebraic Long Method

Divide the first term of the dividend (the polynomial to be divided) by the first term of the divisor. This gives the first term of the quotient. Multiply the divisor by the first term of the quotient. Subtract the product from the dividend then bring down the next term.

How to calculate long division method? ›

How to perform long division?
  1. Starting from left to right, divide the first digit in the dividend by the divisor. ...
  2. Continue the problem by dividing the divisor into the number formed by the combination of the previous and subsequent digit of the dividend.

How do you find the decimal answer in long division? ›

There are three steps to performing long division with decimals:
  1. Eliminate the decimal point from the divisor, if any.
  2. Perform long division as usual.
  3. Use the same decimal place for the quotient as in the dividend.

How do you call the answer in division? ›

In a division, the first number (the amount being divided) is called the dividend; the second number (whatever the dividend is being divided by), is called the divisor; the answer is called the quotient.

References

Top Articles
Latest Posts
Recommended Articles
Article information

Author: Melvina Ondricka

Last Updated:

Views: 5281

Rating: 4.8 / 5 (68 voted)

Reviews: 91% of readers found this page helpful

Author information

Name: Melvina Ondricka

Birthday: 2000-12-23

Address: Suite 382 139 Shaniqua Locks, Paulaborough, UT 90498

Phone: +636383657021

Job: Dynamic Government Specialist

Hobby: Kite flying, Watching movies, Knitting, Model building, Reading, Wood carving, Paintball

Introduction: My name is Melvina Ondricka, I am a helpful, fancy, friendly, innocent, outstanding, courageous, thoughtful person who loves writing and wants to share my knowledge and understanding with you.