Long Division
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. This lesson will give you an overview of the long division method.
| 1. | What is Long Division? |
| 2. | Parts of Long Division |
| 3. | How to Do Long Division? |
| 4. | FAQs on Long Division |
What is Long Division?
In Math, 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 division to see the divisor, the dividend, the quotient and the remainder.
Parts of Long Division
Here are the terms related to division which are also considered as the parts of long division. They are the same terms that are used in regular division.
- Dividend
- Divisor
- Quotient
- Remainder
Have a look at the table given below in order to understand the terms related to division with reference to the example shown above.
| Dividend | The number which has to be divided. | 75 |
| Divisor | The number which will divide the dividend. | 4 |
| Quotient | The result of division. | 18 |
| Remainder | The leftover part or the number that can't be divided further. | 3 |
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.
It requires the construction of a tableau. 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 steps given below to see how long division takes place.
- Step 1: Take the first digit of the dividend. 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 number (if present).
- Step 5: Repeat the same process.
Let's have a look at the examples given below for a better understanding of the concept.
Case 1: When the first digit of the dividend is equal to or greater than the divisor
Let's consider an example: Divide 435 ÷ 4
- Here, the first digit of the dividend is 4 and it is equal to the divisor. So, 4 ÷ 4 =1. 1 is written on top.
- Subtract: 4-4=0,
- Bring the second digit of the dividend down and place it beside 0.
- Now, 3<4. Hence, we write 0 as the quotient and bring down the next digit of the dividend and place it beside 3.
- Now, we have 35 as the new dividend. 35 > 4. 35 is not divisible by 4, but we know that 4 × 8 = 32, so, we go for it.
- Write 8 as the quotient. Subtract: 35-32=3.
- 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.
Let's consider another example: Divide 735 ÷ 9
- 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.
- 73 is not divisible by 9 but we know that 9 × 8 = 72 so, we go for it.
- Write 8 as the quotient and subtract: 73-72=1.
- Bring down 5. The number to be considered now is 15.
- Since 15 is not divisible by 9 but we know that 9 × 1 = 9, so, we take 9.
- Subtract: 15-9=6. Write 1 as the quotient.
- Now, 6<9. Thus, remainder=6 and quotient=81.
Case 3: When the divisor doesn't go with the first digit of the dividend.
Let's solve one more example: Divide 3640 ÷ 15
- Since the first digit of the dividend is not divisible by the divisor, we consider the first two digits (36).
- Now, 36 is not divisible by 15 but 15 × 2=30, so, write 2 as the quotient.
- Write 30 below 36 and subtract: 36-30=6.
- Since 6<15, we will bring down 4 from the dividend to make it 64.
- 64 is not divisible by 15 but 15 × 4 = 60, so, write 4 as the quotient.
- Write 60 below 64 and subtract: 64-60=4.
- Since 4<15, bring down 0 from the dividend to make it 40.
- Since 40 is not divisible by 15 but 15 × 2=30, so, write 2 as the quotient.
- Write 30 below 40 and subtract: 40-30=10.
- Now 10<15. Thus, remainder=10 and quotient=242.
Important Notes:
Given below are a few important points that would help you while working with long division:
- The dividend is always greater than the divisor and the quotient.
- The remainder is always smaller than the divisor.
- For division, the divisor cannot be 0.
- Division is repeated subtraction, so we can check our quotient by repeated subtractions as well.
- We can check the quotient and the remainder of division using the following 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.
Long division problems also include problems related to long division polynomials and long division with decimals.
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 as the normal long division. For more details about long division with decimals, visit the Dividing Decimals page.
Long Division Solved Examples
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Example 1: Ron planted 75 trees equally in 3 rows. How many trees did he plant in each row?
Solution:
Total number of trees planted by Ron = 75. Number of rows = 3. To find the number of trees in each row, we have to divide 75 by 3 because there is an equal number of trees in each of the three rows.
Therefore, the number of trees in each row = 25
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Example 2: $4000 need to be distributed among 25 men for the work completed by them at a construction site. Calculate the amount given to each man.
Solution:
The total amount is $4000. The number of men at work = 25. We have to calculate the amount given to each man. To do so, we have to divide 4000 by 25 using the long division method.
Each man will be given $160. Therefore, the amount given = $160.
FAQs on Long Division
How Do I Do Long Division?
The following steps explain the process of long division:
- Write the dividend and the divisor at their respective positions.
- Take the first digit of the dividend.
- 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 numbers in the dividend to be carried down, we continue with the same process until there are no more numbers left in the dividend.
What are the 5 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: D for Divide. Consider the first digit of the dividend. 5>2. 5 is not divisible by 2.
- Step 2: M for Multiply. We know that 2 × 2 = 4, so, we write 2 as the quotient.
- Step 3: S for Subtract. 5-4=1 and 1<2. (After writing the product 4 below the dividend, we subtract them).
- Step 4: B for Bring down. 1<2, so we bring down 2 from the dividend and we get 12 as the 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 as the quotient. 12-12=0.
Therefore, the quotient is 26 and the remainder is 0.
How Do you Do Long Division With 2 Digits?
Consider both the digits of the divisor and check for the divisibility of the first two digits of the dividend. Proceed with the division in the same way as we divide regular numbers.
What is Long Division of Polynomials?
In algebra, long division of polynomials is an algorithm to divide a polynomial by another polynomial of the same or the lower degree, using the long division method. For example, (4x2 - 5x - 21) is a polynomial which 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 the same way as the normal long division. It follows the steps 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 tenth digit.
- Divide and bring down the other digit in sequence.
- Divide until 0 is obtained in the remainder.
What is Long Division Symbol Called?
The divisor and the dividend are separated by a right parenthesis 〈)〉 or a vertical bar 〈|〉 whereas, the dividend and the quotient are separated by a vinculum or an overbar. The combination of these two symbols is referred to as long division symbol or division bracket.
How do you Divide When the Divisor is Bigger Than the Dividend?
In this case of division, we can simply keep on adding zeros to the dividend until it becomes appropriate to divide further. Then, we can divide the quotient by the same powers of 10 for the final answer once we get the division done correctly.