In this article, we will discuss the Long division definition, parts of long division, How to do long division. You can also check the solved examples of long division for a better understanding of the concept. We have explained the detailed steps on how to perform long division by considering few examples. Refer to them and apply the concept for real-time problems you come across.
Long Division – Definition
This method used for dividing large numbers into small ones that are simple enough to perform. It will break down large numbers into series of simple steps. It is the common method used to solve problems on division.
Parts of Long Division
Parts of the Long division are the same terms related to the division. They are four parts1. Dividend 2.Divisor 3. Quotient 4.Remainder. The number that has to be divided is called the dividend. The number that divides the dividend is called the divisor. The quotient is the result of division. The remainder is the leftover part of the dividend after division.
For Example 17%3
Here, 17 is the dividend,
3 is the divisor,
5 is the quotient,
2 is the remainder.
How to do Long Division?| Steps to be followed for Long Division
The divisor, the dividend are separated by a right parenthesis 〈)〉 or vertical bar 〈|〉, and the dividend is separated from the quotient by a vinculum (an overbar). Now, the following steps written below are considered for how long division takes place.
- Step 1: Let’s take the first digit of the dividend. Check if the digit is equal to or greater than the divisor.
- Step 2: Then divide the dividend by the divisor and write the answer on top as the quotient.
- Step 3: Subtract the number from the digit and write the difference below.
- Step 4: In the dividend if the next digit exists bring down the next digit.
- Step 5: Repeat the same process.
Carefully look at the examples given below for a better understanding of the concept.
Case 1: Steps to be followed when the first digit of the dividend is equal to or greater than the divisor in the long division
Let’s consider an example: Divide 548 ÷ 5
- Here, the first digit of the dividend is 5 and it is equal to the divisor. So, 5 ÷ 5 =1. 1 is written on top.
- Subtract: 5-5=0,
- Bring down the second digit of the dividend and place it besides 0.
- Now, 4<5. Hence, we write 0 as the quotient and bring down the next digit of the dividend and place it besides 4.
- Now, we have 48 as the new dividend. 48> 5. 48 is not completely divisible by 5, but we know that 5 × 9 = 45, so, we go for it.
- Write 9 as the quotient. Subtract: 48-45=3.
- 3<4. Thus, 3 is the remainder and 109 is the quotient.
Case 2: Steps to be followed when the first digit of the dividend is less than the divisor in the long division
Let’s consider another example: Divide 438 ÷ 5
- 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.
- 43 is not divisible by 5 but we know that 5 × 8 = 40 so, we go for it.
- Write 8 as the quotient and subtract 43-40=3.
- Bring down 8. The number to be considered now is 38.
- Since 38 is not divisible by 5 but we know that 5 × 7 = 35, so, we go for it.
- Subtract: 38-35=3. Write 7 as the quotient.
- Now, 3<5. Thus, remainder=3 and quotient=87.
Case 3: In the long division, When the divisor doesn’t go with the first digit of the dividend
Let’s solve one more example: Divide 3638 ÷ 5
- Since the first digit of the dividend is not divisible by the divisor, we consider the first two digits (36).
- Now, 36 is not completely divisible by 5 but 5 × 7=35, so, write 7 as the quotient.
- Write 35 below 36 and subtract 36-35=1.
- Since 1<15, we will bring down 3 from the dividend to make it 13.
- 13 is not divisible by 5 but 5 × 2 = 10, so, write 2 as the quotient.
- Write 10 below 13 and subtract 13-10=3.
- Since 2<15, bring down 8 from the dividend to make it 38.
- Since 38 is not divisible by 5 but 5 × 7=35, so, write 7 as the quotient.
- Write 35 below 38 and subtract 38-35=3.
- Now 3<5. Thus, remainder=3 and quotient=727.
Important Notes to Remember while Performing Long Division
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.
- The division is repeated subtraction, so we can check our quotient by repeated subtractions as well.
- We can check the quotient and the remainder of the 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 with decimals and long division polynomials.
Long Division with Decimals
Long division with decimals can be easily done just as the normal long division. Long division with decimals steps is the same as normal long division. Steps to be followed for long division are as follows:
- Write the division in the standard form.
- First, 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.
For example, consider the decimal number 331.250,5
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.