Long division method - Long division questions and answers pdf

Long division method – Long division questions and answers pdf

Table of Contents

Long division method – Long division questions and answers pdf; Long division is a process to divide large numbers in a convenient way. The number which we divide into smaller groups is known as a dividend, the number by which we divide it is called the divisor, the value got after doing the division is the quotient, and the number left after the division is called the remainder.

Step 1: Take the first digit of the dividend from the left. 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.

How to 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 from the left.
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 digits in the dividend to be carried down, we continue with the same process until there are no more digits left in the dividend

What are the 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: Consider the first digit of the dividend which is 5 in this example. Here, 5 > 2. 5 is not divisible by 2.
Step 2: We know that 2 × 2 = 4, so, we write 2 as the quotient.
Step 3: 5 – 4 = 1 and 1 < 2 (After writing the product 4 below the dividend, we subtract them).
Step 4: 1 < 2, so we bring down 2 from the dividend and we get 12 as the new 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 in the quotient, and 12 – 12 = 0 (remainder).

Therefore, the quotient is 26 and the remainder is 0.

Use the video below to check how to apply for Steps of Long Division

Part of a video titled Grade 5 Math #2.6, Divide by a 2 Digit Divisor, Long Division

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. If the first 2 digits of the dividend are less than the divisor, then consider the first three digits of the dividend. Proceed with the division in the same way as we divide regular numbers.

Long Division

It follows the same steps as that of long division, namely, –

divide,
multiply,
subtract,
bring down and repeat or find the remainder. Here’s an example of long division with decimals.

Terminology Used in Division

There are four important terms used in division. These are

dividend
divisor
quotient
and remainder.

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. The steps of long division are given below:

Here, the first digit of the dividend is 4 and it is equal to the divisor. So, 4 ÷ 4 = 1. So, 1 is written on top as the first digit of the quotient.
Subtract: 4 – 4 = 0.
Bring the second digit of the dividend down and place it besides 0.
Now, 3<4. Hence, we write 0 as the quotient and bring down the next digit of the dividend and place it besides 3.
Now, we have 35 as the new dividend. 35 > 4. 35 is not divisible by 4, so we look for the number just less than 35 in the table of 4. We know that 4 × 8 = 32 < 35 so, we go for it.
Write 8 in the quotient. Subtract: 35 – 32 = 3.
3<4. Thus, 3 is the remainder and 108 is the quotient.

Long Division steps

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 in 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 in the quotient.
Now, 6<9. Thus, remainder = 6 and quotient = 81.

Divide 735 by 9 using long division method

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 first digit in 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 in 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 in the quotient.
Write 30 below 40 and subtract 40 – 30 = 10.
Now 10<15. Thus, remainder = 10 and quotient = 242.

Divide 3640 by 15 using Long Division method