Calculate Long Division of Numbers
In this case, we will learn to divide numbers into two categories. One is division with remainder and the other is division without remainder.
Long Division with Remainder
In this, we will learn about two cases:
Case 1: When the first digit of the dividend is greater than or equal to the divisor
Example: Find quotient and remainder when 341 is divided by 3.
Solution:
Step 1: Observe the dividend from Left Hand Side. We find that first digit is 3 which is equal to dividend.
Step 2: Write 1 in the Quotient column and write three below the first digit of dividend 342 as 3 is the multiple of 3 which is nearest to the first digit of the dividend which is also 3. Find the difference we get 3 – 3 = 0.
Step 3: In this step bring down the second digit of the dividend beside 0. Write 1 in quotient column as 3 is the multiple of 3 which is nearest to 4. Subtract 4 – 3 we get 1.
Step 4: In this step bring down the last digit 1 of the dividend beside the 1 that was left in step 4.
Step 5: Write 3 in the Quotient column as 9 is the multiplier of 3 which is nearest to 11. Subtract 11 – 9 we get 2. Now no digit of the remainder is left.
Hence, we find that on dividing 341 by 3 we get 113 as the quotient and 2 as the remainder.
Case 2: When the first digit of the dividend is less than the divisor
For Example, Divide 541 by 7.
Step 1: Observe that the first digit of dividend is 5 which is less than 7 hence we can not proceed division with the first digit. Thus we need to divide the first two digits of the dividend i.e. 54 by 7.
Step 2: Write 7 in the Quotient column as 49 is the multiple of 7 which is nearest to 54. Subtract 54 – 49 we get 5.
Step 3: Write the last digit 1 of the dividend beside 5 which is obtained in step 2.
Step 4: Divide 51 by 7. Write 7 in the quotient column because 49 is the multiple of 7 nearest to 51. Subtract 51 – 49, we get 2.
Hence, on dividing 541 by 7 we get 77 as quotient and 2 as remainder.
Long Division without Remainder
In this case, the steps are the same as Division with Remainder just only one difference that here remainder at the end of differentiation is zero.
Let us understand it with an example.
Example: Divide 436 by 4.
Solution:
Step 1: Observe that the first digit of dividend is equal to divisor i.e. both are 4 here.
Step 2: Write 1 in quotient column as 4 is the nearest multiple to itself. Subtract 4 – 4 we get zero.
Step 3: Write down the next digit of dividend i.e. 3 beside the zero obtained in step 2. We see that 3 is less than 4 which is the divisor hence we need to put 0 in the quotient.
Step 4: Write down the next digit of dividend i.e. 6 beside 3 obtained in the previous step. Now we have 36.
Step 5: Write 9 in the quotient column as 36 is the multiple of 4 which is nearest and equal to 36. Subtract 36 – 36, we get zero.
Hence on dividing 436 by 4, we get 109 as the quotient and 0 as the remainder.
Long Division Method
Long Division is a technique of dividing numbers, algebraic expressions, and decimals stepwise and sequentially. In this technique the number which is to be divided is called Dividend, the number which divides is called Divisor, the number which we get as a result of division is called a Quotient, and the number which is left as extra on dividing is called Remainder.
In this article, we will learn in detail about the long division method, the components of the long division method, the Division Algorithm, the division of numbers, decimals, and algebraic expression.
Table of Content
- What is Long Division Method?
- Components of Long Division Method
- How to do Long Division?
- Calculate Long Division of Numbers
- Long Division by 2-Digit Number
- Long Division of Polynomials
- Long Division with Decimal
- Division of Decimals by a Whole Number
- Dividing a Number to Decimal Places
- Long Division Application
- Division by Repeated Subtraction
- Division Algorithm
- Long Division Problems
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