Long Division Method
by Daisy, Jul 11 2023
Introduction
Division is one of the four elementary operations in arithmetic, which involves combining numbers to create new ones. The other operations include addition, subtraction, and multiplication.
The long division method incorporates the principles of division, multiplication, and subtraction simultaneously.
This approach not only focuses on division, but also requires students to comprehend the application of long division as well as the significance of divisors, dividends, and multiples.
In mathematics, long division problems offer a systematic technique for dividing larger numbers into smaller groups or segments, allowing complex problems to be broken down into more straightforward steps.
For instance, if 5 people are sharing a pie using this method and the pie is divided into 10 equal pieces, each individual would receive 2 slices.
Various symbols, such as "x ÷ y" or "x/y" , are used to represent division.
This article provides long division worksheets and problems for practice.
Components of Division
Now, let's learn about the parts of a long division problem using some examples!
- The Dividend: This is the number you want to divide.
- The Divisor: This is the number you are dividing with.
- The Quotient: This is the answer you get.
- The Remainder: If the answer isn't a whole number, the leftover part is called the remainder.
So, we can say:
Dividend ÷ Divisor = Quotient
Five Steps to Solve Long Division
In this section, we are going to learn how to do long division step-by-step using these 5 easy steps:
- Divide: First, check how many times the divisor can fit into the first part of the dividend (from left to right). Write the number above the dividend as the first part of the quotient.
- Multiply: Now, multiply the divisor by that number (the first part of the quotient) and write the result below the dividend.
- Subtract: Next, subtract the result (from Step 2) from the first part of the dividend.
- Bring down: After subtracting, bring down the next number in the dividend (if there's any left) and attach it to the remaining part. Now, repeat Step 1 with this new number.
- Remainder: Continue these steps until you can't divide anymore or you reach the end of the dividend. The final leftover part is called the remainder. If there's no remainder, then the division is complete, and you have your quotient.
Exciting Facts about Long Division
Rule #1 : When dividing a number by 1, the quotient is the number itself. It's like splitting our reflection into one equal piece: we still have the same number.
Example:
(a) 4620 ÷ 1 = 4620
(b) 8325 ÷ 1 = 8325
(c) 3901 ÷ 1 = 3901
Rule #2: When dividing a number by the same number, the quotient is always 1. It's like fitting one whole puzzle piece into a matching space.
Example:
(a) 120 ÷ 120 = 1
(b) 750 ÷ 750 = 1
(c) 999 ÷ 999 = 1
Rule #3: Dividing any number by 0 is meaningless. It's like trying to solve a puzzle with no clues – impossible!
Example:
(a) 23 ÷ 0 = (no meaning)
(b) 47 ÷ 0 = (no meaning)
Rule #4: Dividing 0 by any number results in 0 as the quotient.
Example:
(a) 0 ÷ 10 = 0
(b) 0 ÷ 55 = 0
Summary
In conclusion, long division is an essential skill in arithmetic, allowing students to solve complex problems by breaking them down into simpler steps. This method not only emphasises division but also incorporates multiplication, subtraction, and an understanding of elements such as divisors, dividends, and multiples.
Some exciting rules about long division include dividing any number by 1, dividing a number by itself, dividing any number by 0, and dividing 0 by any number. By following a step-by-step process and practising with provided worksheets, learners can master long division and unlock the magic behind this fundamental mathematical operation.