Introduction
Long division is a fundamental mathematical skill that many of us learn in school, yet it plays a significant role in our daily lives. From dividing complex recipes to calculating tips, proficiency in long division can save time and prevent errors. This article aims to provide a step-by-step tutorial on how to long divide efficiently, including common mistakes, practice problems and alternative methods.
Step-by-Step Tutorial
The process of long division entails dividing two or more numbers using the standard algorithm. Let us break it down into simple steps.
Step 1: Write the divisor on the left side of the line, while the dividend is on the right side.
Step 2: Divide the first digit of the dividend by the divisor; write the quotient on top of the division line, above the dividend.
Step 3: Multiply the quotient by the divisor and write the result underneath the first digit of the dividend.
Step 4: Subtract the result obtained in step 3 from the first digit of the dividend. Write the remainder under the first digit of the dividend.
Step 5: Bring down the next digit of the dividend next to the remainder written in step 4. Place this new number after the remainder as the new dividend.
Step 6: Repeat steps 2 to 5 until there are no digits left in the dividend.
To illustrate this process, let us consider the division of 567 by 6.
“`
94
____________
6 | 567
“`
Step 1: We start by placing 6 on the left side of the division line and the dividend, 567, on the right side.
Step 2: The first digit of the dividend is 5. We divide 5 by 6. Since 6 cannot divide 5, we take the first two digits, which are 56. 6 can divide 56 seven times. So, we write 7 above the 6.
“`
7
____________
6 | 567
“`
Step 3: We multiply 7 by 6, which is equal to 42, and write it underneath 56.
“`
7
____________
6 | 567
42
“`
Step 4: We subtract 42 from 56, which is equal to 14. We write 14 underneath the 42.
“`
7
____________
6 | 567
42
____
14
“`
Step 5: We bring down the next digit of the dividend, which is 7.
“`
94
____________
6 | 567
42
____
14
7
“`
Step 6: We repeat steps 2 to 5 until the entire dividend is evaluated.
“`
94
____________
6 | 567
42
____
14
7
____
0
“`
The final answer is 94, and the remainder is 0.
Common Mistakes to Avoid
Many people make common mistakes when learning how to long divide. Here are some of the errors and tips on how to avoid them.
Mistake 1: Misunderstanding the classic long division rules.
Tip: Start with a clear understanding of the long division process by reviewing each step. Practice with different inputs to reinforce this understanding.
Mistake 2: Not keeping the numbers aligned and labelled in the division.
Tip: Always leave space as you write the numbers and make sure to align all the digits and the operations signs so that the calculation is clear.
Mistake 3: Ignoring remainders, especially when they occur in the middle of the division.
Tip: Always look out for and account for remainders in the division process. An unchecked remainder can lead to an incorrect result.
Practice Problems
The key to becoming proficient in long division is through practice. Here are a few practice problems to aid with the concept, with solutions provided.
Problem 1: Divide 34 by 6.
“`
5
____________
6 | 34
“`
Solution: 6 can divide 34, 5 times, leaving a remainder of 4. Thus, the quotient is 5, and the remainder is 4.
Problem 2: Divide 254 by 15.
“`
16
____________
15 | 254
“`
Solution: 15 can divide 25, once. Write 1 above the 5. 15 multiplies by 1 and is subtracted from 25, leaving 10. The next digit, 4, is brought down beside the remainder. Now we need to divide 104 by 15. 15 does not divide into 10, so we bring down another digit from the dividend, which is 4. We can divide 104 by 15, six times. Write 6, the quotient, above 4. Multiplying 15 by 6, we obtain 90, which is subtracted from 104 and leaves a remainder of 14. Therefore, the quotient is 16 with a remainder of 14.
Alternative Methods
There are several alternative methods for long division such as chunking, partial quotient division, and others.
Chunking is a method where the dividend is divided into manageable chunks and then divided by the divisor. This method is helpful when dividing larger numbers.
Partial Quotient Division is a method that, instead of estimating or guessing the number of times the divisor divides into the dividend, subtracts multiples of the divisor from the dividend one at a time.
While alternative methods to long division may be handy in some instances, it is essential to note that classic long division is the most commonly used and reliable method in most scenarios.
Real-World Applications
Long division plays a significant role in real-world situations, making it an essential skill for everyone to have. Here are some examples of how long division is useful in everyday life.
Cooking: Long division is used for dividing larger recipes into smaller portions. This is particularly useful when halving a recipe to adjust portion sizes.
Finance: It is useful for calculating a tip when dining out, determining the number of shares to purchase in the stock market and balancing a checkbook.
DIY: It also comes in handy for dividing wood or tile floor area when cutting or planning a room layout.
Conclusion
Understanding how to long divide and use it efficiently is crucial for everyone. This article has provided a step-by-step tutorial, common mistakes, practice problems and alternative methods that the readers can use to improve their long division skills. With practice, anyone can master the art of long division and apply it in various real-world scenarios.
