Lengthy division is a mathematical technique used to divide massive numbers that can not be simply divided by psychological arithmetic or a calculator. It might appear daunting at first, however with a step-by-step method and a few apply, anybody can grasp this talent.
Lengthy division entails breaking down the division course of right into a collection of smaller steps. The important thing to this technique is to maintain monitor of the numbers and their placements all through the division course of.
Earlier than delving into the detailed steps, let’s perceive the essential ideas and phrases utilized in lengthy division. The dividend is the quantity being divided, the divisor is the quantity dividing the dividend, and the quotient is the reply or results of the division. The rest is the quantity left over after the division is full.
learn how to do lengthy division
Lengthy division entails a step-by-step course of to divide massive numbers.
- Arrange the issue
- Divide the primary digits
- Multiply and subtract
- Convey down the following digit
- Repeat the method
- Examine your reply
- Deal with remainders
- Follow, apply, apply!
With constant apply, you may grow to be proficient in lengthy division and be capable of remedy advanced division issues with ease.
Arrange the issue
To start lengthy division, you must arrange the issue accurately. This entails writing the dividend and divisor within the correct format.
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Write the dividend
Write the quantity you need to divide (the dividend) on high of a horizontal line.
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Write the divisor
Write the quantity you might be dividing by (the divisor) exterior the division image, to the left of the dividend and barely under it.
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Draw a horizontal line
Draw a horizontal line under the dividend, extending all the way in which to the precise.
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Write placeholders
If the dividend has fewer digits than the divisor, write placeholders (zeros) to the left of the dividend till it has the identical variety of digits because the divisor.
Upon getting arrange the issue accurately, you may start the division course of.
Divide the primary digits
Upon getting arrange the issue accurately, you may start dividing the primary digits.
Step 1: Ranging from the left, divide the primary digit of the dividend by the primary digit of the divisor. If the divisor is bigger than the primary digit of the dividend, write a zero above the dividend and transfer to the following digit.
Step 2: Upon getting a digit above the dividend that’s bigger than or equal to the primary digit of the divisor, divide them. Write the end result above the dividend, immediately above the digit you divided.
Step 3: Multiply the divisor by the digit you simply wrote above the dividend. Write the product under the dividend, lining up the place values.
Step 4: Subtract the product from the dividend, writing the end result under. That is known as the rest.
Now that you’ve divided the primary digits, you may carry down the following digit from the dividend and proceed the division course of.
Multiply and subtract
Upon getting divided the primary digits and introduced down the following digit from the dividend, you must multiply and subtract.
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Multiply the divisor by the digit you wrote above the dividend
Multiply the divisor by the digit you wrote above the dividend, immediately above the digit you divided. Write the product under the dividend, lining up the place values.
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Subtract the product from the dividend
Subtract the product from the dividend, writing the end result under. That is known as the rest.
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Convey down the following digit from the dividend
Convey down the following digit from the dividend and place it subsequent to the rest. This creates a brand new quantity that you’ll divide within the subsequent step.
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Repeat the method
Repeat the method of dividing the primary digits, multiplying, and subtracting till you could have introduced down all of the digits from the dividend.
By following these steps, you’ll finally attain a the rest of zero, which signifies that the division is full and you’ve got discovered the quotient.
Convey down the following digit
After you could have multiplied the divisor by the digit above the dividend and subtracted the product from the dividend, you must carry down the following digit from the dividend.
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Find the following digit within the dividend
Discover the following digit within the dividend, to the precise of the digit you simply introduced down.
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Place the following digit subsequent to the rest
Place the following digit subsequent to the rest, creating a brand new quantity.
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Proceed the division course of
Proceed the division course of with the brand new quantity. Divide the primary digit of the brand new quantity by the divisor, and repeat the steps of multiplying, subtracting, and bringing down the following digit.
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Repeat till the division is full
Preserve repeating the method of bringing down the following digit and dividing till you could have introduced down all of the digits from the dividend and reached a the rest of zero.
By bringing down the following digit and persevering with the division course of, you’ll finally attain the ultimate reply, which is the quotient.
Repeat the method
Upon getting introduced down the following digit from the dividend, you must repeat the method of dividing, multiplying, and subtracting till you attain a the rest of zero.
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Divide the primary digit of the brand new quantity by the divisor
Divide the primary digit of the brand new quantity (created by bringing down the following digit) by the divisor.
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Write the end result above the dividend
Write the results of the division above the dividend, immediately above the digit you divided.
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Multiply the divisor by the digit you simply wrote
Multiply the divisor by the digit you simply wrote above the dividend. Write the product under the dividend, lining up the place values.
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Subtract the product from the dividend
Subtract the product from the dividend, writing the end result under. That is the brand new the rest.
Preserve repeating these steps till you could have introduced down all of the digits from the dividend and reached a the rest of zero. At this level, the division course of is full and you’ve got discovered the quotient.
Examine your reply
Upon getting accomplished the lengthy division course of and reached a quotient, it is essential to test your reply to verify it’s right.
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Multiply the divisor by the quotient
Multiply the divisor by the quotient. Write the product under the dividend, lining up the place values.
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Subtract the product from the dividend
Subtract the product from the dividend. The end result ought to be the rest.
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Examine the rest
If the rest is zero, then your reply is right. If the rest just isn’t zero, then there may be an error in your division course of and you must test your work.
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Recheck your work
Should you discover an error, return and thoroughly test every step of your division course of till you discover the error.
By checking your reply, you may guarantee that you’ve carried out the lengthy division accurately and obtained the correct quotient.
Deal with remainders
In lengthy division, typically chances are you’ll encounter a the rest that’s not zero after finishing the division course of. This is learn how to deal with remainders:
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Examine the rest
After you could have accomplished the division and reached a quotient, test the rest. If the rest is zero, then you could have discovered the precise quotient.
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Specific the rest as a fraction
If the rest just isn’t zero, you may categorical it as a fraction. The denominator of the fraction is the divisor, and the numerator is the rest.
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Write the quotient as a blended quantity
To jot down the quotient as a blended quantity, mix the entire quantity half (quotient) and the fractional half (the rest fraction). The entire quantity half is the quantity you obtained from the division course of, and the fractional half is the rest expressed as a fraction.
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Simplify the blended quantity (optionally available)
If attainable, you may simplify the blended quantity by changing the fractional half to a decimal or by discovering a typical issue between the entire quantity half and the numerator of the fractional half.
By dealing with the rest accurately, you may categorical the quotient in several varieties, together with as a blended quantity or a decimal, relying on the context and the extent of precision required.
Follow, apply, apply!
The important thing to mastering lengthy division is apply. Listed here are some ideas for efficient apply:
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Begin with easy issues
Start with division issues that contain smaller numbers and fewer digits. It will assist you to grasp the essential ideas and construct confidence.
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Step by step enhance the problem
As you grow to be extra snug with the method, problem your self with extra advanced division issues. It will assist you to develop your problem-solving expertise and develop your understanding.
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Use a wide range of sources
There are a lot of sources obtainable that will help you apply lengthy division, reminiscent of on-line tutorials, printable worksheets, and academic video games. Discover completely different sources to search out those that work finest for you.
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Examine your work
After fixing every drawback, test your reply to verify it’s right. It will assist you to establish any errors and reinforce the proper steps.
Constant apply will assist you to develop fluency and accuracy in lengthy division, making it a beneficial talent for fixing mathematical issues.
FAQ
When you have any additional questions on lengthy division, try these often requested questions and their solutions:
Query 1: What’s lengthy division used for?
Reply 1: Lengthy division is used to divide massive numbers that can not be simply divided by psychological arithmetic or a calculator. It’s a technique for locating the quotient and the rest when one quantity is split by one other.
Query 2: How do I arrange an extended division drawback?
Reply 2: To arrange an extended division drawback, write the dividend (the quantity being divided) on high of a horizontal line, and the divisor (the quantity dividing the dividend) exterior the division image, barely under and to the left of the dividend. Draw a horizontal line under the dividend to separate the quotient and the rest.
Query 3: What is step one in lengthy division?
Reply 3: Step one in lengthy division is to divide the primary digit of the dividend by the primary digit of the divisor. Write the end result above the dividend, immediately above the digit you divided.
Query 4: How do I deal with remainders in lengthy division?
Reply 4: When you have a the rest after finishing the division, you may categorical it as a fraction. The denominator of the fraction is the divisor, and the numerator is the rest.
Query 5: How can I test my reply in lengthy division?
Reply 5: To test your reply, multiply the divisor by the quotient and subtract the product from the dividend. If the result’s zero, then your reply is right.
Query 6: How can I apply lengthy division?
Reply 6: You’ll be able to apply lengthy division by beginning with easy issues and regularly rising the problem. Use a wide range of sources, reminiscent of on-line tutorials, printable worksheets, and academic video games, to make your apply extra participating and efficient.
Query 7: What are some ideas for doing lengthy division shortly and precisely?
Reply 7: Follow often to enhance your velocity and accuracy. Use psychological math tips, reminiscent of multiplication and subtraction information, to simplify calculations. Preserve your work organized and test every step fastidiously to keep away from errors.
Bear in mind, lengthy division is a talent that improves with apply. Preserve working towards, and you will grow to be extra assured and proficient in fixing division issues of various complexity.
Now that you’ve a greater understanding of lengthy division, let’s discover some extra tricks to make the method even simpler.
Ideas
Listed here are some sensible ideas that will help you grasp lengthy division:
Tip 1: Perceive the ideas clearly
Earlier than you begin working towards lengthy division, be sure you have a transparent understanding of the essential ideas, reminiscent of dividend, divisor, quotient, and the rest. It will assist you to grasp the method extra simply.
Tip 2: Begin with smaller numbers
Start your apply with division issues involving smaller numbers. It will can help you give attention to the steps and methods with out getting overwhelmed by massive numbers.
Tip 3: Use multiplication and subtraction information
Multiplication and subtraction information may be your allies in lengthy division. Use these information to simplify calculations mentally and velocity up the method.
Tip 4: Preserve your work organized
Manage your work neatly and clearly. Write the dividend, divisor, quotient, and the rest in separate sections. It will assist you to maintain monitor of the numbers and keep away from errors.
Tip 5: Examine your work often
After every step within the lengthy division course of, test your work to make sure that you’re heading in the right direction. It will assist you to establish and proper any errors early on, stopping them from propagating all through the division.
Tip 6: Follow often
Constant apply is vital to mastering lengthy division. Put aside a while every day or week to apply division issues. The extra you apply, the extra snug and proficient you’ll grow to be.
Bear in mind, lengthy division is a talent that requires endurance and apply. By following the following pointers and dedicating time to apply, you’ll develop the boldness and expertise to resolve division issues effectively and precisely.
Now that you’ve a greater understanding of lengthy division and a few sensible ideas that will help you alongside the way in which, let’s summarize the important thing factors and conclude this information.
Conclusion
Lengthy division is a beneficial mathematical talent that enables us to divide massive numbers precisely and effectively. All through this information, we’ve got explored the steps concerned in lengthy division, from establishing the issue to dealing with remainders.
Bear in mind the important thing factors we mentioned:
- Arrange the issue accurately: Write the dividend on high, the divisor exterior the division image, and draw a horizontal line under the dividend.
- Divide the primary digits: Divide the primary digit of the dividend by the primary digit of the divisor and write the end result above the dividend.
- Multiply and subtract: Multiply the divisor by the digit you simply wrote above the dividend and subtract the product from the dividend.
- Convey down the following digit: Convey down the following digit from the dividend and repeat the method of dividing, multiplying, and subtracting.
- Examine your reply: Multiply the divisor by the quotient and subtract the product from the dividend. If the result’s zero, your reply is right.
With apply, you’ll develop fluency and accuracy in lengthy division. Bear in mind to start out with smaller numbers and regularly enhance the problem as you grow to be extra snug with the method. Use multiplication and subtraction information to simplify calculations and maintain your work organized to keep away from errors.
Lengthy division is a talent that can serve you effectively in numerous educational and sensible conditions. Whether or not you might be fixing math issues, engaged on monetary calculations, or just dividing substances for a recipe, lengthy division gives a dependable technique for locating quotients and remainders.
So, embrace the problem of lengthy division, apply often, and you’ll quickly grasp this important mathematical talent.
