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How to do long division A mathematical process used to divide a large number by a smaller number is called long division. How to do long division is a common question asked by many students, as it can be a challenging task to perform without proper understanding and practice. If you want to know how to do long division, read the content below.
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Contents
How to do long division?
Long division is a mathematical operation used to divide two large numbers. It involves breaking down the division process into smaller, manageable steps, which makes it easier to work with large numbers. In this guide, we will explain how to do long division step-by-step, so you can master this important math skill.
Step 1: Write the division problem
The first step in long division is to write the problem down. The division problem consists of two numbers, the dividend and the divisor. The dividend is the number being divided, while the divisor is the number dividing the dividend. Write the dividend on the left side of the page and the divisor on the right side of the page.
Step 2: Divide the first digit of the dividend by the divisor
The next step is to divide the first digit of the dividend by the divisor. Write the quotient (the result of the division) above the dividend. If the quotient is a whole number, write it on top of the dividend. If it is not a whole number, write the whole number part above the dividend and the remainder below the dividend.
Step 3: Multiply the divisor by the quotient
The next step is to multiply the divisor by the quotient. Write the result (the product) below the dividend, lining up the digits in the ones place.
Step 4: Subtract the product from the dividend
The next step is to subtract the product from the dividend. Write the difference (the result of the subtraction) below the product.
Step 5: Bring down the next digit of the dividend
The next step is to bring down the next digit of the dividend. Write the digit next to the difference.
Step 6: Repeat the process
Repeat the process from step 2 to step 5 until there are no more digits to bring down from the dividend. If there is a remainder after the last step, write it as a fraction.
How to do long division with polynomials?
Long division with polynomials is similar to long division with numbers, but instead of dividing numbers, you will be dividing polynomials. This process is important in algebra and can help simplify complex expressions. In this guide, we will explain how to do long division with polynomials step-by-step.
Step 1: Write the problem
Write the dividend and divisor polynomials in long division format, with the dividend on the left and the divisor on the right. Make sure that the polynomials are written in descending order of degrees, with the highest degree term first.
Step 2: Divide the first term of the dividend by the first term of the divisor
Divide the first term of the dividend by the first term of the divisor. Write the quotient on top of the division symbol.
Step 3: Multiply the quotient by the divisor
Multiply the quotient by the divisor. Write the product under the dividend polynomial.
Step 4: Subtract the product from the dividend
Subtract the product from the dividend. Write the difference below the product.
Step 5: Bring down the next term of the dividend
Bring down the next term of the dividend. Write the term next to the difference.
Step 6: Repeat the process
Repeat steps 2 to 5 until there are no more terms to bring down from the dividend. The last term in the quotient is the remainder, if there is one.
Step 7: Write the answer
Write the quotient polynomial as the answer to the division problem.
Example:
Let’s use the problem (4x^3 + 5x^2 – 7x + 8) ÷ (x^2 – 2x + 3) to demonstrate the long division process.
Step 1: Write the problem
Write (4x^3 + 5x^2 – 7x + 8) on the left side of the page and (x^2 – 2x + 3) on the right side of the page.
Step 2: Divide the first term of the dividend by the first term of the divisor
Divide 4x^3 by x^2. The quotient is 4x. Write 4x on top of the division symbol.
Step 3: Multiply the quotient by the divisor
Multiply 4x by (x^2 – 2x + 3). The product is 4x^3 – 8x^2 + 12x. Write the product under the dividend polynomial.
Step 4: Subtract the product from the dividend
Subtract 4x^3 – 8x^2 + 12x from 4x^3 + 5x^2 – 7x + 8. The difference is 13x^2 – 7x + 8. Write the difference below the product.
Step 5: Bring down the next term of the dividend
Bring down -7x next to the difference.
Step 6: Repeat the process
Divide 13x^2 by x^2. The quotient is 13. Multiply 13 by (x^2 – 2x + 3). The product is 13x^2 – 26x + 39. Subtract 13x^2 – 26x + 39 from 13x^2 – 7x + 8. The difference is 19x – 31. Bring down 0. Divide 19x by x^2. The quotient is 0. Write 0 on top of the division symbol. Multiply 0 by (x^2 – 2x + 3). The product is 0. Subtract 0 from 19x – 31.
How to do long division with decimals?
Long division with decimals can be tricky, but it’s an essential skill to have in math. It involves dividing two numbers with a decimal point. Here are the steps to follow when doing long division with decimals:
Step 1: Write the division problem
Write the division problem in long division format, with the dividend on the left side of the symbol and the divisor on the right side. Make sure to align the decimal points of both numbers.
Step 2: Move the decimal point
Move the decimal point in the divisor to the right until it becomes a whole number. Move the same number of decimal places to the right in the dividend.
Step 3: Divide as usual
Perform the division as you would with whole numbers. Divide the first digit of the dividend by the divisor. Write the quotient above the dividend. Then multiply the divisor by the quotient, and write the result below the dividend. Subtract the product from the dividend to get the remainder.
Step 4: Bring down the next digit
Bring down the next digit of the dividend, and continue dividing until there are no more digits left to bring down.
Step 5: Place the decimal point
Place the decimal point in the quotient directly above the decimal point in the dividend.
Step 6: Check your work
Once you’ve completed the long division problem, check your work by multiplying the quotient by the divisor and adding the remainder. The result should be equal to the dividend.
Example:
Let’s use the problem 12.345 ÷ 3.4 to demonstrate the long division process.
Step 1: Write the division problem
Write 12.345 on the left side of the symbol and 3.4 on the right side of the symbol. Align the decimal points.
Step 2: Move the decimal point
Move the decimal point in 3.4 to the right until it becomes a whole number. Move the same number of decimal places to the right in 12.345. The problem becomes 123.45 ÷ 34.
Step 3: Divide as usual
Divide 12 by 3 to get 4. Write 4 above the line. Then multiply 4 by 3.4 to get 13.6. Write 13.6 below 12. Subtract to get 0.4. Bring down the next digit, which is 4. Divide 4 by 3 to get 1.3. Write 1 above the line. Multiply 3.4 by 1 to get 3.4. Write 3.4 below 4. Subtract to get 0.6.
Step 4: Bring down the next digit
Bring down the next digit, which is 5.
Step 5: Place the decimal point
Place the decimal point in the quotient directly above the decimal point in the dividend. The answer is 3.625.
Step 6: Check your work
To check your work, multiply 3.625 by 3.4 and add the remainder, 0.4. The result should be equal to 12.345.
How to do long division with 2 digits?
Long division with two digits is similar to long division with one digit, but it involves dividing a larger number by a two-digit number. Here are the steps to follow when doing long division with two digits:
Step 1: Write the division problem
Write the division problem in long division format, with the dividend on the left side of the symbol and the divisor on the right side. Make sure to align the digits properly.
Step 2: Divide the first digit
Divide the first digit of the dividend by the two-digit divisor. Write the quotient above the dividend.
Step 3: Multiply and subtract
Multiply the quotient by the divisor and subtract the result from the first part of the dividend.
Step 4: Bring down the next digit
Bring down the next digit of the dividend and write it next to the remainder from the previous step.
Step 5: Divide and repeat
Divide the new number (the remainder plus the new digit) by the divisor. Write the quotient above the new number.
Step 6: Multiply and subtract again
Multiply the new quotient by the divisor and subtract the result from the new number.
Step 7: Repeat until there are no more digits
Repeat steps 4-6 until there are no more digits in the dividend.
Step 8: Write the remainder (if any)
If there is a remainder, write it next to the quotient as a fraction.
Example:
Let’s use the problem 258 ÷ 12 to demonstrate the long division process.
Step 1: Write the division problem
Write 258 on the left side of the symbol and 12 on the right side of the symbol. Align the digits properly.
Step 2: Divide the first digit
Divide 25 by 12 to get 2. Write 2 above the line.
Step 3: Multiply and subtract
Multiply 2 by 12 to get 24. Subtract 24 from 25 to get a remainder of 1.
Step 4: Bring down the next digit
Bring down the next digit, which is 8. Write it next to the remainder, so we have 18.
Step 5: Divide and repeat
Divide 18 by 12 to get 1. Write 1 above the line.
Step 6: Multiply and subtract again
Multiply 1 by 12 to get 12. Subtract 12 from 18 to get a remainder of 6.
Step 7: Repeat until there are no more digits
Bring down the last digit, which is 0. Write it next to the remainder, so we have 60. Divide 60 by 12 to get 5. Write 5 above the line. Multiply 5 by 12 to get 60. Subtract 60 from 60 to get a remainder of 0.
Step 8: Write the remainder (if any)
Since the remainder is 0, we don’t need to write it as a fraction. The answer is 21, so 258 ÷ 12 = 21.
What is long division?
Long division is a mathematical method used to divide large numbers, such as whole numbers or decimals, into smaller numbers. It is a more complex method than simple division, but it allows for the division of numbers with many digits or numbers with decimals. Long division is commonly used in mathematics and science, and it is an essential skill for many practical applications.
The long division process involves breaking down a division problem into a series of simpler steps. In this method, the dividend, which is the number being divided, is written on the left side of a division symbol, while the divisor, which is the number doing the dividing, is written on the right side of the symbol. The quotient, which is the answer to the division problem, is written above the dividend, and the remainder, which is the amount left over after division, is written next to the quotient.
The process begins by dividing the first digit of the dividend by the divisor to obtain a quotient. Then, this quotient is multiplied by the divisor to get a partial product, which is subtracted from the dividend to obtain a remainder. This remainder is then combined with the next digit of the dividend, and the process is repeated until all digits of the dividend have been used.
Long division is a fundamental skill in mathematics and is used to solve a variety of problems, from simple arithmetic to more complex mathematical operations. It is also used in practical applications, such as calculating measurements in science and engineering, computing financial ratios, and calculating tax rates.
Parts of long division
Long division is a mathematical method that allows us to divide large numbers or polynomials into smaller ones. It is a process that involves several steps and requires a good understanding of arithmetic and mathematical operations. The parts of long division include the dividend, divisor, quotient, remainder, and sometimes the divisor and dividend coefficients.
The dividend is the number being divided. It is typically written on the left side of the division symbol, and it can have any number of digits. For example, in the problem 1278 ÷ 6, the dividend is 1278.
The divisor is the number doing the dividing. It is typically written on the right side of the division symbol and is a smaller number than the dividend. In the example 1278 ÷ 6, the divisor is 6.
The quotient is the answer to the division problem. It is typically written above the dividend and is found by dividing the dividend by the divisor. For example, in the problem 1278 ÷ 6, the quotient is 213.
The remainder is the amount left over after division. It is typically written next to the quotient and is found by subtracting the product of the quotient and divisor from the dividend. In the example 1278 ÷ 6, the remainder is 0.
In some cases, there are also divisor and dividend coefficients, which are constants that multiply the divisor and dividend. For example, in the problem 2x^2 + 7x + 5 ÷ 3x + 2, the divisor coefficient is 3 and the dividend coefficient is 2. These coefficients are important because they affect the division process and the final result.
The long division process involves several steps, including dividing, multiplying, and subtracting, until a quotient and remainder are obtained. Each step requires careful attention to arithmetic and mathematical operations, as well as an understanding of the parts of long division. By mastering the parts of long division and the process itself, it is possible to divide even very large numbers or polynomials quickly and accurately.
How to do long division – FAQ
1. What is long division?
Long division is a mathematical process used to divide a larger number by a smaller number.
2. Why do we need to learn long division?
Long division is a foundational skill in mathematics and is used in various mathematical applications.
3. What are the basic concepts of long division?
The basic concepts of long division include the dividend, divisor, quotient, and remainder.
4. What is the dividend in long division?
The dividend is the number being divided in a long division problem.
5. What is the divisor in long division?
The divisor is the number dividing the dividend in a long division problem.
6. What is the quotient in long division?
The quotient is the answer to the division problem.
7. What is the remainder in long division?
The remainder is the amount left over after the division process is complete.
8. How do I set up a long division problem?
To set up a long division problem, write the dividend under the long division symbol and the divisor outside the symbol.
9. What is the first step in long division?
The first step in long division is to divide the first digit of the dividend by the divisor.
10. What do I do after I divide the first digit of the dividend by the divisor?
After dividing the first digit of the dividend by the divisor, you multiply the quotient by the divisor and subtract it from the dividend.
11. How do I know when to stop in long division?
You stop in long division when there are no more digits to bring down from the dividend.
12. How do I handle remainders in long division?
Remainders in long division are written as a fraction with the remainder as the numerator and the divisor as the denominator.
13. Can I use long division to divide decimals?
Yes, long division can be used to divide decimals.
14. How do I handle decimals in long division?
When dividing decimals in long division, move the decimal point to the right until the divisor is a whole number.
15. What if the divisor is larger than the dividend in long division?
If the divisor is larger than the dividend in long division, the quotient will be 0 with the dividend as the remainder.
16. Can I use long division to divide fractions?
Yes, long division can be used to divide fractions.
17. How do I handle fractions in long division?
To divide fractions in long division, convert them to their equivalent decimal form.
18. What if the quotient in long division is a repeating decimal?
If the quotient in long division is a repeating decimal, round it to the nearest hundredth.
19. How do I check my long division answer?
You can check your long division answer by multiplying the quotient by the divisor and adding the remainder.
20. How can I improve my long division skills?
You can improve your long division skills by practicing regularly and seeking help from a teacher or tutor when needed.
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