Long division is a fundamental mathematical skill that allows us to divide large numbers. In this tutorial, we will guide you step-by-step through the process of solving the division problem: what is 48 divided by 3 using long division. By understanding the terms and following the method, you’ll gain confidence in solving division problems.
Key Takeaways:
- Long division is a method used to divide two numbers.
- Understanding the terms, such as dividend and divisor, is crucial in the long division process.
- The first step in long division is setting up the division problem.
- Dividing the first digit, subtracting, and bringing down the next digit are essential steps in long division.
- By finalizing the calculation, you can determine the quotient and remainder.
Introduction to Long Division
Long division is a method used to divide two numbers. It involves breaking down the division into smaller steps to find the quotient and remainder. By following the long division process, we can find the answer to the division problem.
In the case of 48 divided by 3, 48 is the dividend and 3 is the divisor. The dividend is the number being divided, and the divisor is the number by which we divide the dividend.
Long division is a fundamental mathematical skill that is useful for solving a wide range of division problems. Let’s dive into the long division process to see how it works.
Long Division Process
The long division process can be broken down into the following steps:
- Divide: Divide the first digit of the dividend by the divisor and write the result (quotient) above the division line.
- Multiply: Multiply the divisor by the quotient and write the result below the dividend.
- Subtract: Subtract the result from step 2 from the current digit of the dividend and write the difference below.
- Bring Down: Bring down the next digit of the dividend to form a new dividend.
- Repeat: Repeat steps 1 to 4 until there are no more digits in the dividend.
- Quotient: The final quotient is the answer to the division problem.
- Remainder: If there is a remainder after dividing all the digits, it is written as a fraction or decimal.
Understanding the terms and following these steps will help you master the long division process and solve division problems efficiently.
Step 1: Setting Up the Division Problem
In order to begin the long division process, it’s important to set up the division problem correctly. Let’s take a look at how to do that.
First, we need to place the divisor and dividend in the right position. The divisor, which is the number we’re dividing by, goes on the left side. In this case, our divisor is 3.
On the right side, we place the dividend, which is the number being divided. For our example problem, the dividend is 48.
This setup is crucial because it determines how we will proceed with the rest of the long division steps. By placing the divisor and dividend in their proper positions, we ensure a smooth and accurate calculation.
Now that we have set up the division problem, we can move on to the next step of the long division process.
Step 2: Dividing the First Digit
In step 2 of the long division process, we begin by dividing the first digit of the dividend, which is 4, by the divisor, which is 3.
To find the quotient, we determine how many times the divisor can go into the digit. In this case, 3 can go into 4 one time.
We place the quotient, which is 1, above the division line.
Next, we multiply the divisor (3) by the quotient (1), resulting in 3. This product is written below the first digit of the dividend.
To visualize this step, refer to the table below:
| 1 | |
|---|---|
| 3 | 4 |
| – | |
| 3 | |
By dividing the first digit, we have found the first part of the quotient. We will continue with the remaining steps to find the final answer.
Step 3: Subtracting and Bringing Down
After dividing the first digit and finding the quotient, we proceed to step 3 of the long division process. In this step, we subtract the result from the previous step, which is 3, from the second digit of the dividend, which is 8. The difference is 5. We write this difference below the 3 and place the 5 in the new quotient position.
The next step is to bring down the next digit, which is 8, to form the new dividend for the next division calculation.
Let’s visualize this step with an example:
| Dividend | | | Divisor | | | Quotient | | | Remainder |
|---|---|---|---|---|---|---|
| 48 | | | 3 | | | 1 | | | |
| -3 | | | 5 | ||||
| 5 |
In this example, after dividing the first digit and finding a quotient of 1, we subtract 3 from 8, resulting in a difference of 5. We bring down the next digit, which is 8, to continue the long division calculation.
By performing this step in the long division process, we are gradually working towards finding the final quotient and remainder.
Step 4: Dividing the New Dividend
In step 4, we divide the new dividend by the divisor to find the quotient. Let’s apply this step to our example problem of 48 divided by 3.
To begin, our new dividend is 58. We divide 58 by 3 to determine how many times the divisor can be evenly divided into the new dividend.
58 ÷ 3 = 18
The quotient is 18, which represents the number of times the divisor can be divided into the new dividend. We place this quotient above the division line.
| 18 | |
|---|---|
| 3 | 54 |
Next, we multiply the divisor by the quotient. Multiplying 3 by 18 gives us 54. We write this result below the new dividend.
Now, we have completed step 4 of long division.
Step 5: Subtracting and Bringing Down Again
In this step of the long division process, we subtract the result from the previous step (54) from the third digit of the dividend (8). The difference is 4, which is written below the 54.
Since there are no more digits to bring down, we move on to the next step where we finalize the calculation.
| Dividend | Divisor | Quotient | Product | Difference |
|---|---|---|---|---|
| 48 | 3 | 16 | 48 | 4 |
| 54 | -4 |
Key Steps Recap:
- Set up the division problem by placing the divisor (3) on the left and the dividend (48) on the right.
- Divide the first digit of the dividend (4) by the divisor (3), resulting in a quotient of 1.
- Subtract the product of the divisor (3) and quotient (1) from the second digit of the dividend (8), which gives us a difference of 5. Bring down the next digit (8).
- Divide the new dividend (58) by the divisor (3), finding a quotient of 18.
- Subtract the product of the divisor (3) and quotient (18) from the third digit of the dividend (8), resulting in a difference of 4. Since there are no more digits to bring down, proceed to the final step.
- Finalize the calculation with a quotient of 16 and a remainder of 0, indicating that 48 can be evenly divided by 3.
Step 6: Finalizing the Calculation
In step 6, we have completed the long division process. We have found the quotient, which is 16, and this is the answer to the division problem. Since there are no more digits to bring down, our calculation is finished.
The remainder in this case is 0, indicating that 48 can be evenly divided by 3. This means that there is no remainder or fraction left over when dividing 48 by 3, and the division is exact.
Congratulations! You have successfully completed the long division process to find the quotient and remainder. This method allows you to divide large numbers and solve complex division problems with ease.
By following the steps of long division, you can tackle division problems efficiently and accurately. With practice, you will become more confident in your ability to find both the quotient and remainder, providing the complete solution to division calculations.
Using a Calculator and Additional Methods
While long division can be a reliable method for solving division problems, there are other ways to calculate 48 divided by 3. Using a calculator, we can quickly find the answer as 16. Additionally, we can express 48/3 as a mixed fraction, 16 0/3, which shows the quotient as a whole number with a remainder.
If you prefer a more efficient approach, using a calculator can save you time and effort. Simply input 48 ÷ 3 into the calculator, and it will generate the result of 16. This method is especially useful when dealing with larger numbers or complex division problems.
Another alternative method for division is expressing the quotient as a mixed fraction. In the case of 48 divided by 3, we can write it as 16 0/3. The whole number, 16, represents the number of times 3 can be divided evenly into 48. The fraction, 0/3, indicates that there is no remainder, as 48 is divisible by 3 without any leftover value.
Comparison of Methods
| Method | Explanation | Result |
|---|---|---|
| Long Division | A step-by-step process of dividing the dividend by the divisor | 16 |
| Calculator | Using a calculator to perform the division calculation | 16 |
| Mixed Fraction | Expressing the quotient as a whole number with a remainder | 16 0/3 |
Comparing the different methods, all three approaches yield the same result of 16. However, the calculato
Conclusion
Mastering long division is a valuable skill that empowers us to solve complex division problems with confidence. By understanding the step-by-step process and familiarizing ourselves with the terms involved, such as dividend and divisor, we can successfully tackle challenging calculations like 48 divided by 3.
Long division provides a systematic approach to division, breaking down the problem into manageable steps. With practice, we can improve our speed and accuracy, honing our mathematical abilities.
While long division is an effective method, it’s important to note that there are alternative approaches available. Using calculators can provide quick solutions, while expressing the result as a mixed fraction showcases the quotient and remainder in a different way.
By continuously practicing long division and exploring additional problems, we can reinforce our understanding and become proficient in this fundamental mathematical skill. Long division is a tool that opens doors to more advanced mathematical concepts, making it an essential technique to master.
Remember, the journey to mastering long division begins with grasping the basics, progressing through each step, and building confidence through practice. Embrace the power of this mathematical technique and unlock your potential to solve division problems with ease.
Additional Long Division Problems
If you’re looking to sharpen your long division skills and get some extra practice, we’ve got a set of random division problems for you to tackle. These additional exercises will help reinforce your understanding of long division and provide you with more opportunities to apply the step-by-step process.
Here are some of the division problems you can solve:
- 48 divided by 4 using long division
- 10 divided by 209 using long division
- 444 divided by 861 using long division
- 102 divided by 387 using long division
- 735 divided by 798 using long division
…
Feel free to solve as many of these problems as you’d like. You can check your answers by using the long division process. Remember, practice makes perfect, so keep at it!
Happy long dividing!
FAQ
What is long division?
Long division is a mathematical method used to divide large numbers. It involves breaking down the division into smaller steps to find the quotient and remainder.
How do you set up a long division problem?
To set up a long division problem, place the divisor on the left side and the dividend on the right side. This arrangement is important for the subsequent steps of the long division process.
How do you divide the first digit in long division?
In long division, you divide the first digit of the dividend by the divisor. Write the quotient above the division line and multiply the quotient by the divisor to get the result, which is written below the first digit of the dividend.
What do you do after dividing the first digit in long division?
After dividing the first digit, you subtract the result from the previous step from the second digit of the dividend. Write the difference below the result and bring down the next digit to form the new dividend for the next step.
How do you divide the new dividend in long division?
To divide the new dividend in long division, divide it by the divisor. Write the quotient above the division line and multiply the quotient by the divisor to get the result, which is written below the new dividend.
What do you do after dividing the new dividend in long division?
After dividing the new dividend, you subtract the result from the previous step from the third digit of the dividend. Write the difference below the result. If there are no more digits to bring down, move to the next step.
How do you finalize the calculation in long division?
To finalize the calculation in long division, check if there are any more digits to bring down. If not, the quotient is the answer to the division problem. The remainder is the difference in the last step. If the remainder is 0, it indicates that the dividend can be evenly divided by the divisor.
Are there alternative methods to solve division problems?
Yes. You can use a calculator to quickly find the answer to a division problem. Additionally, division can be expressed as a mixed fraction to show the quotient as a whole number with a remainder.
How can I practice my long division skills?
To practice your long division skills, you can solve additional division problems. Here are some examples: [List of division problems].
Why is long division an important mathematical skill?
Long division is a valuable technique for solving division problems. By understanding the steps and terms involved, you can confidently solve complex division problems and develop problem-solving skills.
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