Welcome to our guide on solving the division problem **48 divided by 3 using long division**. In this article, we will provide you with a step-by-step process to tackle this problem effectively. Whether you’re a student or just refreshing your math skills, this guide will help you understand and apply long division to find the solution.

Long division is a fundamental method for solving division problems. By breaking down the process into manageable steps, you can easily work through complex calculations like **48 divided by 3**. Let’s dive in and discover how to solve this problem using long division.

### Key Takeaways:

- Long division is a method used to solve division problems like
**48 divided by 3**. - Understanding the terms involved, such as
**dividend**and**divisor**, is crucial for setting up the long division problem correctly. - The process involves dividing, multiplying, and subtracting to find each digit of the quotient.
- The
**final solution for 48 divided by 3 using long division**is 16. - Using a calculator is an alternative, but learning long division enhances mathematical skills.

## Understanding the Terms

In the division problem **48 divided by 3**, it’s important to understand the terms involved. The number 48 is referred to as the *dividend*, while 3 is called the *divisor*. Knowing these terms will help you set up the long division problem correctly and proceed with the steps.

“Mathematics is the language with which God has written the universe.” – Galileo Galilei

Now that we have identified the **dividend** and **divisor**, let’s take a closer look at their roles in the long division process. The **dividend** is the number that is being divided, in this case, 48. It represents the total quantity or value that needs to be divided into equal groups.

The **divisor**, on the other hand, is the number by which the dividend is divided. In our example, the divisor is 3. It specifies the size of each group we are trying to create from the dividend.

Understanding the terms dividend and divisor is crucial for setting up the long division problem accurately. By clearly identifying these terms, we can proceed with the step-by-step process to find the quotient and remainder, if applicable.

### Visual Representation:

Dividend | Divisor |
---|---|

48 | 3 |

Now that we have established the terms dividend and divisor, let’s move on to the next section to learn how to set up the long division problem using these values.

## Setting Up the Long Division Problem

The first step in solving **48 divided by 3 using long division** is to set up the problem. To do this, follow these simple steps:

- Write the divisor (3) on the left side of the division bar.
- Write the dividend (48) on the right side of the division bar.
- Create a division bar between the divisor and the dividend.

The setup will look like this:

3 | |
---|---|

48 |

“Setting up the long division problem correctly is crucial for solving division problems. By clearly organizing the divisor and dividend, you can approach the problem systematically, making it easier to find the quotient and remainder.”

Now that you have set up the long division problem, you are ready to proceed to the next step and solve **48 divided by 3 using long division**.

## Step-by-Step Guide for Long Division

Long division is a multi-step process that allows us to divide larger numbers, such as 48 divided by 3, with ease and accuracy. By following each step carefully, you’ll be able to solve the problem correctly and obtain the correct answer.

**Step 1: Divide the first digit****Step 2: Multiply and subtract****Step 3: Repeat the process****Step 4: Final solution**

To begin, divide the first digit of the dividend (4) by the divisor (3). In this case, 4 divided by 3 is 1 with a remainder of 1.

Next, multiply the divisor (3) by the quotient obtained from the previous step (1). The product is 3. Subtract this result from the corresponding digit of the dividend (48) to obtain the new partial dividend (15).

Now, bring down the next digit of the dividend (5) and perform the division process again. Divide the partial dividend (15) by the divisor (3) to get a new quotient and remainder. Continue this process until there are no more digits in the dividend.

Once you have completed the long division process and there are no more digits to bring down, you have found the final solution. In the case of 48 divided by 3, the quotient is 16 with no remainder.

By following this step-by-step guide for long division, you can successfully solve division problems like 48 divided by 3 and achieve accurate results. Practice this method regularly to enhance your mathematical skills and become proficient in long division.

## Step 1 – Dividing the First Digit

In the first step of long division, we divide the first digit of the dividend (4) by the divisor (3). This step is crucial in determining how many times the divisor can be divided into the first digit. By performing this calculation, we can write the result above the division bar, laying the foundation for the subsequent steps.

Let’s take a look at an example to illustrate this process:

Dividend | 48 |
---|---|

Divisor | 3 |

Quotient – Step 1 | 1 |

As shown in the table, the first digit of the dividend (4) is divided by the divisor (3), resulting in a quotient of 1. This value is then written above the division bar as we proceed to the next step of long division.

With the first digit successfully divided, we can move on to the next step of long division, which involves multiplying and subtracting. This process allows us to progress further in solving the division problem 48 divided by 3.

## Step 2 – Multiplying and Subtracting

After determining the quotient in the previous step, we continue with the next step of long division: multiplying and subtracting. This step helps us bring down the next digit of the dividend and move forward in the division process. Let’s break it down:

### Multiplying

Once we have the quotient from the previous step, which is 1 in this case, we multiply it by the divisor (3). This calculation gives us the product that we will subtract from the dividend. In the case of 48 divided by 3, the multiplication would look like this:

3 x 1 = 3

### Subtracting

After finding the product, we write it below the dividend and subtract it from the corresponding digit. In this case, we subtract 3 from the first digit of the dividend (4):

4 – 3 = 1

This subtraction result represents the remainder after dividing the first digit of the dividend by the divisor. We bring down the next digit (in this case, 8) and proceed with the division process.

To illustrate the process, here’s an example:

Step | Calculation | Result |
---|---|---|

Step 1 | 3 x 1 | 3 |

48 – 3 | 45 |

By multiplying the divisor (3) by the quotient (1) and subtracting the result from the first digit of the dividend (4), we have obtained a new dividend (45) to continue the long division process.

In the next section, we will explore Step 3 and continue dividing until we obtain the final solution for 48 divided by 3.

## Step 3 – Repeat the Process

Now that we have completed the previous steps of long division for the problem 48 divided by 3, it’s time to move on to step 3. In this step, we will repeat the process to continue finding the next digit of the quotient.

To do this, we need to bring down the next digit from the dividend, which in this case is 8. We then divide this digit by the divisor, 3, to determine how many times 3 can be divided into 8. The result is written above the division bar as the next digit of the quotient.

Next, we multiply the divisor, 3, by the result we just obtained and write the answer below the dividend. In this case, 3 multiplied by 2 is 6. We then subtract this result from the corresponding digit of the dividend, which is 8. The difference is 2.

Now, we repeat the process by bringing down the next digit from the dividend, which is 0. We divide 20 (the result we obtained in the previous step) by 3 to find the next digit of the quotient. The result, 6, is written above the division bar.

We then multiply the divisor, 3, by 6 and write the result, 18, below the dividend. Subtracting 18 from 20 leaves us with a difference of 2.

The next digit to bring down from the dividend is 0. We divide 20 by 3 to find the next digit of the quotient. The result, 6, is again written above the division bar.

Multiplying the divisor, 3, by 6 gives us 18. Subtracting 18 from 20 leaves us with a difference of 2.

We have now reached the end of the dividend, and there are no more digits to bring down. At this point, we have obtained a quotient of 16, with no remainder. This means that the solution to 48 divided by 3 is 16.

Step | Dividend | Divisor | Quotient | Multiplication | Subtraction |
---|---|---|---|---|---|

1 | 48 | 3 | 1 | 3 x 1 = 3 | 4 – 3 = 1 |

2 | 18 | 3 | 6 | 3 x 6 = 18 | 18 – 18 = 0 |

3 | 20 | 3 | 6 | 3 x 6 = 18 | 20 – 18 = 2 |

## The Final Solution

After going through the step-by-step long division process, we have arrived at the **final solution for 48 divided by 3 using long division**. The quotient obtained from the division is 16 with no remainder.

“Long division is a fantastic method to divide numbers accurately, like in the case of 48 divided by 3. It allows us to break down the problem into manageable steps and obtain the result. The final solution for this division is 16, and it signifies the number of times the divisor, 3, can go into the dividend, 48, without any remainder. Long division is a valuable skill to have when dealing with more complex division problems, and it’s essential to practice and master this technique.”

Understanding the final solution is crucial to validating our calculation and ensuring its accuracy. By obtaining a quotient of 16 with no remainder, we confirm that our division has been completed correctly. This solution provides a precise answer to the problem and resolves any uncertainty regarding the division of 48 by 3.

Now that we have the final solution, let’s recap the steps we took to reach this answer:

- Set up the long division problem, placing the divisor (3) on the left side and the dividend (48) on the right side of the division bar.
- Divide the first digit of the dividend (4) by the divisor (3) to determine the quotient (1).
- Multiply the divisor (3) by the quotient (1) and subtract the result (3) from the corresponding digit of the dividend (4). This step yields a remainder of 1 and brings down the next digit (8).
- Repeat the division process for the new dividend (18) by dividing the first digit (1) by the divisor (3) to obtain a new quotient (6).
- Continue multiplying and subtracting until all the digits have been processed.
- Reach the final division step with no more digits to bring down, resulting in a quotient of 16 with no remainder.

This step-by-step approach ensures an accurate division result and contributes to a deeper understanding of long division as a mathematical concept.

Remember, long division is just one method for solving division problems. In the next section, we will explore alternative calculation methods for 48 divided by 3 and discuss how they differ from long division.

## Using a Calculator

If you prefer a quicker alternative to long division, you can use a calculator to find the result of 48 divided by 3. Simply input the numbers and let the calculator do the math for you. In this case, the calculator will provide you with the answer: *16*.

While using a calculator is convenient, it’s important to note that understanding the long division process can deepen your understanding of mathematical concepts. It allows you to visualize the division process and develop problem-solving skills that can be useful in other scenarios.

## Exploring Other Calculation Methods

Besides long division, there are other approaches to calculate 48 divided by 3. One alternative method is to express the answer as a mixed fraction. In this case, the mixed fraction equivalent of 16 is 16 0/3.

By exploring different calculation methods, you can enhance your mathematical skills and gain new perspectives on problem-solving. Here’s an example of how you can represent the division 48 divided by 3:

Method | Result |
---|---|

Long Division | 16 |

Mixed Fraction | 16 0/3 |

While long division is a widely used method, exploring these alternatives can provide a deeper understanding of mathematical concepts and improve your problem-solving skills.

“Exploring different approaches to calculation not only broadens your mathematical toolkit but also encourages creative thinking and problem-solving.”

## Conclusion

Long division is a powerful method for solving division problems, including the calculation of 48 divided by 3. By carefully following the step-by-step process and grasping the underlying terms involved, you can confidently find the quotient and remainder for any given division problem. Remember, practice makes perfect, so continue honing your skills to become proficient in long division.

Throughout this article, we have explained the intricacies of long division, from understanding the roles of the dividend and divisor to setting up the problem and executing the step-by-step guide. With a clear understanding of the concepts and a systematic approach, you can tackle division problems effectively.

Long division provides a structured and organized approach to division problems, allowing you to break down complex calculations into manageable steps. It is a fundamental skill that serves as a building block for more advanced mathematical concepts.

As the saying goes, “Practice makes perfect.” By solving various division problems using long division, you can strengthen your mathematical abilities, develop problem-solving skills, and enhance your overall numeracy.

Remember, understanding long division is not limited to finding the answer—it fosters a deeper comprehension of mathematical processes and nurtures critical thinking. So, embrace the challenge, keep practicing, and unlock the mastery of long division!

Now that you have a firm grasp of how to solve 48 divided by 3 using long division, why not put your skills to the test with more division problems? Let’s reinforce your knowledge with an additional practice exercise.

### Practice Exercise: Long Division

Divide the following numbers using long division:

Division Problem | Quotient | Remainder |
---|---|---|

72 ÷ 8 | 9 | 0 |

85 ÷ 7 | 12 | 1 |

105 ÷ 5 | 21 | 0 |

## Additional Long Division Problems

If you’re looking to sharpen your long division skills even further, we’ve got you covered. Below, you’ll find a curated list of additional randomly generated long division problems. These exercises are designed to help you reinforce your understanding of long division and enhance your problem-solving abilities in mathematics.

By practicing with these **additional long division problems**, you’ll gain confidence in dividing larger numbers and improve your accuracy in finding quotients and remainders. Remember, repetition is key when it comes to mastering long division, so don’t hesitate to tackle these problems as often as you’d like.

Whether you’re preparing for an upcoming math exam or simply want to brush up on your division skills, these extra long division problems will provide you with valuable practice. So, grab a pencil and paper, and dive into the world of long division. With perseverance and consistent practice, you’ll soon find yourself tackling complex division problems with ease!

## FAQ

### What is long division?

Long division is a mathematical method used to divide large numbers into smaller groups to find the quotient and remainder.

### How do you solve 48 divided by 3 using long division?

To solve 48 divided by 3 using long division, you follow a step-by-step process that involves dividing, multiplying, and subtracting until there are no more digits to bring down.

### What are the terms involved in 48 divided by 3 using long division?

In the division problem 48 divided by 3, 48 is the dividend, and 3 is the divisor.

### How do you set up the long division problem for 48 divided by 3?

To set up the long division problem for 48 divided by 3, place the divisor (3) on the left side and the dividend (48) on the right side, creating a division bar.

### What is step-by-step long division for 48 divided by 3?

Step-by-step long division for 48 divided by 3 involves dividing the first digit, multiplying and subtracting, and repeating the process until there are no more digits to bring down.

### What is the first step in long division for 48 divided by 3?

The first step in long division for 48 divided by 3 is to divide the first digit of the dividend (4) by the divisor (3) to determine how many times the divisor can be divided into the first digit.

### What is step 2 in long division for 48 divided by 3?

Step 2 in long division for 48 divided by 3 involves multiplying the divisor (3) by the result from step 1 (1 x 3 = 3) and subtracting this result from the corresponding digit of the dividend (4 – 3 = 1).

### What is step 3 in long division for 48 divided by 3?

Step 3 in long division for 48 divided by 3 is to repeat the previous steps of dividing, multiplying, and subtracting with the next digit of the dividend (8).

### What is the final solution for 48 divided by 3 using long division?

The **final solution for 48 divided by 3 using long division** is 16 with no remainder.

### How can I use a calculator to solve 48 divided by 3?

Using a calculator, you can input 48 divided by 3, and the calculator will provide you with the result, which in this case is 16.

### Are there alternative methods to calculate 48 divided by 3?

Yes, besides long division, you can express the answer as a mixed fraction, which would be 16 0/3. Exploring different methods can enhance your mathematical skills and problem-solving abilities.

### Are there additional long division problems to practice?

Yes, we provide a list of additional randomly generated long division problems that can help reinforce your understanding of long division and improve your problem-solving abilities.

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