Have you ever wondered **how to divide numbers manually**? Specifically, how to solve **72 divided by 8 using long division**? In this step-by-step tutorial, we will guide you through the division process and show you how to calculate the quotient and remainder. Say goodbye to relying on calculators and discover the beauty of **solving division problems** manually!

### Key Takeaways:

- Long division is a methodical process for dividing numbers manually.
- By following the step-by-step division process, you can calculate the quotient and remainder.
- Understanding long division is beneficial for improving mathematical understanding and problem-solving abilities.
- Dividing numbers manually is an alternative to using calculators and provides a deeper understanding of division.
- Stay tuned for a detailed breakdown of 72 divided by 8 using the long division method!

## Understanding the Terminology

Before we start the long division process, let’s clarify the terms involved.

The number being divided, in this case, 72, is called the *dividend*.

The number we are dividing by, here it is 8, is called the *divisor*.

Understanding these terms will help us accurately break down the division problem and proceed with the long division calculation.

## Step-by-Step Guide for 72 Divided by 8

Now let’s break down the steps of long division for 72 divided by 8. We will explain each step in detail, guiding you through the process so that you can follow along and understand the calculations involved.

### Step 1: Set up the Division Problem

To begin, we need to set up the division problem. Place the **divisor**, which is 8, on the left side and the **dividend**, which is 72, on the right side. This layout allows us to perform the calculations systematically.

### Step 2: Find the Quotient for the First Digit

Next, let’s find the quotient for the first digit. In this case, the first digit of the **dividend** is 7. Divide 7 by 8, which gives us 0. Write this quotient on top.

### Step 3: Multiply and Subtract

Now, we multiply the **divisor** (8) by the quotient (0), which gives us 0. Subtract this result from the corresponding digit of the **dividend** (72). The difference becomes the new dividend for the next step. In this case, 72 – 0 = 72.

### Step 4: Move Down the Next Digit

After subtracting, we move down to the next digit. This digit, 2, becomes the new rightmost digit of the remainder, and we continue the division process.

### Step 5: Repeating the Division Process

Repeat steps 2 to 4 with the new dividend. Find the quotient, multiply, and subtract until you have processed all the digits of the dividend.

### Step 6: The Final Quotient and Remainder

As you reach the end of the long division process, the final quotient is the number you have on top, and the remainder is the number at the bottom. In this case, the final quotient for 72 divided by 8 is 9, with a remainder of 0.

By following these step-by-step instructions, you can successfully solve division problems using the long division method. Practice with different numbers to improve your skills in **solving division problems**.

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

Step 1 | 72 divided by 8 |

Step 2 | 7 divided by 8 (quotient: 0) |

Step 3 | 0 multiplied by 8 (subtraction: 0) |

Step 4 | 72 – 0 (remainder: 72) |

Step 5 | 2 divided by 8 (quotient: 0) |

Step 6 | 0 multiplied by 8 (subtraction: 0) |

Step 7 | 0 – 0 (remainder: 0) |

## Step 1 – Setting up the Division Problem

Before we dive into the long division process for 72 divided by 8, it’s crucial to set up the division problem correctly. This ensures a systematic approach to the calculations. Let’s take a look at how to layout the **divisor** and dividend:

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

72 | 8 |

By placing the divisor on the left side and the dividend on the right side, we establish the foundation for the subsequent steps of the long division process.

## Step 2 – Finding the Quotient for the First Digit

In step 2 of the long division process for 72 divided by 8, we determine the quotient for the first digit of the dividend divided by the divisor. Let’s take a closer look at how this works:

**Dividend:**The number being divided, in this case, is 72.**Divisor:**The number we are dividing by, which is 8.**First Digit:**The first digit of the dividend is 7.**Quotient:**To find the quotient, we determine how many times the divisor can go into the first digit of the dividend.

When we divide 7 by 8, the divisor goes into the first digit 0 times. Therefore, the quotient for the first digit is 0.

Let’s illustrate this step with a table:

Step | Description | Calculation |
---|---|---|

Step 2 | Finding the Quotient for the First Digit | 7 ÷ 8 = 0 |

Now that we have determined the quotient for the first digit, we can move on to the next step in the long division process.

Continue reading to learn more about the remaining steps in the long division calculation for 72 divided by 8.

## Step 3 – Multiplying and Subtracting

In step 3 of the long division process, we perform multiplication and subtraction to continue solving the division problem. Let’s dive into the details of this crucial step.

We start by multiplying the divisor, which in our case is 8, by the quotient obtained in the previous step. The quotient represents the number of times the divisor goes into the current digit of the dividend. By multiplying the divisor and quotient, we obtain a result that we will use for the subtraction.

Next, we write the result of the multiplication below the corresponding digit of the dividend. This allows us to subtract the result from the digit of the dividend, finding the difference between the two values. The goal of this subtraction is to eliminate the portion of the dividend that has been accounted for by the multiplication.

We repeat this process of multiplication and subtraction for each digit of the dividend until we have processed all of them. By performing these calculations step by step, we gradually narrow down the dividend and get closer to finding the final quotient and remainder.

“Multiplying and subtracting are the key operations in long division. They help us break down the division problem into manageable steps and simplify the calculation process.” – Math Expert

By multiplying and subtracting in each step, we refine our division calculation and make progress towards finding the solution. This step is essential in long division as it allows us to handle each digit of the dividend systematically and accurately.

Now that we understand the significance of multiplication and subtraction in long division, let’s move on to the next step, where we will learn about moving down the next digit of the dividend and continuing the division process.

## Step 4 – Moving Down the Next Digit

Once we have subtracted the result of the previous step from the current digit of the dividend, we need to continue the long division process by moving down to the next digit. This new digit becomes the new rightmost digit of the remainder, and we incorporate it into the dividend for the subsequent calculations.

Let’s illustrate this step with the example of 72 divided by 8:

Divisor | Dividend | Quotient | Product | Remainder |
---|---|---|---|---|

8 | 72 | 9 | 72 | 0 |

In the previous step, we obtained a quotient of 9 and subtracted the product of 8 multiplied by 9 from the initial digit of the dividend, which is 7. The remainder after this subtraction is 0. Now, we move down to the next digit, which is 2. This digit becomes the new rightmost digit of the remainder, and we continue the division process with it as part of the dividend.

By incorporating the next digit, we ensure that the results of the subsequent calculations reflect the division of the entire dividend, leading us closer to the final quotient and remainder.

## Step 5 – Repeating the Division Process

Once we have moved down to the next digit, it’s time to repeat the long division steps we have followed so far. This allows us to continue the division process until all the digits of the dividend have been processed.

In this step, we repeat the process of finding the new quotient, multiplying, and subtracting, just as we did in the previous steps. By repeating these **long division iterations**, we ensure that every digit of the dividend is accounted for and properly divided by the divisor.

This repetition is crucial to accurately solving the division problem. It guarantees that we don’t miss any digits and maintain the integrity of the division process.

Let’s illustrate the step of repeating the division process with an example:

Dividend: 72

Divisor: 8

After moving down to the next digit, which is 2, we repeat the following steps:

- Divide 2 (the new rightmost digit of the dividend) by 8 to find the quotient. In this case, 8 goes into 2, 0 times.
- Multiply the divisor (8) by the quotient (0) to get 0.
- Subtract 0 from the current digit of the dividend (2) to get 2.

We have now processed all the digits of the dividend, and the division process is complete.

Below is a visual representation of the repeating division process:

The above image visually demonstrates the steps we repeated in the long division process for the example division problem.

By consistently following these **long division iterations**, we ensure that each digit of the dividend is appropriately divided and accounted for. This systematic approach allows us to **solve division problems manually** with accuracy and confidence.

## Step 6 – The Final Quotient and Remainder

After following the step-by-step process of long division, we finally arrive at the solution to our division problem. The final quotient and remainder are the key components that represent the outcome of the division calculation.

**Final Quotient:** The final quotient is the number we have on top after completing all the division steps. It signifies how many times the divisor, in this case, 8, goes into the dividend, which is 72. The quotient gives us the whole number part of the division result.

**Remainder:** The remainder is the number at the bottom that remains after dividing the dividend by the divisor. It represents the amount left over when the division process is complete and the divisor cannot go into the dividend any further. The remainder is an essential component of the division result, as it indicates that the division is not evenly divisible.

To better illustrate the final quotient and remainder for the division problem 72 divided by 8, let’s use a visual table:

Dividend | Divisor | Quotient | Remainder |
---|---|---|---|

72 | 8 | 9 | 0 |

In this case, the final quotient is 9, indicating that the divisor, 8, goes into the dividend, 72, 9 times. The remainder is 0, indicating that there is no amount left over after dividing evenly.

Understanding the final quotient and remainder is crucial in interpreting the results of **long division calculations**. These values provide a comprehensive solution to the division problem, capturing both the whole number part and any leftovers.

## Other Ways to Calculate 72 Divided by 8

While long division is a tried and true method for calculating division problems like 72 divided by 8, there are alternative approaches available. These methods offer different ways to arrive at the division result and can be convenient depending on the specific scenario.

### Using a Calculator

One of the easiest and quickest ways to calculate 72 divided by 8 is by using a calculator. By simply entering the numbers and pressing the division button, the calculator will provide the result. In this case, entering 72 ÷ 8 will give us the quotient of 9. Using a calculator can save time, especially when dealing with more complex division problems.

### Expressing the Result as a Mixed Fraction

Another way to represent the division result of 72 divided by 8 is by using a mixed fraction. A mixed fraction consists of a whole number and a fraction. In the case of 72 ÷ 8, the result can be expressed as 9 0/8. The whole number, 9, represents the quotient, while the fraction, 0/8, indicates that there is no remainder.

Overall, these alternative methods provide additional perspectives on the division result and may be useful in different contexts. Whether you choose to use a calculator or express the result as a mixed fraction, it’s important to understand the process and know how to interpret the different representations.

## Conclusion

In conclusion, long division is a methodical process that allows us to divide numbers manually. By following the step-by-step approach, we can accurately solve division problems like 72 divided by 8.

**Mastering long division** is a valuable skill that helps improve mathematical understanding and problem-solving abilities. It enables us to break down complex division problems into manageable steps, making it easier to find the quotient and remainder.

Through practice and repetition, you can become proficient in long division and confidently solve a variety of division problems. With mastery of long division, you’ll develop a solid foundation in math, paving the way for success in more advanced mathematical concepts.

## FAQ

### What is long division?

Long division is a method of manually dividing numbers, step by step, to find the quotient and remainder.

### How do I solve 72 divided by 8 using long division?

To solve **72 divided by 8 using long division**, you follow a step-by-step process. First, set up the division problem correctly, then find the quotient for the first digit, multiply and subtract, move down to the next digit, repeat the division process, and finally, obtain the final quotient and remainder.

### What are the terms used in long division?

In long division, the number being divided is called the dividend, and the number we are dividing by is called the divisor.

### Why is it important to understand the terms involved in long division?

Understanding the terms involved in long division, such as dividend and divisor, helps us accurately break down the division problem and proceed with the long division calculation.

### How do I set up the division problem in long division?

To set up the division problem in long division, you place the divisor on the left side and the dividend on the right side. This layout helps you perform the calculations systematically.

### How do I find the quotient for the first digit in long division?

To find the quotient for the first digit in long division, divide the first digit of the dividend by the divisor. Write this quotient on top and continue with the division process.

### What do I do after finding the quotient for the first digit in long division?

After **finding the quotient** for the first digit in long division, you multiply the divisor by the quotient and subtract the result from the corresponding digit of the dividend. This process of multiplication and subtraction continues until you have processed all the digits of the dividend.

### How do I move down to the next digit in long division?

After subtracting the result of the previous step from the current digit of the dividend, you move down to the next digit. This digit becomes the new rightmost digit of the remainder, and you continue the division process with this new digit as part of the dividend.

### How many times do I repeat the long division process?

You repeat the long division process for each digit of the dividend, moving down and performing the same steps until you have processed all the digits.

### How do I obtain the final quotient and remainder in long division?

As you reach the end of the long division process, the final quotient is the number you have on top, and the remainder is the number at the bottom. These values represent the solution to the division problem.

### Are there other ways to calculate 72 divided by 8?

Yes, besides long division, you can use a calculator to get the result, which in this case would be 9. You can also express the result as a mixed fraction, which would be 9 0/8.

### Why is it important to learn long division?

Learning long division is important as it helps improve mathematical understanding and problem-solving abilities. It is a valuable skill for **solving division problems** manually.

## Leave a Reply