679 ÷ 4? Long Division Steps & Solution Explained!

Aug 5, 2025 by Omar Yusuf 51 views

Dividing 679 by 4: A Step-by-Step Guide to Long Division

Hey guys! Let's dive into a math problem today that many of us encounter: dividing 679 by 4. This isn't just about finding the right answer; it's about understanding the process of long division. We'll break it down step-by-step, so you'll not only get the correct result but also grasp the underlying concept. So, grab your pencils and paper, and let’s get started!

Understanding the Basics of Division

Before we jump into the problem, let's quickly recap what division actually means. Think of division as splitting a whole into equal groups. In our case, we’re taking 679 and splitting it into groups of 4. The result will tell us how many of these groups we can make and if there's anything left over (the remainder). Division is one of the four basic arithmetic operations, the others being addition, subtraction, and multiplication. Mastering division is crucial as it forms the backbone for more advanced mathematical concepts like fractions, decimals, and algebra. In the context of real-life applications, division helps us in scenarios like sharing costs among friends, figuring out how many items can fit into boxes, or even calculating the average speed of a car journey. So, whether you are a student tackling homework or just someone who loves mental math challenges, understanding division is a valuable skill to have. Remember, the key to becoming proficient in division is practice, practice, practice! The more you work through different problems, the more confident and quick you'll become. So let's keep practicing together!

When you encounter a division problem, you'll typically see it written in a format like this: 679 ÷ 4. The number being divided (679) is called the dividend, the number we're dividing by (4) is the divisor, the result of the division is called the quotient, and any leftover amount is the remainder. Our goal here is to find both the quotient and the remainder when we divide 679 by 4. To visualize it simply, imagine you have 679 candies, and you want to distribute them equally among 4 friends. How many candies will each friend get, and how many will be left for you to enjoy after the distribution? This is precisely what we aim to solve. Understanding these terminologies is essential as they provide a clear language for discussing and solving division problems. Also, knowing what each term represents helps in translating real-world scenarios into mathematical problems. For example, if a question asks you to find how many times a certain number fits into another number, you instantly know it's a division problem. Similarly, if you're asked to split a total amount into equal parts, division comes to your rescue. So let's proceed with our division problem, keeping in mind that we're trying to find the quotient and the remainder – the main players in our division game!

Step-by-Step: Dividing 679 by 4

Let's perform long division to solve 679 ÷ 4. We'll break it down into manageable steps:

Set up the problem: Write the problem in the long division format. The dividend (679) goes inside the division symbol, and the divisor (4) goes outside. It should look something like this:

4 | 679

Setting up the problem correctly is the first crucial step in long division. This arrangement helps us organize the calculation process systematically. The dividend, which is the number being divided, nestles comfortably inside the "house" (the division symbol), while the divisor, the number we are dividing by, stands proudly outside. Think of it as dividing a treasure (the dividend) among a group (represented by the divisor). The way we set it up visually guides us through the steps of how many times the divisor can fit into parts of the dividend, and what remains after each step. If the setup is incorrect, you might end up miscalculating the quotient and the remainder. So, before you begin any calculation, always double-check that you've placed the dividend and divisor in their correct positions. This small act of precision will save you from potential errors and make the whole division process smoother and more understandable. Remember, a good start is half the battle won in mathematics!

Divide the first digit: Look at the first digit of the dividend (6). How many times does 4 go into 6? It goes in once (1 x 4 = 4). Write '1' above the 6.

   1
4 | 679

Here, we're focusing on the largest place value of our dividend, the hundreds place. We ask ourselves, “How many whole groups of 4 can we make from 6 hundreds?” Since 4 fits into 6 once, we write the '1' directly above the 6 in the quotient space. This '1' represents 1 hundred, because it aligns with the hundreds place in the dividend. Think of it like this: if you have 600 apples and you're packing them into boxes of 4, this step tells you how many full boxes you can make from just the first 600 apples. This initial step is vital because it sets the scale for the rest of the division process. It’s all about breaking down the dividend into smaller, manageable chunks. If you incorrectly assess how many times the divisor goes into the first digit, it can throw off the entire calculation. So, take your time in this step, and always double-check your multiplication. A confident start here builds momentum and accuracy for the rest of the long division journey. So, we've got '1' on top – we're on our way!

Multiply and subtract: Multiply the '1' by the divisor (4). 1 x 4 = 4. Write '4' below the 6 and subtract. 6 - 4 = 2.

This step is a crucial part of the long division process where we bridge multiplication and subtraction. We multiply the quotient digit we just wrote (1) by the divisor (4), resulting in 4. This '4' represents the portion of the dividend we've accounted for in this step. We then write this '4' directly below the digit we initially divided (6) and subtract. The subtraction (6 - 4 = 2) gives us the remainder from this particular division step. This remainder, '2', tells us how much is left over after taking out the largest possible groups of 4 from the hundreds place. Imagine you initially had 600 apples, and you packed 400 of them into boxes. The '2' here signifies the remaining 200 apples that are yet to be packed. This multiply-and-subtract sequence helps us systematically reduce the dividend into smaller, more manageable amounts. By accurately performing this step, we ensure that we're progressing towards the final answer while keeping track of what still needs to be divided. Mistakes in either multiplication or subtraction here can lead to an incorrect remainder and ultimately, a wrong quotient. So, let's take our time, double-check our arithmetic, and keep moving towards the solution with precision!

Bring down the next digit: Bring down the next digit of the dividend (7) next to the 2. You now have 27.

Bringing down the next digit is like calling in reinforcements! After dealing with the hundreds place, we move on to the tens place. The '7' in 679 represents 7 tens. We bring it down next to the remainder '2', which effectively transforms the '2' into '27'. Now, this '27' represents 27 tens, combining the remainder from the hundreds division (which is 2 hundreds or 20 tens) with the original 7 tens. This step is crucial because it allows us to continue the division process with the next place value. Think of it as unpacking the remaining 200 apples and adding them to the 70 apples you had initially. Now you have a total of 270 apples to work with. By bringing down the digit, we're ensuring that we're accounting for every part of the dividend. It's a systematic way of breaking down the larger problem into smaller, more manageable parts. Without this step, we would be ignoring the remaining portion of the dividend, leading to an inaccurate result. So, the act of bringing down the next digit is a vital link in the chain of long division, helping us maintain accuracy and completeness in our calculation. Let's keep going, we're getting closer!

Divide again: How many times does 4 go into 27? It goes in 6 times (6 x 4 = 24). Write '6' above the 7.

Now, with our new number, 27, we repeat the division process. We ask ourselves, “How many times can 4 go into 27?” Thinking about our multiplication facts, we know that 4 times 6 equals 24, which is the closest we can get to 27 without going over. So, we write '6' in the quotient space, directly above the '7' that we brought down. This '6' represents 6 tens, as it aligns with the tens place. In terms of our apple analogy, we're figuring out how many groups of 4 we can make from the 270 apples. This step highlights the iterative nature of long division – we’re repeating the process of dividing, multiplying, and subtracting until we’ve processed all the digits of the dividend. It's like following a recipe step by step, ensuring that each ingredient is properly incorporated. Choosing the correct quotient digit at this stage is crucial for accuracy. If we picked a number too small, we wouldn't be dividing as much as we could at this stage, and if we picked a number too large, our subtraction in the next step would result in a negative number, signaling an error. So, we carefully consider the multiples of the divisor and pick the largest one that fits comfortably within our current dividend portion. With '6' placed confidently above the '7', we're ready to move on to the next step in our division journey!

Multiply and subtract: Multiply the '6' by the divisor (4). 6 x 4 = 24. Write '24' below the 27 and subtract. 27 - 24 = 3.

Just like before, we're solidifying our quotient digit by multiplying and subtracting. We take the '6' we just placed in the quotient and multiply it by our divisor, 4. This gives us 24, which we write directly below the 27. This '24' represents the portion of the 27 tens that we’ve accounted for. Then, we subtract 24 from 27, resulting in 3. This '3' is our remainder after dividing the tens place. In our apple scenario, this means after packing groups of 4 from the 270 apples, we have 30 apples left over. This multiply-and-subtract cycle is the engine that drives long division. It allows us to quantify how many groups of the divisor we can make from the current portion of the dividend and what remains after forming those groups. The accuracy of this step is paramount. A mistake in multiplication or subtraction will ripple through the rest of the calculation, potentially leading to a wrong answer. So, we pause, double-check, and ensure that our numbers align and our arithmetic is sound. The remainder we get here will play a key role in the next stage, as we bring down the final digit and continue our division journey. We're on the right track, so let’s keep this momentum going!

Bring down the last digit: Bring down the last digit of the dividend (9) next to the 3. You now have 39.

We're in the home stretch now! It's time to bring down the final digit of our dividend, the '9', which represents 9 ones. We place this '9' right next to the '3', our previous remainder, transforming it into '39'. Now, this '39' represents 39 ones, combining the remainder from the tens division (which is 3 tens or 30 ones) with the original 9 ones. Bringing down the last digit is a clear signal that we’re dealing with the final stage of the division process. It ensures that we account for every single part of the dividend, leaving no ones behind! Think of it as adding the last 9 apples to the 30 apples we had left earlier. Now we have 39 apples in total that we need to divide into groups of 4. This step is often a moment of anticipation in long division, as it sets the stage for finding the ultimate quotient digit and the final remainder. Without bringing down the last digit, our division would be incomplete, and our answer would be inaccurate. So, we carefully bring down the '9', setting the stage for the final act of our division play. We're almost there – let's finish strong!

Divide again: How many times does 4 go into 39? It goes in 9 times (9 x 4 = 36). Write '9' above the 9.

We've arrived at the final quotient digit! With '39' as our new focus, we ask the familiar question: