Dividing 402 By 5: A Step-by-Step Guide

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Hey guys! Today, we're diving into a common math problem: dividing 402 by 5. It might seem tricky at first, but with a step-by-step approach, it becomes super easy. We'll break it down in a way that everyone can understand. Whether you're a student tackling homework or just brushing up on your math skills, this guide is for you. So, let’s get started and make dividing 402 by 5 a breeze!

Understanding Division

Before we jump into the specifics, let's quickly recap what division actually means. In simple terms, division is splitting a number into equal groups. When we say 402 divided by 5, we’re asking, "How many groups of 5 can we make from 402?" or "If we split 402 into 5 equal parts, how big will each part be?" Division is the inverse operation of multiplication, meaning it helps us “undo” multiplication. For example, if 10 divided by 2 equals 5, it's because 5 multiplied by 2 equals 10. Understanding this fundamental concept is crucial before we tackle more complex divisions. Division is used everywhere in daily life, from splitting a bill with friends to figuring out how many items can fit into boxes. Mastering it not only helps with math class but also with real-world problem-solving.

The Parts of a Division Problem

It's also important to know the terminology used in division:

  • Dividend: This is the number being divided (in our case, 402).
  • Divisor: This is the number we are dividing by (in our case, 5).
  • Quotient: This is the result of the division (the answer we're looking for).
  • Remainder: This is the amount left over if the dividend cannot be divided equally by the divisor.

Knowing these terms will make it easier to follow along as we break down the division process. Think of the dividend as the total amount you have, the divisor as the number of groups you want to make, the quotient as the number of items in each group, and the remainder as the leftover items. With these basics in mind, we're well-prepared to tackle dividing 402 by 5. So, let’s move on to the actual steps and see how this all works in practice!

Step-by-Step Guide to Dividing 402 by 5

Okay, let's get down to business and break down how to divide 402 by 5. We'll use the long division method, which helps to organize our work and makes the process super clear. Don't worry if you haven't done long division in a while; we'll go through each step slowly and carefully. Grab a pen and paper, and let's work through it together!

Step 1: Set Up the Problem

First things first, let's set up the problem using the long division symbol, which looks like a sideways L with a line over the top. We write the dividend (402) inside the “house” and the divisor (5) outside on the left. This setup visually organizes our division problem and helps us keep track of each step. It's like building the framework for a house – get this right, and the rest will follow smoothly. So, go ahead and write down the long division symbol, put 402 inside, and 5 outside. Ready for the next step? Great, let’s move on!

Step 2: Divide the First Digit

Now, we start dividing. Look at the first digit of the dividend, which is 4. Can 5 go into 4? Nope, because 4 is smaller than 5. So, we move on to consider the first two digits of the dividend, which are 40. Now we ask ourselves, “How many times does 5 go into 40?” Think about your multiplication facts! 5 times what equals 40? That's right, 5 times 8 equals 40. So, we write 8 above the 0 in the quotient (the answer space above the division symbol). This step is crucial because it sets the foundation for the rest of the calculation. If you're not sure about your multiplication facts, it might be helpful to have a multiplication chart handy. Once we've figured out how many times 5 goes into the first part of the dividend, we're ready to move on to the next step, which involves multiplication and subtraction. So, let’s keep going!

Step 3: Multiply and Subtract

Alright, we've figured out that 5 goes into 40 eight times. Now, we multiply the divisor (5) by the number we just wrote in the quotient (8). So, 5 times 8 equals 40. We write this 40 directly below the 40 in the dividend. Next, we subtract: 40 minus 40 equals 0. This subtraction step tells us how much of the dividend we've accounted for so far. If the result of the subtraction is 0, it means we've divided that part of the dividend perfectly. If it's a number other than 0, it means we have a remainder to carry over. In this case, we have 0, which is perfect! But we're not done yet. We still have the last digit of the dividend to deal with. So, let’s move on to the next step, which involves bringing down the next digit.

Step 4: Bring Down the Next Digit

We've taken care of the first two digits of the dividend, so now it's time to bring down the next digit. In this case, we bring down the 2 from 402 and write it next to the 0 that we got from our subtraction. So now we have the number 2. This step is important because it keeps the division process flowing smoothly. We're essentially saying, “Okay, we’ve divided the first part, now let’s see what we can do with the next part.” Bringing down the digit helps us continue the division process systematically. Now, with the 2 brought down, we have a new number to work with, and we ask ourselves the same question we did before: How many times does 5 go into this new number? Let’s find out in the next step!

Step 5: Repeat the Process

Now we have 2. How many times does 5 go into 2? Well, 5 doesn't go into 2 at all, because 2 is smaller than 5. So, we write a 0 in the quotient above the 2 in the dividend. This 0 is crucial because it holds the place value in our answer. Even though 5 doesn't go into 2 a whole number of times, we still need to acknowledge that by placing a 0 in the quotient. Next, just like before, we multiply the divisor (5) by the number we just wrote in the quotient (0). So, 5 times 0 equals 0. We write this 0 below the 2 and subtract: 2 minus 0 equals 2. This leaves us with a remainder of 2. Since there are no more digits to bring down from the dividend, we've reached the end of our division process. So, what does this remainder mean? Let’s find out in the final step!

Step 6: Determine the Remainder

We've reached the end of our division, and we have a remainder of 2. This means that 402 cannot be divided perfectly by 5. The 2 is what's left over after we've divided as much as we can. So, how do we express this in our answer? We write the remainder as “R2” next to the quotient. So, our final answer is 80 R2. This tells us that 402 divided by 5 equals 80 with a remainder of 2. In other words, we can make 80 groups of 5 from 402, and we'll have 2 left over. Understanding the remainder is key to fully grasping division. It shows us the part that doesn’t fit perfectly into the groups we’re making. And that’s it! We’ve successfully divided 402 by 5 using long division. You did it!

Expressing the Remainder as a Decimal

Now, sometimes, instead of writing the remainder as “R2,” we want to express it as a decimal. This gives us a more precise answer. Don't worry, it's not as scary as it sounds! We'll just add a couple of extra steps to our long division process.

Step 1: Add a Decimal Point and a Zero

After we’ve reached the remainder (which was 2 in our case), we add a decimal point to the end of the dividend (402) and also to the quotient (above the division symbol). Then, we add a zero to the end of the dividend after the decimal point, turning our remainder problem into 20. This is like saying we’re going to continue dividing into the fractions of the whole numbers. By adding the decimal point and zero, we’re essentially extending the division process into the decimal places, allowing us to get a more accurate result.

Step 2: Continue Dividing

Now we treat the 20 just like we would any other number in our long division. We ask ourselves, “How many times does 5 go into 20?” The answer is 4, because 5 times 4 equals 20. So, we write 4 in the quotient after the decimal point. Next, we multiply the divisor (5) by the number we just wrote in the quotient (0.4). So, 5 times 0.4 equals 2.0. We write this 2.0 below the 20 and subtract: 20 minus 20 equals 0. This means we’ve divided the remainder perfectly, and we have no more leftovers. The beauty of converting the remainder to a decimal is that we can get an exact answer, without any “R” notation. It gives us a more complete picture of the division result.

Step 3: Write the Final Answer

Since we have a remainder of 0, we're done! Our final answer is 80.4. This means that 402 divided by 5 equals 80.4 exactly. Expressing the remainder as a decimal gives us a more precise answer and can be particularly useful in situations where you need to be very accurate, like in scientific calculations or financial transactions. So, you see, turning a remainder into a decimal is just a few extra steps that give us a more refined result. You’ve now mastered another important division skill!

Expressing the Remainder as a Fraction

Another way to handle the remainder is to express it as a fraction. This is a fantastic option when you want to show the exact proportion of the leftover amount in relation to the divisor. Let’s see how this works with our example of 402 divided by 5.

Step 1: Identify the Remainder and Divisor

First, we need to remember what our remainder and divisor are. In our division of 402 by 5, we found that the remainder is 2 and the divisor is 5. These two numbers are the key ingredients for our fraction. The remainder is what we have left over, and the divisor is the number we were dividing by. Think of it like this: the remainder is the part of the pie that’s left, and the divisor is the number of people we were originally sharing the pie with.

Step 2: Create the Fraction

To express the remainder as a fraction, we simply put the remainder over the divisor. So, in our case, the remainder 2 becomes the numerator (the top number) of the fraction, and the divisor 5 becomes the denominator (the bottom number). This gives us the fraction 2/5. This fraction represents the portion of the divisor that is left over after the division. It’s a precise way of showing the remaining amount, and it fits perfectly into the concept of fractions representing parts of a whole.

Step 3: Write the Final Answer

Now we combine the whole number part of our quotient (which was 80) with the fraction we just created (2/5). So, our final answer is 80 2/5. This means that 402 divided by 5 equals 80 and two-fifths. This is a mixed number, combining a whole number and a fraction. Expressing the remainder as a fraction is especially useful when you need to maintain precision and show the exact proportion of the leftover amount. It’s a common way to express division results in various contexts, from cooking recipes to measuring ingredients. So, now you know how to turn a remainder into a fraction, adding another valuable tool to your math toolkit!

Real-World Applications

Okay, so we've learned how to divide 402 by 5, but you might be thinking,