Dividing 78 By 6: A Step-by-Step Guide

Dec 3, 2025 by Alex Johnson 39 views

Hey there! Ever found yourself staring at a division problem like 78 ÷ 6 and feeling a bit puzzled? Don't worry, you're not alone! Division can seem tricky, but once you break it down into smaller steps, it becomes much easier to handle. In this guide, we'll walk through how to solve 78 divided by 6, making sure every step is clear and simple. So, grab a pen and paper, and let's dive in!

Understanding Division

Before we jump into the problem, let's quickly recap what division actually means. At its core, division is about splitting a total into equal groups. Think of it like sharing a bag of candies among friends. If you have 78 candies and want to share them equally among 6 friends, you're essentially performing the division 78 ÷ 6. The answer will tell you how many candies each friend gets.

In mathematical terms, the number being divided (78 in our case) is called the dividend. The number we're dividing by (6) is the divisor, and the answer we get is the quotient. So, our goal is to find the quotient when we divide 78 by 6.

Understanding these terms can help you approach any division problem with confidence. It's like having the right tools for the job – knowing what each part of the problem represents makes the solution much clearer. Now that we've got the basics down, let's get to solving our problem.

Step-by-Step Solution

Step 1: Setting Up the Problem

The first thing we need to do is set up our division problem. We write the dividend (78) inside the division symbol (also known as the long division symbol) and the divisor (6) outside to the left. It should look something like this:

      ______
6  | 78

This setup helps us organize our work and makes it easier to follow each step. Think of it as laying out all your ingredients before you start cooking – it ensures you don't miss anything important.

Step 2: Dividing the First Digit

Now, we start by looking at the first digit of the dividend, which is 7. We ask ourselves, "How many times does 6 go into 7?" Well, 6 goes into 7 one time. So, we write a 1 above the 7 in our setup:

     1_____
6  | 78

This 1 represents the first digit of our quotient. It's like saying, "Each friend gets at least one candy from the start." Now, we need to figure out how many candies are left after this initial distribution.

Step 3: Multiplying and Subtracting

Next, we multiply the 1 (which we just wrote above) by the divisor (6). 1 multiplied by 6 is 6. We write this 6 under the 7 in the dividend:

     1_____
6  | 78
    6

Now, we subtract this 6 from the 7. 7 minus 6 is 1. We write the 1 below the line:

     1_____
6  | 78
    6
    --
    1

This subtraction tells us how much is left after we've divided 6 from the first part of the dividend. We have 1 remaining, which is less than our divisor (6), so we're on the right track. It's like saying, "After giving each friend one candy, we have one candy left over."

Step 4: Bringing Down the Next Digit

Now, we bring down the next digit of the dividend (8) and write it next to the 1 that we have remaining. This gives us 18:

     1_____
6  | 78
    6
    --
    18

Bringing down the next digit is like combining the remaining candy with the next batch we need to distribute. Now, we have 18 to divide, which is a larger number and easier to work with.

Step 5: Dividing the New Number

Now we ask ourselves, "How many times does 6 go into 18?" The answer is 3. So, we write a 3 next to the 1 in our quotient, above the 8 in the dividend:

This 3 is the next digit in our quotient. It's like saying, "Each friend gets three more candies."

Step 6: Multiplying and Subtracting Again

We multiply the 3 by the divisor (6). 3 multiplied by 6 is 18. We write this 18 under the 18 we already have:

Now, we subtract this 18 from the 18. 18 minus 18 is 0. We write the 0 below the line:

This final subtraction gives us 0, which means there is no remainder. We've divided all the candies perfectly!

Step 7: The Answer

Since we have a 0 remainder, our division is complete. The quotient, which is the answer to our division problem, is 13. This means that 78 divided by 6 is 13.

So, 78 ÷ 6 = 13.

Congratulations! You've just solved a division problem using long division. It might seem like a lot of steps, but with practice, it becomes second nature.

Practice Makes Perfect

The best way to get comfortable with division is to practice. Try solving a few more problems on your own, and you'll find that it becomes easier and easier. Here are a few tips to keep in mind:

Write it out: Always write out the problem using the long division setup. This helps keep your work organized.
Go step-by-step: Follow each step carefully, and don't rush. It's better to take your time and get it right.
Check your work: After you get an answer, you can check it by multiplying the quotient by the divisor. If you get the dividend, you know you're on the right track.
Use resources: There are plenty of online resources and videos that can help you practice division. Don't hesitate to use them!

Real-World Applications of Division

Division isn't just a math concept you learn in school; it's something we use in our daily lives all the time. Think about it – whenever you're sharing food, splitting costs, or figuring out how many items fit into a certain space, you're using division.

For example, imagine you're planning a road trip with friends and need to split the cost of gas. If the total cost of gas is $78 and there are 6 of you, you'd use division (78 ÷ 6) to find out how much each person owes. In this case, each person would owe $13.

Or, let's say you're baking cookies for a party and you have 78 cookies to arrange on 6 plates. Again, you'd use division (78 ÷ 6) to figure out how many cookies to put on each plate. You'd put 13 cookies on each plate.

Seeing how division applies to real-world situations can make it feel less like an abstract concept and more like a practical skill.

Conclusion

So, there you have it! We've walked through the process of dividing 78 by 6 step by step. Remember, division is all about breaking a larger number into equal groups, and with a little practice, you can tackle any division problem. Keep practicing, and you'll become a division pro in no time!

If you're eager to delve deeper into the world of mathematics and explore more division examples, check out Khan Academy's Arithmetic Section for additional resources and practice problems.