Long Division: 31 Divided By 3 Explained!

Oct 31, 2025 by Admin 42 views

Hey guys! Let's break down how to solve the division problem 31 ÷ 3 using long division. Long division can seem a bit tricky at first, but once you get the hang of the steps, it becomes much easier. So, grab a pen and paper, and let’s dive in!

Understanding Long Division

Before we start, it's good to understand what long division actually does. Essentially, long division helps us break down a larger division problem into smaller, more manageable steps. When we divide 31 by 3, we want to find out how many times 3 fits into 31, and if there's anything left over (the remainder). This method is super useful for any division problem, especially when you're dealing with larger numbers that you can't easily do in your head.

Think of it like this: You have 31 candies and want to share them equally among 3 friends. Long division will tell you how many candies each friend gets, and how many candies you have left for yourself!

Now, let’s get started with the actual steps.

Setting Up the Problem

First things first, we need to set up our long division problem correctly. Here’s how it should look:

      ______
 3  | 31

Here, 3 is the divisor (the number we are dividing by), and 31 is the dividend (the number being divided). The line above the dividend is where we will write our quotient (the answer).

Make sure you align the numbers correctly to avoid confusion later on. A neat setup is half the battle when it comes to long division!

Step-by-Step Long Division

Now, let's go through each step to solve 31 ÷ 3:

Step 1: Divide the First Digit

Look at the first digit of the dividend (31), which is 3. Ask yourself: How many times does 3 fit into 3? The answer is 1.

Write the 1 above the 3 in the dividend:

      1_____
 3  | 31

Step 2: Multiply

Next, multiply the number you just wrote in the quotient (1) by the divisor (3). So, 1 × 3 = 3.

Write this 3 below the first digit of the dividend:

      1_____
 3  | 31
      3

Step 3: Subtract

Subtract the number you just wrote (3) from the first digit of the dividend (3). So, 3 - 3 = 0.

Write the 0 below the line:

Step 4: Bring Down

Bring down the next digit of the dividend (1) next to the 0.

Now we have 01, which is just 1.

Step 5: Repeat the Process

Now, repeat the process with the new number (1). Ask yourself: How many times does 3 fit into 1? Since 3 is larger than 1, it doesn't fit at all. So, the answer is 0.

Write the 0 next to the 1 in the quotient:

Multiply the new digit in the quotient (0) by the divisor (3). So, 0 × 3 = 0.

Write this 0 below the 1:

Subtract the number you just wrote (0) from the 1. So, 1 - 0 = 1.

Write the 1 below the line:

Step 6: Remainder

Since there are no more digits to bring down, the 1 at the bottom is our remainder.

The Answer

So, 31 ÷ 3 = 10 with a remainder of 1. We can write this as:

31 ÷ 3 = 10 R 1

This means that 3 fits into 31 ten times, with 1 left over. In our candy example, each of the three friends gets 10 candies, and you have 1 candy left for yourself.

Checking Your Work

To make sure we got the correct answer, we can check our work. Multiply the quotient (10) by the divisor (3), and then add the remainder (1):

(10 × 3) + 1 = 30 + 1 = 31

Since this equals the dividend (31), we know our answer is correct!

Long Division with Decimals

Sometimes, you might want to continue the division to get a decimal answer instead of a remainder. Here’s how to do that:

Step 1: Add a Decimal Point and Zero

Add a decimal point to the end of the dividend (31) and write a 0 after it.

 3  | 31.0

Also, add a decimal point to the quotient, right after the 10:

Step 2: Bring Down the Zero

Bring down the 0 next to the remainder 1.

Now we have 10.

Step 3: Continue Dividing

Ask yourself: How many times does 3 fit into 10? The answer is 3.

Write the 3 after the decimal point in the quotient:

Multiply the new digit in the quotient (3) by the divisor (3). So, 3 × 3 = 9.

Write this 9 below the 10:

Subtract the number you just wrote (9) from the 10. So, 10 - 9 = 1.

Write the 1 below the line:

Step 4: Repeat (If Needed)

If you want more decimal places, you can add another 0 to the dividend and continue the process. In this case, if we bring down another 0, we get 10 again. So, we’ll get another 3 in the quotient, and the process will repeat.

You can see that the 3s will keep repeating. So, we can write the answer as:

31 ÷ 3 ≈ 10.33 (approximately)

Tips for Long Division

Here are a few tips to help you master long division:

Write Neatly: Keep your numbers aligned to avoid mistakes.
Take it Step-by-Step: Follow each step carefully and don’t rush.
Check Your Work: Always check your answer to make sure it’s correct.
Practice Regularly: The more you practice, the easier it will become!

Real-World Applications

Long division isn’t just something you learn in school; it has practical uses in everyday life. For example:

Splitting Costs: If you and your friends go out to dinner and want to split the bill evenly, you can use long division to figure out how much each person owes.
Cooking: When you’re adjusting a recipe to serve more or fewer people, you might need to use division to calculate the new ingredient amounts.
Home Improvement: If you’re tiling a floor or painting a wall, you might need to divide measurements to figure out how many tiles or how much paint you need.

Conclusion

So, there you have it! Dividing 31 by 3 using long division gives us 10 with a remainder of 1, or approximately 10.33 if we use decimals. Remember to take it one step at a time, and don't be afraid to practice. With a little patience, you’ll become a long division pro in no time!

Keep practicing, and you'll find that long division becomes second nature. Good luck, and have fun dividing! Remember, every great mathematician started somewhere, and you're well on your way! Don't get discouraged if it seems tough at first. Like any skill, it gets easier with practice. And who knows, maybe you'll discover a new, even more efficient way to divide! The possibilities are endless. Happy calculating!