How to Solve Long Division Problems: Step-by-Step Guide

Long division can seem challenging at first, but with a clear, step-by-step approach, you can master it! Let's break down the process using the example of 5,129 ÷ 23.

### Step 1: Set It Up
Begin by writing the division problem in long division format. Place the divisor (23) outside the division bracket and the dividend (5,129) inside. It should look like this:

```
_______
23 | 5,129
```

### Step 2: Divide the First Digit(s)
Next, look at the first digit of the dividend. Since 23 is larger than 5, we consider the first two digits, which are 51. Ask yourself how many times 23 can fit into 51 without exceeding it. In this case:
- 23 × 2 = 46
- 23 × 3 = 69 (too high)
This means we can use 2, which fits.

### Step 3: Multiply and Subtract
Write the 2 above the division bracket, directly over the second digit of 51. Multiply 23 by 2 to get 46, and then subtract this from 51:

```
2
_______
23 | 5,129
-46
_______
5
```

Now, bring down the next digit (2) from the dividend, making it 52.

### Step 4: Repeat the Process
Now, divide 52 by 23. Again, how many times does 23 fit into 52?
- 23 × 2 = 46
- 23 × 3 = 69 (too high)
So, we use 2 again. Write it above the division bracket:

```
22
_______
23 | 5,129
-46
_______
52
-46
_______
6
```

Now, bring down the next digit (9) to get 69.

### Step 5: Final Division
Now divide 69 by 23:
- 23 × 3 = 69 (perfect fit)
Write 3 above the bracket:

```
223
_______
23 | 5,129
-46
_______
52
-46
_______
69
-69
_______
0
```

Since there’s no remainder, the final answer is 223. Therefore, 5,129 ÷ 23 = 223.

### Real-World Applications
Understanding long division is essential not just in math class but also in real-life scenarios, such as calculating costs, splitting bills, or determining quantities in recipes. Mastering these skills enhances critical thinking and problem-solving abilities, making you more confident in your math skills.

Remember, practice is key! Try solving the other problems listed, and you'll soon find that long division becomes much easier with time. Each problem is an opportunity to refine your skills and grow your understanding of mathematics.