How to Divide by a Two-Digit Number: Step-by-Step Guide

Dividing by a two-digit number can seem challenging at first, but with the long division method, you can master it easily. This guide will walk you through the steps needed to find the quotient and remainder when dividing numbers like 5,129 by 23.

### Step-by-Step Long Division Process

1. **Set Up the Problem**: Write the dividend (the number you're dividing, e.g., 5,129) under the long division symbol and the divisor (the two-digit number you're dividing by, e.g., 23) outside.

2. **Estimate How Many Times the Divisor Fits**: Start by looking at the first two digits of the dividend. For 5,129, we consider 51. Ask yourself, how many times does 23 fit into 51? The answer is 2 times since 23 x 2 = 46.

3. **Multiply and Subtract**: Multiply 23 (the divisor) by 2 (the quotient you just calculated) to get 46. Write this number below 51 and subtract it. 51 - 46 = 5. Bring down the next digit from the dividend, which is 2, making it 52.

4. **Repeat the Process**: Now, you have 52. How many times does 23 fit into 52? It fits 2 times again (23 x 2 = 46). Write 2 above the line next to the previous 2, making it 22. Multiply and subtract again: 52 - 46 = 6. Bring down the next digit from the dividend, which is 9, making it 69.

5. **Continue Dividing**: Now, how many times does 23 fit into 69? It fits exactly 3 times (23 x 3 = 69). Write this 3 above the line, making your quotient 223. Subtract 69 from 69 to get 0.

6. **Complete the Division**: Since there are no more digits to bring down from the dividend, the division is complete. The quotient is 223, and there is no remainder.

### Example Problems
- **18 ) 6,948**: Estimate how many times 18 fits into the first part of 6,948. Repeat the steps, and remember to write down your work.
- **32 ) 7,264**: Start with 72, estimate how many times 32 fits, and follow the long division steps.

### Real-World Applications
Understanding how to divide by a two-digit number is crucial in everyday situations, such as calculating prices, splitting bills, or handling measurements in recipes. The ability to perform long division also strengthens your overall math skills, which are foundational for higher-level mathematics.

With practice, you will find that long division becomes quicker and easier. Remember, every time you practice, you're training your brain for better problem-solving skills. So grab your pencil and paper, and let’s tackle these problems one at a time!