Question

How can you efficiently subtract multi-digit numbers?

Answer 1

Efficiently subtracting multi-digit numbers requires a systematic approach. Here are some steps and techniques to help you perform multi-digit subtraction effectively:

### Standard Algorithm
1. **Align the Numbers:** Write the larger number on top and the smaller number directly below it, making sure to align the digits by place value (units, tens, hundreds, etc.).

2. **Subtract from Right to Left:** Start from the rightmost digit (the units place) and work your way to the left. Subtract each digit of the bottom number from the top number.

3. **Borrowing:** If the digit on the top is smaller than the digit directly below it, you need to borrow from the next left digit:
- Decrease the next left digit by 1.
- Add 10 to the current digit.
- Now, subtract as usual.

### Example:
Consider 582 - 347:

```
582
- 347
-----
```

1. **Units Place:** 2 - 7. (Not enough, so we borrow 1 from 8 in the tens place.)
- 8 becomes 7, and 2 becomes 12.
- 12 - 7 = 5

2. **Tens Place:** 7 - 4 = 3

3. **Hundreds Place:** 5 - 3 = 2

So, 582 - 347 = 235.

### Mental Math Strategies
For quicker calculations, especially when subtracting from round numbers or using complementary numbers, consider these strategies:

1. **Round and Adjust:** Round the top number to a more manageable number, perform the subtraction, then adjust:
- Example: To subtract 199 from 500, think of it as 500 - 200 + 1 = 301.

2. **Using Complements:** Subtracting from 10, 100, etc., can simplify calculations:
- Example: For 870 - 297, you can think of it as 870 - 300 + 3 = 573.

3. **Breakdown:** Break down numbers into smaller parts:
- Example: 562 - 239 can be broken down as 562 - 200 - 30 - 9 = 323.

### Practice
The more you practice, the faster you'll become. Try different techniques and see which ones work best for you in various scenarios.

### Summary
Using the standard algorithm with the right-to-left method and borrowing when necessary, along with mental math techniques, will help you subtract multi-digit numbers efficiently and accurately.