Here are a few examples demonstrating how to add numbers quickly using mental math techniques:

**Example 1: Adding Two-Digit Numbers**
Add: 47 + 68

- Start with the units (ones) digit: 7 + 8 = 15. Write down 5 and mentally carry over 1.
- Move to the tens digit: 4 + 6 + 1 (carried over) = 11.

The sum is 115.

**Example 2: Adding Three-Digit Numbers**
Add: 356 + 482

- Start with the units digit: 6 + 2 = 8.
- Move to the tens digit: 5 + 8 = 13. Write down 3 and mentally carry over 1.
- Move to the hundreds digit: 3 + 4 + 1 (carried over) = 8.

The sum is 838.

**Example 3: Adding Large Numbers by Chunking**
Add: 2,345 + 1,789

- Add the thousands: 2,000 + 1,000 = 3,000.
- Add the hundreds: 300 + 700 = 1,000.
- Add the tens and ones: 40 + 80 = 120.

The sum is 3,000 + 1,000 + 120 = 4,120.

**Example 4: Using Complementary Numbers**
Add: 87 + 46

- Find the difference between the larger number and 10 (87 - 10 = 77).
- Add the complement of the smaller number (46 + 3 = 49).
- Add the results: 77 + 49 = 126.

This technique is particularly useful when one of the numbers is close to a multiple of 10.

**Example 5: Adding Decimals**
Add: 32.57 + 12.89

- Start with the tenths digit: 5 + 9 = 14. Write down 4 and carry over 1.
- Move to the hundredths digit: 7 + 8 + 1 (carried over) = 16.
- Add the whole numbers: 32 + 12 = 44.

The sum is 44.16.

Practice these techniques regularly, and you'll become faster and more accurate at adding numbers mentally. Start with simpler calculations and gradually move on to more complex ones as you build your mental math skills.