Multiply by multiples of 10, 100, and 1,000

Understanding how to multiply by multiples of 10 is a key mental math skill that makes larger calculations much easier.

The Zero Trick:
When you multiply a whole number by 10, 100, or 1,000, you simply add the same number of zeros to the end of the number.
*   Multiply by 10: Add one zero. (e.g., 8 x 10 = 80)
*   Multiply by 100: Add two zeros. (e.g., 8 x 100 = 800)
*   Multiply by 1,000: Add three zeros. (e.g., 8 x 1,000 = 8,000)

Multiplying by Multiples (like 30, 400, 5000): This uses a two-step process: 1. Multiply the non-zero digits. 2. Count and add all the zeros from the original numbers.

Visual Example: 6 x 400

1.  Multiply the digits: 6 x 4 = 24
2.  Count the zeros: The number 400 has two zeros.
3.  Add the zeros: Take the 24 and add two zeros to the end.
    *   2,400

Another Example: 50 x 80

1.  Multiply the digits: 5 x 8 = 40
2.  Count the zeros: 50 has one zero, and 80 has one zero. That's two zeros in total.
3.  Add the zeros: Take the 40 and add two more zeros.
    *   4,000
    *(Be careful here! The zero from 5x8=40 is part of the product, you still add the two zeros from 50 and 80)*

Key Idea: This works because of place value. 6 x 400 is the same as 6 x 4 x 100. We do 6 x 4 first (24), and then multiply by 100 (add two zeros).

Practice multiplying by multiples!

Basic Zero Trick: 1. 7 x 100 = ? 2. 12 x 1,000 = ? 3. 45 x 10 = ?

Multiply the Multiples: 4. 3 x 200 = ? 5. 6 x 80 = ? 6. 40 x 50 = ? 7. 9 x 5,000 = ? 8. 70 x 300 = ?

Word Problems: 9. A factory produces 500 toys every day. How many toys does it produce in 7 days? 10. Each bus can hold 60 passengers. How many passengers can 20 buses hold? 11. If a company sells 300 cars every month, how many cars do they sell in a year (12 months)?

Challenge Problems: 12. 400 x ? = 8,000 13. 50 x ? = 2,000 14. A whale weighs 80 tons. If 1 ton is 2,000 pounds, how many pounds does the whale weigh?