Hello, Math Wizards! 🧙♂️
Today, we’re going to learn a super cool trick for multiplying two-digit numbers that have the same first digit and last digits that add up to 10. This trick will make you look like a math genius! Ready? Let’s dive in!
The Magic Trick
Here’s how the trick works:
Steps of the Trick
- Find the First Digit: Look at the first digit of both numbers. It should be the same for both. For example, with 83 and 87, both start with 8.
- Multiply the First Digit by the Next Higher Digit: Multiply the first digit by the number that comes right after it. For 8, the next number is 9. So, 8 × 9 = 72.
- Multiply the Last Digits: Now, multiply the last digits of both numbers. They should add up to 10. For 83 and 87, 3 + 7 = 10, so 3 × 7 = 21.
- Put It Together: Combine the two results. The first part is 72, and the second part is 21. So, 83 × 87 = 7221!
Why Does This Trick Work?
This trick works because of a neat pattern in numbers:
When you multiply two numbers with the same first digit and last digits that add up to 10, you’re actually doing something special. The first part of the answer comes from multiplying the first digit by the next higher number. The second part comes from multiplying the last digits together. This pattern is why the trick works every time!
Example 1: 84 × 86
- Number: 84 × 86
- First Digit: 8 (Next number is 9)
- Multiply: 8 × 9 = 72
- Last Digits: 6 × 4 = 24
- Answer: 7224
Example 2: 33 × 37
- Number: 33 × 37
- First Digit: 3 (Next number is 4)
- Multiply: 3 × 4 = 12
- Last Digits: 3 × 7 = 21
- Answer: 1221
Try It Yourself!
Now it’s your turn! Enter two numbers with the same first digit and last digits that add up to 10, and see the magic happen!