Like the concept from last Tuesday, this idea is much simpler than its title suggests. It showed up 12 times this year--10 of those times at question # 13. Before solving these problems, make sure the following conditions are met:
- Both numbers are 2-digit integers.
- The tens digits are the same.
- The units digits add up to 10.
Number Dojo Level: 73
This concept is SquareEnd5's first cousin. If you don't know yet how to square numbers ending in 5, please review that now so you can see the pattern of operations involved.
How to solve:
- Multiply the units digits and write this product down as the last 2 digits of your answer. (If the product is 9, write down 09 instead of 9).
- Multiply the common tens digit by its upper neighbor (itself plus 1). Write this down in front of what you wrote in step 1. You're done!
Example 1: 42 x 48
- Multiply the units digits. 2 x 8 = 16; write this down.
- Multiply the common tens digit (4) by its upper neighbor (5). 4 x 5 = 20; write this in front. The answer is 2016.
Example 2: 29 x 21
- Multiply the units digits. 9 x 1 = 9; write it as 09.
- Multiply the common tens digit (2) by its upper neighbor (3). 2 x 3 = 6; write this in front. The answer is 609.
Example 3: 94 x 96
- Multiply the units digits. 4 x 6 = 24; write this down.
- Multiply the tens digit by its upper neighbor. 9 x 10 = 90; write this in front. The answer is 9024.
Example 4: 6.7 x 6.3
- Don't let the decimals fool you. 7 x 3 = 21; write this down.
- Multiply 6 x 7 to get 42 and write this in front. Remember that there will be 2 decimal places, so the answer is 42.21.
Example 5: 198 x 192
- This will work with 3-digit numbers, as long as the first 2 digits are the same in both numbers. Multiply the units digits. 8 x 2 = 16; write this down.
- Multiply 19 x 20 to get 380; write this in front. The answer is 38016.
Up Next for Middle School: MultDistrib2