- The “9-trick”: To add 9 to any number, first add 10, and then subtract 1. Can you think of an easy way to add 76 + 99? Change it to 75 + 100. How about 385 + 999? How would you add 39 + 28 in your head? Let 39 become 40… which reduces 28 to 27. The addition is now 40 + 27. Yet another way is by thinking of compensation: 39 is one less than 40, and 28 is two less than 30. So, their sum is three less than 70.
- Doubles + 1: For example, 5 + 6 is just one more than 5 + 5, or 9 + 8 is just one more than 8 + 8.
- Use addition facts when adding bigger numbers: Once you know that 7 + 8 = 15, then you will also be able to do all these additions in your head:
- 70 + 80 is 15 tens, or 150
- 700 + 800 is 15 hundreds, or 1500
- 27 + 8 is 20 and 15, which is 35. Or, think this way: since 7 + 8 is five more than ten, then 27 + 8 is five more than the next ten.
- Subtract by adding: This is a very important principle, based on the connection between addition and subtraction. For example, to find 8 − 6, think, “Six plus what number makes 8?” In other words, think of the missing number addition 6 + ___ = 8. The answer to that is also the answer to 8 − 6. This principle comes in especially handy with subtractions such as 13 − 7, 17 − 8, 16 − 9, and other basic subtraction facts where the minuend is between 10 and 20. But you can also use it in multitudes of other situations. For example, 63 − 52 is easier to solve by thinking of addition: 52 + 11 makes 63, so the answer to 63 − 52 is 11.
- Five times a number: Here’s a nifty trick you might not know about. To find 5 times any number, first multiply that number times ten, then take half of that. For example, 5 × 48 can be found by multiplying 10 × 48 = 480, and taking half of the result, which gives us 240. Of course, you can also use this strategy for such multiplication facts as 5 × 7 or 5 × 9.
- Four and eight times a number: If you can double numbers, you already have this down pat! To find four times a number, double that number twice. For example, what is 4 × 59? First find double 59, which is 118. Then double that, and you get 236. Similarly, eight times a number just means doubling three times. As an example, to find 8 × 35 means doubling 35 to get 70, doubling 70 to get 140, and (once more) doubling 140 to get 280.
- Multiply in parts: This strategy is very simple, and in fact it is the foundation for the standard multiplication algorithm. You can find 3 × 74 mentally by multiplying 3 × 70 and 3 × 4, and adding the results. We get 210 + 12 = 222. Another example: 6 × 218 is 6 × 200 and 6 × 10 and 6 × 8, which is 1200 + 60 + 48 = 1308.
8. Practice all the above! Without trying out and practicing these skills, no one could master it. Keep learning, and soon you will have no errors!
