When asked what my favorite number is, the answer is easy. It’s the fabulous number 9. No matter whether you are adding, subtracting, multiplying or dividing, there are tricks that make finding the answer easy. Math is all about patterns. Once you see the pattern and understand it, problem solving becomes easy.
Let’s start with addition. First, we know that 1+9=10. Know this information is the first step to understanding how easy finding the sum of 9 and any number. Let’s take the example of 9+3.
First, I take the 1 from the 3 and I add it to 9, which gives me 10. This leaves me with 2. 2+10=12 Notice that the sum of the number 12 in the answer is equal to 3 (1+2) Here’s another example:
17 1+9=10, 7+10=17; 1+7=8
Subtraction has a similar shortcut to addition. Let’s take a look at the problem 16-9. Once again we look at what we know, 9+1= 10. The difference between 16 and 10 is 6. I still have to add the 1 that I added to 9 to the 6. Therefore, 16-9=7. Notice that when I take the number 16 and add the two digits (1+6), I get 7, which is also the answer to the problem. Here’s another example:
Notice, that the digits in 14, when added together equal 5. This works when I subtract 9 from any number. Here’s another example.
15 2+4=6 and 1+5=6
Just like addition and subtraction, multiplication has some neat tricks. Let’s look for the pattern by lining the facts up vertically.
There are a couple of patterns that we can observe with the facts lined up in this manner. First, we notice that the digits in the tens column progress from 0-9 and the digits in the ones column progress from 9-0. Secondly, the sum of the digits of each product is equal to nine. This is a pretty neat trick and a great way to remember the facts.
Another way to find the products of 9 is by using your hands. Place your hands palms down on the table. Count from the pinky on the left hand the number that you are multiplying 9 by. When you get to the number, fold that finger under. The fingers that are up on the left of the folded finger are the number of tens and the fingers remaining up to the right of the folded finger are the number of ones in the answer. So if I’m multiplying 3×9, I’ll fold the middle finger on my left hand. This leaves two fingers to the left of the middle finger up. This tells me that I have two tens or twenty. I have 7 fingers to the right of the middle finger or seven ones. 20+7=27, the product of 3×9.
Let’s look at a division problem: . I can determine whether the dividend (7425) can be divided evenly by 9 by finding the sum of the digits in the dividend. If the sum is a multiple of 9, the quotient will have no remainder. Since 7+4+2+5=18, I know that the quotient will have no remainder.
No matter what operation I do with nines, there is an easy pattern that I can follow to determine the answer.