When asked what my favorite number is, the answer is easy. It’s the incredible number 9. Some tricks make finding the solution easy, whether adding, subtracting, multiplying, or dividing. Math is all about patterns. Once you see the pattern and understand it, problem-solving becomes easy.
ADDITION
Let’s start with addition. First, we know that 1+9=10. Knowing 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 add the 1 from the 3 to 9, which gives me 10. This leaves me with 2. 2+10=12. Notice that the sum of 12 in the answer equals 3 (1+2). Here’s another example:
9+817 1+9=10, 7+10=17; 1+7=8SUBTRACTION
Subtraction has a similar shortcut to addition. Let’s take a look at the problem 16-9. Again we look at what we know, 9+1= 10. The difference between 16 and 10 is 6. I then add the 1 to 6 to get 7, the difference. 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:
14– 9 5Notice that the digits in 14, when added together, equal 5. This works when I subtract 9 from any number. Here’s another example.
24– 9 15 2+4=6 and 1+5=6MULTIPLICATION
Just like addition and subtraction, multiplication has some neat tricks. Let’s look for the pattern by lining the facts up vertically.
We can observe some patterns with the facts lined up in this manner. First, we notice that the digits in the tens column progress from 0-9, and those in the one’s column progress from 9-0. Secondly, the sum of each product’s numbers equals nine. This is a neat trick and a great way to remember the facts.
Another way to find the products of 9 is by using your hands. Place both 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 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 4×9, I’ll fold the fourth finger on my left hand. This leaves three fingers to the left of the fourth finger. This tells me that I have three tens or thirty. I have six fingers to the right of the fourth finger or six ones. 30+6=36, the product of 4×9.
DIVISION
Let’s look at a division problem 7425÷9. I can determine whether the dividend (7425) can be divided evenly by 9 by finding the sum of the digits in the dividend. The quotient will have no remainder if the sum is a multiple of 9. 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.