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9's Multiplication Facts: Learn the Patterns and Improve Your Mental Math



Generally, an elementary student is expected to answer 100 multiplication facts within 5 minutes. However, many middle school and high school students have trouble completing the 5 minute quiz with 100% accuracy. One of the stumbling blocks to finish or to get 100% correct is generally the 9 facts. So, after reviewing some basic concepts of multiplication, I like to show the students a few patterns that will make memorization easier and retainable. After you review the patterns, challenge yourself by playing the matching game at the end of this article.



Pattern 1


Take a look at the first digit in all of the answers(product). They are in numerical order from 0 to 9. Now, look at the second digits in the product. What do you notice? The numbers are in descending order from 9 to 0.


9 x 1 = 0 9

9 x 2 = 1 8

9 x 3 = 2 7

9 x 4 = 3 6

9 x 5 = 4 5

9 x 6 = 5 4

9 x 7 = 6 3

9 x 8 = 7 2

9 x 9 = 8 1

9 x 10 = 9 0


How to apply: If you are still learning your multiplication facts and you have a test soon, on the day of the test, write your 9 times table on your test paper before you begin, and you can use the above pattern to ensure they are correct. This eliminates frustration during the test and saves time and reduces finger counting.



Pattern 2

Can you see the pattern between the second factor and the first digit in the answer (product) of each multiplication fact?


For example: 9 x 2 = 18; the second factor is 2 and the first digit in the product is 1.


9 x 3 = 27; the second factor is 3 and the first digit in the product is 2.


9 x 4 = 36; the second factor is 4 and the first digit is 3.

Yes! The first digit in the product is one less than the second factor.




Pattern 3

If you add the digits of the product, they add up to nine.


9 x 2 = 18; 1 + 8 = 9


9 x 3 = 27; 2 + 7 = 9


9 x 4 = 36; 3 + 6 = 9

This is true for all the 9 facts thru 9 x 10.



Application: There are a few more patterns but these three patterns will help you learn the facts quickly. Here’s how:


Keep pattern 2 and 3 in mind to answer the following questions.


9 x 4 = ? Remember Pattern 2 states that the first digit in the answer is one less than the 2nd factor. So, the first digit in the answer is “3”


9 x 4 = 3?


Since, the sum of the digits in the answer must equal 9, ask , “3 plus what number equals 9?” the response is “6.” Put the two numbers together. Thus


9 x 4 = 36


Try another one.


9 x 8 = _ ;


1st digit = _______( the first digit is one less than 8)


2nd digit = _______ (the first digit plus what number equals 9)

Put the two numbers together. Therefore, 9 x 8 = 72.



PRACTICE!, PRACTICE!, PRACTICE!



Now you no longer have to count on your fingers. Next teach three other people this strategy and you’ll learn them even faster. Start practicing now by clicking the blue start button below.




Tip: Graphing paper helps to keep students numbers aligned and neat on a page. Also, graphing paper is great to use for drawing arrays, charts, and graphs for linear equations.



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