9s multiplication facts
The 9s multiplication facts have a reliable digit pattern: the first digit of the product is one less than the number being multiplied by 9, and the two digits of the product always sum to 9. So 9 × 7: first digit = 7 − 1 = 6, second digit = 9 − 6 = 3, giving 63. This trick covers every 9s fact from 9×2 through 9×9 and is taught in Saxon Math Intermediate 4 as part of 4th grade multiplication fluency. The 9s also connect to the finger trick — fold the nth finger and count left for tens, right for ones.
Key Concepts
Property When multiplying by nine, the first digit of the product is one less than the number being multiplied, and the sum of the product's two digits is nine.
Example 1. $9 \times 7$: The first digit is $7 1=6$. The second digit is $9 6=3$. So, $9 \times 7 = 63$. 2. $9 \times 4$: The first digit is $4 1=3$. The second digit is $9 3=6$. So, $9 \times 4 = 36$.
Explanation Multiplying by nine is a neat trick! First, subtract one from the number you are multiplying by nine to find the first digit of the answer. Then, find the number you must add to that first digit to get a total of nine. That number is the second digit of your answer.
Common Questions
What is a trick for learning the 9 times table?
For 9 × n: the tens digit of the answer is n − 1, and the ones digit is 9 minus the tens digit. For 9 × 6: tens digit = 5, ones digit = 9 − 5 = 4, so 9 × 6 = 54. The two digits always add to 9.
How does the finger trick work for the 9 times table?
Hold up all 10 fingers. To find 9 × 4, fold down your 4th finger. Count fingers to its left (3) for the tens digit and fingers to its right (6) for the ones digit: 9 × 4 = 36.
Why do the digits of every multiple of 9 add up to 9?
It's a property of base-10 arithmetic. Every multiple of 9 from 18 to 81 has digits that sum to 9 (1+8, 2+7, 3+6, etc.). For larger multiples, the digit sum eventually reduces to 9 repeatedly.
When do students learn the 9 times table?
The 9s multiplication facts are part of the 4th grade multiplication fluency curriculum. Saxon Math Intermediate 4 covers them alongside other fact families, using the digit-pattern trick to make memorization faster.
What are all the 9 times table facts?
9×1=9, 9×2=18, 9×3=27, 9×4=36, 9×5=45, 9×6=54, 9×7=63, 9×8=72, 9×9=81, 9×10=90. Notice each answer's digits sum to 9.
How does knowing the 9s help with other math?
Fluent 9s facts speed up multi-digit multiplication and division. They also connect to patterns in number theory and make mental math much faster for problems involving 9, 18, 27, 36, and other multiples.