Nine groups are one short of ten
To multiply a whole number by 9, multiply it by 10 and subtract the original number. Ten equal groups contain one more group than nine.
For 9 × 7, ten groups of seven make 70. Remove one group of seven: 70 − 7 = 63.
The step comes from the distributive property explained by OpenStax: (10 − 1) × 7 = 10 × 7 − 1 × 7.
Build the table with the same rule
Use the same method for 9 × 4: 40 − 4 = 36. For 9 × 8, work out 80 − 8 = 72.
The first ten positive multiples are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90. Each new entry adds one more group of nine. You can check a remembered answer against that pattern.
It also works beyond the small table
Try 9 × 28. Ten groups make 280. Removing one group means subtracting 28, not just subtracting one.
Split the subtraction if it helps: 280 − 20 = 260, then 260 − 8 = 252. So 9 × 28 = 252.
For 9 × 0, the method gives 0 − 0 = 0 too.
Remove a group, not one item
The common slip is to calculate 70 − 1 for 9 × 7. But the extra group contains seven items. Remove all seven to get 63.
This extends rounding and adjusting: choose the nearby calculation that is easy, then undo exactly the extra amount you introduced.