Multiplication by 9, step by step
The nine times table looks like the hardest and is secretly the most patterned in the grid.
The question
8 × 9
8×9
8 × 9=9 × 8
8 × 10=80
80−8=72
8×9=72
- 8 × 9 means 8 groups with 9 in each one — 8 rows of 9. The answer counts everything in all of them, not one row.
- Added up, that is 9 written 8 times — nobody wants to do that. Turn it round: 9 × 8 is the same amount, and it is only 9 lots of 8 to add instead.
- Nines are the easy ones. 8 × 10 = 80, and nine groups is one group short of ten — so take one 8 back off: 80 − 8 = 72.
- So 8 × 9 = 72.
How it works.
- 01
8 × 9 means 8 groups with 9 in each one — 8 rows of 9. The answer counts everything in all of them, not one row.
- 02
Added up, that is 9 written 8 times — nobody wants to do that. Turn it round: 9 × 8 is the same amount, and it is only 9 lots of 8 to add instead.
- 03
Nines are the easy ones. 8 × 10 = 80, and nine groups is one group short of ten — so take one 8 back off: 80 − 8 = 72.
- 04
So 8 × 9 = 72.