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
808=72
8×9=72
  1. 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.
  2. 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.
  3. 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.
  4. So 8 × 9 = 72.

How it works.

  1. 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.

  2. 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.

  3. 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.

  4. 04

    So 8 × 9 = 72.