Prealgebra for Two-Year Colleges/Appendix (procedures)/Multiplication table

x	0	1	2	3	4	5	6	7	8	9
0	0	0	0	0	0	0	0	0	0	0
1	0	1	2	3	4	5	6	7	8	9
2	0	2	4	6	8	10	12	14	16	18
3	0	3	6	9	12	15	18	21	24	27
4	0	4	8	12	16	20	24	28	32	36
5	0	5	10	15	20	25	30	35	40	45
6	0	6	12	18	24	30	36	42	48	54
7	0	7	14	21	28	35	42	49	56	63
8	0	8	16	24	32	40	48	56	64	72
9	0	9	18	27	36	45	54	63	72	81

1. What pattern do you notice if you fold the table across the diagonal?

The numbers are the same on either side of the diagonal; the table is symmetrical.

1. Explain this pattern mathematically.

We get the same answer when we change the order of the factors. For example, 8*5 = 5*8. This is called the commutative rule of multiplication.

1. Write this rule in symbolic notation.

x*y = y*x

1. What happens when you go across the 4’s row?

We are counting up by fours. We add four each time.

1. What happens when you go down the 7’s column?

We are counting up by sevens. We add seven each time.

1. Anything times 1 is...

...the same thing.

1. Write this rule in symbolic notation.

x*1 = x

1. Anything times 0 is...

...zero.

1. Write this rule in symbolic notation.

x*0 = 0