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

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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 |

- 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.*

- 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.*

- Write this rule in symbolic notation.

*x*y = y*x*

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

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

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

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

- Anything times 1 is...

*...the same thing.*

- Write this rule in symbolic notation.

*x*1 = x*

- Anything times 0 is...

*...zero.*

- Write this rule in symbolic notation.

*x*0 = 0*