# 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*