# Basic facts

The basic facts refer to all the addition and multiplication problems formed by combinations of one-digit numbers. There are 100 basic addition facts, and 100 basic multiplication facts.

Learning the basic facts is an important aspect of building a strong mathematical foundation. While it is possible for a student to simply use a calculator, or count/calculate a basic fact whenever they come across it, being able to immediately recall the basic facts provides many advantages, particularly for progressing to learning more involved mathematics.

A student who knows all the basic facts does not need to expend any mental energy towards computing the basic facts when tackling new topics. A student who has to spend time computing any basic facts they encounter rather than simply knowing them has an added barrier to learning new topics.

## Learning the basic facts

There are many different ways to approach learning the basic facts. One way is to use addition and multiplication tables as references for practicing the basic facts.

### Addition table

An addition table is a tool that can be used to find all the addition facts. The first row and first column of the table (indicated with a grey background) contain the numbers 1-9, which represent the two addends in an addition problem. The number at which an extension from the row and column of the chosen addends intersect is the sum of the addends.

To solve the problem 2 + 7 using the table, find the addends 2 and 7 on the table. It doesn't matter whether the 2 and 7 are chosen from the row or column first. In either case, the sum is 9, and is found as the intersection of the row and column containing 2 and 7:

2 + 7 = 9

7 + 2 = 9

+ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |

5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |

6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |

9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

In this way, the table can be used to find any addition fact. The table can also be expanded to include more numbers.

## Multiplication table

Multiplication tables are largely similar to addition tables. They work in the same way. The first row and column of the table (indicated with a grey background) contain the factors of the multiplication problem. The number at which an extension from the row and column of the chosen factors intersect is the product of the factors. The diagonal highlighted in green in the multiplication table below shows the squares of the numbers 1-9.

× | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 |

3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 |

4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 |

5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 |

6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 |

7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 |

8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 |

9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 |

The table can be used to find any multiplication fact (for 1-9), and can also be expanded to include more numbers for further practice with basic facts.