# Fact family

A fact family is a group of math facts that use the same set of numbers. Examples include addition, subtraction, mutliplication, and division facts. The use of fact families can be useful for helping children learn about the relationship between operations like addition and subtraction, and multiplication and division.

### Addition and subtraction fact family

An addition and subtraction fact family uses two addends and their sum to form basic facts.

Below are examples of two fact families. One of the fact families is made up of the numbers 3, 4, and 7 while the other is made up of the numbers 8, 0, and 8.

3, 4, and 7: | 8, 0, and 8: | |

3 + 4 = 7 | 8 + 0 = 8 | |

4 + 3 = 7 | 0 + 8 = 8 | |

7 - 4 = 3 | 8 - 0 = 8 | |

7 - 3 = 4 | 8 - 8 = 0 |

One way to think of addition and subtraction fact families is as parts of a whole, where the largest number in the fact family is the whole, and the other two numbers are the two parts that make up the whole. In the first example above, 7 is the whole, so if we subtract 3 from 7, we know that we will have 4 left. If we add 3 to 4, we know we will get 7, and so on. This can help when first learning about addition and subtraction. Real life objects can also be used as a visual aid.

### Multiplication and division fact family

A multiplication and division fact family uses two factors and their product to form basic facts.

One of the fact families is made up of the numbers 4, 6, and 24 while the other is made up of the numbers 5, 0, and 0.

4, 6, and 24: | 5, 0, and 0: | |

4 × 6 = 24 | 5 × 0 = 0 | |

6 × 4 = 24 | 0 × 5 = 0 | |

24 ÷ 6 = 4 | 0 ÷ 5 = 0 | |

24 ÷ 4 = 6 | None (5 ÷ 0 is undefined) |

Multiplication and division facts are typically memorized using a multiplication table, such as the one shown below.

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

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

2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |

3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |

4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 |

5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |

6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 |

7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 |

8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 |

9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 |

10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

To use the multiplication table, choose two values from 1-10 from the outermost grey row and column. Draw imaginary lines from both the numbers (horizontally from the left column; vertically from the top row) and determine the value at which they intersect. This is the product of the two chosen numbers.