# Inversely proportional relationship

**Inversely proportional relationships** are "the more the less"-relationships.

They always **decrease evenly** (proportional).

### Example

A worker needs 12 days. The number of days required **decreases** equally with increasing numbers of workers.

Worker | needed days |
---|---|

1 | 12 |

2 | 6 |

3 | 4 |

4 | 3 |

The graph is a **hyperbola**. It approaches the two axes more and more without reaching them.

!

### Remember

If one doubles (triples, quadruples, ...) an initial value, the assigned value halves (thirds, quarters, ...).

## Constant of inverse proportionality (total size)

If we multiply the assigned size times the initial size in an inversely proportional relationship, we always get the same value.

### Example

Worker | needed days |
---|---|

1 | 12 |

2 | 6 |

3 | 4 |

4 | 3 |

$1\cdot12=\color{blue}{12}$

$2\cdot6=\color{blue}{12}$

$3\cdot4=\color{blue}{12}$

$4\cdot3=\color{blue}{12}$

The constant of inverse proportionality is here 12. It is therefore an inversely proportional relationship.

!

### Remember

The

**constant of inverse proportionality**or the**total size**is the product of initial value (x) and assigned value (y).