# Upper and lower boundary subtraction

If you are looking to subtract one quantity from another and you need to know the possible limits upper boundary and lower boundary use logic.

**NOTE:**

1. Upper boundary `=` Upper boundary `A-` Lower boundary `B`

If you have the largest possible amount and subtract the smallest possible amount this will provide you with the biggest quantity difference possible.

Upper boundary `=` Big `-` Small `=` Largest difference

2. Lower boundary `=` Lower boundary `A-` Upper boundary `B`

If you have the smallest possible amount and subtract the largest possible amount this will provide you with the smallest difference between the two.

Lower boundary `=` Small `-` Big `=` Smallest difference

**Example 1**

Two neighbours grew a sunflower in their gardens. Gail's sunflower grew to `2.3metres` and Davina's grew to `1.8metres`. You found out that the measurement had been made to two significant figures.

What are the maximum and minimum differences between Gail's taller plant and Davina's?

This question is a subtraction question but the first thing you must do is find the maximum and minimum values of each number.

The upper and lower boundary of `2.3metres` is

`2.3m` to 2 significant figures.

`2.ul3` underline the last digit.

`2.ul3\0` look next door

`0` `5` or more raises the score. So `2.25` would raise to `2.3`.

`0` four or less just ignore `2.3499` it would ignore and lower to `2.3`.

This is simplified to `2.35`

So the upper and lower boundary of `2.3metres` is `2.35m` and `2.25m`.

The upper and lower boundary of `1.8metres` is

`1.8m` to 2 significant figures.

`1.ul8` underline the last digit.

`1.ul8\0` look next door

`0` `5` or more raises the score. So `1.75` would raise to `1.8`.

`0` four or less just ignore `1.8499` it would ignore and lower to `1.8`.

This is simplified to `1.85`

So the upper and lower boundary of `1.8metres` is `1.85m` and `1.75m`.

**Summary**

Upper and lower boundary of `2.3metres` is `2.35m` and `2.25m`.

Upper and lower boundary of `1.8metres` is `1.85m` and `1.75m`.

The largest difference between the two heights would be the biggest possible difference between their boundaries.

Upper boundary | `=` | Upper boundary `A` | `-` | Lower boundary `B` | |

Upper boundary | `=` | `2.35` | `-` | `1.75` | `=0.6m` |

Big | Small |

The smallest difference between the two heights would be the smallest possible difference between their boundaries.

Lower boundary | `=` | Lower boundary `A` | `-` | Upper boundary `B` | |

Lower boundary | `=` | `2.25` | `-` | `1.85` | `=0.4m` |

Small | Big |

**Answer:** The maximum and minimum differences between the two plants are `0.6m` and `0.4m`.

**Example 2**

Sheila earns $1800 per month and Mary earns $1200 per month to the nearest $100. What are the minimum and maximum differences in their salary per month?

This question is a subtraction question but the first thing you must do is find the maximum and minimum values of each number.

The upper and lower boundary of `$1800` is

`$1800` to the nearest `$100`.

`1ul8\00` underline the last digit.

`1ul8\00` look next door

`0` `5` or more raises the score. So `1750` would raise to `1800`.

`0` four or less just ignore `1849.9dot9` it would ignore and lower to `1800`.

This is simplified to `1850`

So the upper and lower boundary of `$1800` is `$1850` and `$1750`.

The upper and lower boundary of `$1200` is

`$1200` to the nearest `$100`.

`1ul2\00` underline the last digit.

`1ul2\00` look next door

`0` `5` or more raises the score. So `1150` would raise to `1200`.

`0` four or less just ignore `1249.9dot9` it would ignore and lower to `1200`.

This is simplified to `1250`

So the upper and lower boundary of `$1200` is `$1250` and `$1150`.

**Summary**

Upper and lower boundary of `$1800` is `$1850` and `$1750`.

Upper and lower boundary of `$1200` is `$1250` and `$1150`.

The largest difference between these two monetary sums would be the biggest possible difference between their boundaries.

Upper boundary | `=` | Upper boundary `A` | `-` | Lower boundary `B` | |

Upper boundary | `=` | `$1850` | `-` | `$1150` | `=$700` |

Big | Small |

The smallest difference between these two monetary sums would be the smallest possible difference between their boundaries.

Lower boundary | `=` | Lower boundary `A` | `-` | Upper boundary `B` | |

Lower boundary | `=` | `$1750` | `-` | `$1250` | `=$500` |

Small | Big |

**Answer:** The maximum and minimum differences between their two salaries is `$700` and `$500`.