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.

Use logic to find the upper and lower limits to subtract 2 numbers

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$ .