How to use bounds to solve real world problems

Understanding Bounds

Bounds refers to the smallest and largest possible values of a measurement or quantity.
They are useful in calculations when measurements are rounded, providing a more accurate result.
Each value, be it upper or lower bound, will have an impact on the final result of a calculation depending on the mathematical operation undertaken.

The Lower Bound of a rounded value is the smallest possible value it could originally have been. For example, if a measurement is rounded to 5.6m, the lower bound will be 5.55m if the measurement was rounded to one decimal place.
The Upper Bound is the highest possible value it could originally have been. With the same example of 5.6m, the upper bound would be 5.65m.

In addition and subtraction operations, you should normally add the lower bound of one value to the lower bound of another, and the upper bound of one value to the upper bound of another.
For subtraction, subtract the upper bound of one value from the lower bound of the other.
In multiplication or division, if both values are positive, multiply or divide the lower bound of one value by the lower bound of the other, and the upper bound of one value by the upper bound of the other.
If both values are negative, the same rule applies. However, if one value is negative and the other positive, lower limit of the result is found by multiplying or dividing the lower bound of the positive value by the upper bound of the negative value, and vice versa.

When solving real-world problems using measurements or quantities that have been rounded, choose the appropriate bound based on the context of the problem to perform calculations.
Understand whether the situation needs an overestimate, underestimate or both.
For instance, not to run out of paint while painting a room, you might use the upper bound of the room’s area and lower bound of the coverage rate of the paint.

Not identifying correctly whether to use the lower or upper bound in context of the problem.
Incorrect application of bounds in arithmetic operations, leading to incorrect results.
Overlooking the impact of negative numbers on the rule for multiplication and division.
Neglecting to consider bounds in real-world problems involving measurements or rounded quantities for calculations.