Question

Can the values be added or subtracted? If one value needs to be converted to another, describe the conversion.

27.25 ft² + 38.5 in²

A.
The values cannot be added because one is measuring area and the other is measuring distance.

B.
The values can be added without making a conversion of units because they both measure area.

C.
The values can be added after making a conversion of units because they both measure area.

D.
The values cannot be added because one is measuring area and the other is measuring capacity.

Answer 1

When we talk about units, it is often helpful to describe them in terms of what dimensions they have.

For example, feet are a measure of length, so the measurement 23 feet would be described as having form [length]

kilograms are a measure of mass, so 17 kilograms would be described as having form [mass]

\(\text{meters}^3\) is a measure of volume, so it has form \([\text{length}]^3\)

density is mass/volume, so it has form \([\text{mass}]/[\text{length}]^3\)

If two measurements have the same form, they can be added or subtracted, but only if the measurements are in the same units.

You can add 3 feet (form [length]) and 4 feet (form [length]) directly, because they have the same form and the same units.

You can add 3 feet (form [length]) and 4 inches (form [length]), because they have the same form, but you first must convert at least one of them so that they have the same units

You cannot add 3 feet (form [length]) and 7 kilograms (form [mass]) because they do not have the same form, and no conversion is possible.

Answer 2

By the way, this question deserves a better home than the History section :-)