Apples and Oranges in Teaching The Use of Units
While references to comparing apples and oranges is often a rhetorical device, references to adding apples and oranges are made in the case of teaching students the proper uses of units. Here, the admonition not to "add apples and oranges" refers to the requirement that two quantities with different units may not be combined by addition, although may always be combined by multiplication, so that multiplying apples and oranges is allowed. Similarly, the concept of this distinction is often used metaphorically in elementary algebra.
The admonition is really more of a mnemonic, since in general counts of objects have no intrinsic unit and, for example, a number count of apples may be dimensionless or have dimension fruit; in either of these two cases, apples and oranges may indeed be added.
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Become one movement, energy, delight....”
—William Butler Yeats (1865–1939)
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—Willa Cather (1873–1947)