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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Famous quotes containing the words apples and, apples, oranges, teaching and/or units:
“There was a young lady of Ryde
Who swallowed some apples and died.
The apples fermented
Inside the lamented
And made cider inside her inside.”
—Anonymous.
“He hangs in shades the orange bright,
Like golden lamps in a green night,
And does in the pomegranates close
Jewels more rich than Ormus shows;
He makes the figs our mouths to meet,
And throws the melons at our feet;
But apples plants of such a price
No tree could ever bear them twice.”
—Andrew Marvell (1621–1678)
“I don’t give a hoot in a hollow if there’s oranges and grapes a-crowdin’ us out of bed, I ain’t goin’ to California! This is my country and I belong here. This is my dirt. It’s no good, but it’s mine.”
—Nunnally Johnson (1897–1977)
“The basis of world peace is the teaching which runs through almost all the great religions of the world. “Love thy neighbor as thyself.” Christ, some of the other great Jewish teachers, Buddha, all preached it. Their followers forgot it. What is the trouble between capital and labor, what is the trouble in many of our communities, but rather a universal forgetting that this teaching is one of our first obligations.”
—Eleanor Roosevelt (1884–1962)
“Even in harmonious families there is this double life: the group life, which is the one we can observe in our neighbour’s household, and, underneath, another—secret and passionate and intense—which is the real life that stamps the faces and gives character to the voices of our friends. Always in his mind each member of these social units is escaping, running away, trying to break the net which circumstances and his own affections have woven about him.”
—Willa Cather (1873–1947)