Name: Jenna
Who is asking: Other
Level: Secondary

For any two real numbers, a and b, give a mathematical expression in terms of a and b that will yield the smaller of the two numbers. Your expression should work regardless of whether a>b, a<b, or a=b.

Hi Jenna,

Imagine that you have two lengths, a and b. You can put the two lenghts together to get a + b and you can find the difference in their lengths, |a - b|.

The blue lines are of length a and b (it doesn't matter which is which) and the green line is of length |a-b|. From the diagram a + b -|a - b| is twice the length of the smaller of a and b. Thus

is the length of the smaller of a and b.

Does this expression work if a or b or both are negative or zero?

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