Math CentralQuandaries & Queries


Question from Kenneth:


I read the following in an old textbook:

Display the numbers 27, 18, 26, and 39 so as to form a proportion.

Which set of equal fractions is correct?

18/27 = 26/39

18/26 = 27/39

I thank you for your reply.

Hi Kenneth,

Look at the fractions first and put each of them in lowest terms.

\[\frac{18}{27} = \frac{9 \times 2}{9 \times 3} = \frac23\]


\[\frac{26}{39} = \frac{2 \times 13}{3 \times 13} = \frac23 .\]

Thus the first pair of fractions are equal. Try the second pair.

Since $\large \frac{18}{27} = \frac{26}{39}$ we know that 18:27 as 26:39. What about 18:26 and 27:39?

This makes you wonder, if a:b as c:d then is a:c as b:d? Can you prove or disprove this?


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