Question

Make up a true proportion out of each set of four numbers is it possible to make another proportion using the same set of numbers? 18; 4; 24; 3

Answer 1

• 18 : 3 = 24 : 4
• yes; 3 other proportions are possible

Explanation:

You want a true proportion using the numbers {3, 4, 18, 24}, and you want to know if another proportion can be written with the same numbers.

Proportion

We note that the two smaller numbers have the ratio 3:4 and the two larger numbers have the ratio 3:4, so a proportion can be written. Using the larger number of each corresponding pair on top, one proportion that can be written is ...

`(18)/(3)=(24)/(4)`

Others

Any proportion can be written 4 ways. One way to think of the alternatives is "upside down" and "sideways". Some other possibilities are ...

`(3)/(18)=(4)/(24)\qquad(3)/(4)=(18)/(24)\qquad(4)/(3)=(24)/(18)`

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Additional comment

The cross product of any of these proportions is ...

18·4 = 24·3

Effectively, you can write a true proportion by dividing this equation by one of the left-side numbers and by one of the right-side numbers. There are 4 combinations of pairs of numbers, giving rise to the 4 different proportions shown above. For example, dividing by 18 and 24 gives ...

4/24 = 3/18

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