**Quote:**

What is the criteria to use 2 and 5 ? May I use a different number, for instance 6 and 6?

We have two proportions with a common "participant" (red beans):

6 : 5 (white beans : red beans)

2 : 1 (red beans : black beans)

The both proportions are to the lowest terms.

In order to make one proportion out of these two we need to have the same proportion number of red beans in the both proportions. Such number is the common multiple of 2 and 5. It's better to take the LEAST common multiple, so the new proportion will also be to the lowest terms.

The LCM of 2 and 5 is 10. So we multiply the first proportion by 10/5 = 2 to get 12 : 10.

We multiply the second proportion by 10/2 = 5 to get 10 : 5.

Now we can combine the proportions: 12 : 10 : 5.

If we didn't choose the LEAST common multiple, but just a common multiple, e.g. 20, then the combined proportion would not be to the lowest terms: 24 : 20 : 10.

So now you can answer your question

**Quote:**

…, for instance 6 and 6?

No, because the common "participant" would not have the same proportion number.

36 : 30

12 : 6

So we would not be able to combine them.

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Here is the problem to practice:

Combine the two proportions into one with the lowest terms:

5 : 6 (oranges : bananas)

10 : 7 (bananas : pineapples)