If the denominators were the same for both fractions, then Iris would be correct.
Example: Compare 2/7 with 5/7
Since 2 < 5, this means 2/7 < 5/7
This works because a < b leads to a/c < b/c where c is some positive integer. The inequality sign doesn't flip when you divide both sides by a positive number. In the example above, I divided both sides by 7.
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But what if we wanted to compare 2/7 with 5/1000?
2 < 5 is true but 2/7 < 5/1000 is not true.
We can use a calculator to get a decimal value for each fraction
- 2/7 = 0.2857 approximately
- 5/1000 = 0.005
We see that 2/7 is actually larger than 5/1000
Unfortunately the rule Iris came up with is incorrect.
If she mentioned the denominators being the same, then she would be correct. But overall in general, the claim is not correct.