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Thank you for placing this whole debate and discussion in the right context. The switch from "equivalent" to "equal" was made at least 15 years ago in Canada, USA, Singapore and I believe it is the same in Australia, but I am not sure. The distinction between equal ratios and equal fractions had to be made since 1 out of 2 is the "same as" 4 out of 8 has two meanings in real life applications:

A: As equal ratio (which leads to the concept of proportionality) it means that the numerator is always twice the denominator. In other words the amount being numerated (or taken, given whatever) is always twice the amount being denominated. This rule makes 1 out of 2 "the same as" 16 out of 32. In such a situation, equal ratios are generated by multiplying the numerator and the denominator (i.e. increasing them) by the same number. It leads up to the idea of proportionality.

B: However, Equal Fractions do exist in real life. A Fraction CAN indeed be perfectly Equal to another Fraction i.e. it can represent exactly the SAME quantity. The amounts in equal fractions CAN remain UNCHANGED. This is not possible to do if you multiply the amount being numerated and denominated by the same number. Because by doing so you are INCREASING the quantity (permissible in the rule of "equivalence" as you correctly point out).

I can give Anne 1 out of 2 apples. I can give Joe 16 out of 32 apples. I gave them apples in the same ratio: Half. But I did NOT give the SAME amounts. Anne gets just 1 apple. Joe gets 16! Each received DIFFERENT amounts.

However I CAN give them the same amounts and represent that as an Equal Fraction:

I can do that by SPLITTING the numerator and the denominator INTO SMALLER EQUAL PARTS to maintain the sameness of quantity. Splitting into smaller parts is a Division function, not multiplication. 1 Whole "splits" into "2 halves" if we DIVIDE it by half. It doesn't, of we multiply a whole by 2.

As far as I know, in the UK, schools and text-books have adopted "Equal Fractions" as a norm. The word "equivalent" is no more in use. Or maybe both are in use. In which case there are even more pressing reasons to seek clarity on this. Perhaps the UK Curriculum has not been updated? After all it's not written in stone.

If you google "equal fractions" the correct definition is everywhere to be seen. BUT the conversion (by multiplication) to Equal fractions is following the older tradition of Equivalence, which is one of Ratios (Proportionality) and not of sameness in quantity as currently defined.

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