The mass of a crate of mangoes is `11 12/13` kilograms. The mass of a crate of pineapples is `11 11/12` kilograms. Which is heavier?

The usual way of comparing fractions is with a common denominator. However, in this case the common denominator is quite big.

There is a much easier way if we realise that both crates weight ALMOST 12 kg. They are both only 1 part away from 12 kg.

We know that the larger the number in the denominator, the smaller is the portion.

Therefore `1/13 <1/12`

The crate of mangoes is only `1/13 kg` less than 12 kg.
The crate of pineapples is `1/12kg` less than 12kg.

The crate of mangoes is therefore closer to 12 kg and heavier than the crate of pineapples.

Both numbers have 11 in them. So as we are just determining which is the greater value we only need to look at the fraction parts.

So the question is really saying: which of `12/13" and "11/12` is the greater value?

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The most straight forward way is to compare numerators (top numbers) after changing the denominators (bottom numbers) to be the same.

Multiplying by 1 does not change the value. However, you can change the way a fraction looks by multiplying by 1 in another form.

Consider case(1)`" "12/13xx1 " "->" "12/13xx12/12= 144/(12xx13)`

Consider case(2)`" "11/12xx1" "->" "11/12xx13/13=143/(12xx13)`

Just comparing numerators (top numbers) we observe that case(1) is the greater number.

So `11 12/13` is greater than `11 11/13`