Well, if percentages are just a particular type of fraction, why do we need them? Why can’t we just continue using fractions?
Answer
Because fractions with different denominators cannot be compared at a glance, while percentages always share the denominator 100.
Take the book's own example — sugar makes up 9/34 of Variety 1 and 13/45 of Variety 2.
9/34 × 100 = 26.47%
13/45 × 100 = 28.88%
So Variety 2 is the more sugary one.
Why it happens: To compare 9/34 with 13/45 as fractions you must first bring them to a common denominator — 34 × 45 = 1530 — and compare 405/1530 with 442/1530. A percentage does that same job once and for all by fixing the common denominator at 100 in advance. That is the whole point: percentages are fractions already prepared for comparison.
Q2.
If we want to have the same denominator, why choose 100 in particular? Why not 10, 50, 1000, or 43? Think.
Answer
Any denominator would work in principle. 100 is chosen because it balances two things a comparison needs — fine enough detail and easy mental handling.
It fits our number system. Our numerals are base ten, so 10, 100 and 1000 turn straight into decimals: 31% = 31/100 = 0.31. Moving between fraction, decimal and percentage costs nothing.
Per 10 is too coarse. 9/34 would be 2.647 “per decem” — you need decimals before you have even started.
Per 1000 is too heavy. 9/34 becomes 264.7 per mille — accurate, but hard to picture.
43 is worse than useless. Nothing in our notation makes 43 easy to divide by or to imagine.
Why it happens: A whole number out of 100 already carries two-digit accuracy, which is enough for marks, discounts, taxes and shares of a population — and 100 is small enough that “37 out of 100” is a picture you can hold in your head. Larger bases are used where finer detail matters: rates of disease are quoted per lakh precisely because the numbers per 100 would all round to 0.