Fractions, percentages and ratios are the same idea
Schools teach fractions, percentages and ratios in three different chapters, which leaves most people believing they are three different skills. They are one skill in three notations — multiplicative comparison — plus a single genuine difference that causes nearly every error.
Two of them measure the same thing
A fraction and a percentage both compare a part to the whole. Three quarters is 3 ÷ 4 = 0.75 = 75%. "Per cent" only means "out of a hundred", so a percentage is a fraction with the denominator fixed at 100 so that any two can be compared at a glance. That is its entire advantage: 37/50 against 3/4 takes a moment; 74% against 75% takes none.
Decimals are the same number again, in the notation calculators use internally. Moving between the three is not a conversion in any deep sense — it is rewriting.
The one that is different
A ratio compares parts to each other, not to the whole. This is the trap, and it catches people constantly.
Mix concrete 3:4 and the first ingredient is not 75% of the mix. There are 3 + 4 = 7 parts in total, so it is 3/7 — about 42.86%. The fraction 3/4 and the ratio 3:4 look almost identical on the page and describe different quantities.
The fix is mechanical: to turn a ratio into a percentage, add the parts first, then divide each by that sum. To turn a percentage into a ratio, use the part and the remainder — 75% is the ratio 75:25, which simplifies to 3:1, not 3:4.
Why the same underlying idea
All three answer "how many times bigger". Scaling a recipe, converting a currency, applying a discount, splitting a bill, reading a map scale — every one is multiplying by a factor. Once you see that, the tools become interchangeable: a 3:4 mix scaled to 21 kg is the same operation as finding 42.86% of 21 kg, and both give 9 kg.
This is also why the fraction, percentage and ratio calculators sit together: they are three doors into one calculation, and which one you reach for depends only on how the problem was written down.
Percentage of, percentage change, percentage points
Three more phrases that get used interchangeably and should not be. Percentage of is multiplication: 20% of 60 is 12. Percentage change is the difference divided by the original value — and the choice of original matters, because a rise from 40 to 50 is +25% while the fall from 50 back to 40 is −20%. Increases and decreases of the same percentage never cancel out.
Percentage points is the one that is routinely reported wrongly. A rate moving from 4% to 5% has risen by one percentage point, but by 25 per cent. Both are true; only one of them sounds dramatic, which is why the wrong one gets printed.
A test that catches most mistakes
Say the sentence out loud with "of the whole" or "for every" in it. "Three quarters of the whole" — that is a fraction. "Three for every four" — that is a ratio, and there are seven of them altogether. If the sentence will not take either phrase comfortably, the problem is not the arithmetic, it is that you have not yet decided what is being compared to what.