What a price becomes after a discount, and how much you save.
Multiply the original price by the fraction remaining: at 30% off that is 0.7. An 80 euro item costs 80 × 0.7 = 56 euro. You can also work out the discount and subtract it, but multiplying by the remainder is one step shorter and leaves less room for error.
Divide the difference by the original price and multiply by 100. From 80 euro to 56 euro that is (80 − 56) / 80 × 100 = 30%. The denominator is always the old price — dividing by the new one gives 42.9%, a different number answering a different question.
No. Twenty percent off followed by a further ten percent is not thirty percent but twenty-eight, because the second discount applies to the already reduced price: 0.8 × 0.9 = 0.72. The gap widens as the discounts grow, and shop promotions are often worded to exploit exactly that.
Divide by the fraction remaining rather than adding the same percentage back. If 56 euro is the price after 30% off, the original was 56 / 0.7 = 80 euro. Adding 30% to 56 euro would give 72.80 euro, which is wrong, because the percentage was taken from the larger number.