The FDP trio

To find 50% of something, you can multiply by ½. Could you multiply by 0.5 instead? Of course: 50% = 50/100 = ½ = 0.5. Every percentage has a twin fraction and a twin decimal. Call them the FDP trio (fraction, decimal, percentage).

Whichever is most convenient for the numbers in front of you is the right one to use.

Zubin needs 80% of 75 marks for an A grade. Three routes, same answer:

• fraction: (80/100) × 75 = (4/5) × 75 = 60;
• decimal: 0.8 × 75 = 60;
• proportion: out of 100 he needs 80, so out of 75 he needs (75 × 80)/100 = 60.

Ratios convert too. For millet kanji the ratio of millet to water is 2 : 7. Careful: that's millet to water, not millet to mixture. The mixture is 2 + 7 = 9 parts, so millet to mixture is 2 : 9.

That makes millet 2/9 of the mixture. Estimate before calculating: half of 9 is 4.5, so 2/9 is clearly under 50%; half of 4.5 is 2.25, so it's under 25%; and 20% of 9 is 1.8, so 2/9 is somewhere between 20% and 25%.

Now calculate: (2/9) × 100 = 22.22%. Water is 100 − 22.22 = 77.78%. And 500 mL of mixture holds 5 × 22.22 = 111.1 mL of millet. The estimate was right, which is the point of making it.

One more. A cyclist has done 40% of the Delhi–Agra ride, covering 92 km. How much is left? If 40% is 92 km then 20% is 46 km, so the remaining 60% is 92 + 46 = 138 km. Or solve 40/100 = 92/d for the whole distance, d = 230 km, and subtract: 230 − 92 = 138 km.

Two habits worth keeping from this section: estimate before you calculate, and draw a rough bar (16% of something, for instance, is 4 boxes out of a bar of 25). Both catch mistakes before they happen.