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🧙 The Shrinking Spell of Maths Castle

Master percentage decrease to conquer shop discounts, sale prices and shrinking numbers like a true Maths Wizard!

🧙 Welcome, young apprentice, to Maths Castle! I am the Maths Wizard, and today we cast one of the most powerful spells in the kingdom — the **Shrinking Spell**, also known as **percentage decrease**. Picture this: you spot your dream trainers in a shop window, priced at £60. Then a glowing sign appears: '30% OFF TODAY!' How much will you actually pay? Will you have enough pocket money? This is not just a school puzzle — it is real magic you will use for the rest of your life. Every sale sign, every clearance rack, every 'buy now and save' offer is percentage decrease in disguise. Shops use it constantly, and clever shoppers who understand it never get tricked into overpaying. Even grown-ups sometimes get muddled by discounts! By the end of this lesson, you will calculate savings faster than the shopkeeper can wrap your trainers. You will know exactly what the final price should be, so nobody can ever fool you. Percentage decrease also appears when populations shrink, when temperatures drop, and when your phone battery drains. It is everywhere. So sharpen your wand — I mean pencil — because today you become a master of making numbers shrink safely and correctly. Let the adventure begin! ⭐

So what exactly IS **percentage decrease**? Let me explain clearly. A **percentage** simply means 'out of 100'. When we say something decreases by 30%, we mean it loses 30 parts out of every 100 it started with. Think of a chocolate bar cut into 100 tiny squares. A 30% decrease means 30 squares vanish — poof! — and only 70 squares remain. The word **decrease** always means the number gets *smaller*, never bigger. This is the opposite of percentage increase, where numbers grow. Here is a memorable comparison: imagine a balloon slowly letting out air. A percentage decrease tells you exactly how much air escapes. The **original amount** is the full balloon before any air leaves. The **decrease** is the air that escapes. The **final amount** is the balloon after shrinking. In shops, the original amount is the first price, the decrease is the discount, and the final amount is what you pay at the till. Three ideas, always connected: original, decrease, final. Whenever you meet a percentage decrease question, quietly ask yourself: 'What was the starting number, and how much of it disappears?' Hold those two thoughts, and the rest becomes wonderfully simple. Keep this balloon in your mind — it will guide you.

Now, HOW does the Shrinking Spell actually work? There are two magical routes, and both give the exact same answer. **Route One — Find and Subtract.** First you find the **percentage of the number** that is being taken away, then you subtract it from the original. For example, to decrease £80 by 25%, you find 25% of 80, which is £20, then subtract: £80 − £20 = £60. **Route Two — The Multiplier Method** (my favourite for tricky questions). If something decreases by 25%, then 100% − 25% = 75% *remains*. So you simply find 75% of the original. 75% of £80 = 0.75 × 80 = £60. Same answer! The clever trick is understanding that when you take a percentage *away*, whatever is left is also a percentage. If 25% leaves, 75% stays. If 40% leaves, 60% stays. Always: **remaining % = 100% − decrease %**. To find any **percentage of a number**, remember the golden fact: 1% = the number divided by 100. So 1% of 80 = 0.8, and 25% = 25 × 0.8 = 20. Both routes are correct, but the multiplier method is faster and safer for two-step exam questions. Practise both, then pick your favourite. ⚡

Here is THE METHOD — follow these steps every single time, and you will never go wrong. **Step 1:** Read carefully and identify the **original amount** and the **decrease percentage**. Underline them if it helps. **Step 2:** Find 1% of the original by dividing it by 100. This is your secret building block. **Step 3:** Multiply that 1% value by the decrease percentage to find the **amount being taken away**. **Step 4:** Subtract that amount from the original to reveal the **final answer**. Let me show the multiplier shortcut too: instead of Steps 3 and 4, calculate 100 minus the decrease percentage to find the remaining percentage, then find *that* percentage of the original. For example, decreasing 200 by 15%: remaining = 100 − 15 = 85%. Then 85% of 200 = 0.85 × 200 = 170. Beautiful and quick! **Step 5 (never skip this):** Check your answer makes sense. A decrease should *always* give a number smaller than you started with. If your answer is bigger, something has gone wrong — go back. Also do a rough estimate: 15% is roughly a bit more than a tenth, so the answer should drop by a little more than 20. It dropped by 30. Close enough — sensible! ✅

Let's cast our first simple spell together, step by step. **Question: Decrease £40 by 10%.** Take a deep breath — this is gentle magic. Step 1: The original amount is £40, and the decrease is 10%. Step 2: Find 1% of £40 by dividing by 100: £40 ÷ 100 = £0.40. Step 3: Multiply by 10 to find 10%: £0.40 × 10 = £4. So £4 is being taken away. Step 4: Subtract from the original: £40 − £4 = **£36**. Done! You have paid £36 instead of £40. Now let me show the multiplier shortcut for the very same question, so you can compare. If 10% is removed, then 100% − 10% = 90% remains. Find 90% of £40: 0.90 × 40 = £36. Exactly the same answer — magic confirmed! ⭐ Notice how the final answer, £36, is *smaller* than the starting £40. That is your sign the Shrinking Spell worked correctly. A common wobble here is subtracting the 10 instead of the £4 — remember, the percentage must first be turned into an actual amount of money before you subtract. Always find the *value* of the percentage first. Well done — you have cast your first decrease spell perfectly!

Time for a trickier, two-step spell — the kind that makes many pupils pause. **Question: A £60 coat is reduced by 15% in a sale. What is the new price?** Step 1: Original = £60, decrease = 15%. Here is where students slow down — 15% feels awkward because it is not a neat number like 10% or 50%. Do not panic! Step 2: Find 1% of £60: 60 ÷ 100 = £0.60. Step 3: Multiply by 15: £0.60 × 15 = £9. So the discount is £9. Step 4: Subtract: £60 − £9 = **£51**. The coat now costs £51. Let me prove it with the multiplier method. Remaining percentage = 100 − 15 = 85%. Then 85% of £60 = 0.85 × 60 = £51. Match! The place where pupils commonly trip is thinking the *discount* is the answer. But £9 is only the money saved — the question asks for the *new price*, which is £51. Always reread the question: does it want the saving or the final price? Another wobble is working out 15% wrongly. A safe trick: 15% = 10% + 5%. 10% of 60 = £6, and 5% is half of that = £3, so 15% = £6 + £3 = £9. Same answer, extra confidence!

Now let's see how examiners test this in real GL and CEM papers — and how to beat their traps. **Exam Question: A £250 bicycle is reduced by 12% in a sale. What is the sale price?** Options: A) £220, B) £238, C) £30, D) £286. Let us work carefully. Find 1% of £250: 250 ÷ 100 = £2.50. Multiply by 12 for the discount: £2.50 × 12 = £30. Subtract from original: £250 − £30 = **£220**. The correct answer is **A) £220**. Now, why are the wrong options so tempting? Option C, £30, is the *discount itself* — the amount saved, not the price paid. Pupils who forget to subtract choose this. Option D, £286, comes from mistakenly *adding* the £30 instead of subtracting it — a classic slip when you rush and confuse increase with decrease. Option B, £238, is a sneaky one: it is what you'd get by wrongly taking away only 5% (£12.50) or by miscalculating 12%. Examiners design distractors around these exact errors. The multiplier check: 100 − 12 = 88%, and 0.88 × 250 = £220. Confirmed! 🎯 My advice: always do the multiplier method as a lightning-fast double-check. If both routes agree, mark your answer with total confidence and move on.

Let me warn you about the THREE traps that catch even clever apprentices. **Mistake 1: Giving the discount instead of the final price.** This happens when you stop after finding the percentage value and forget the last subtraction. *Fix:* After every calculation, whisper 'saving or price?' and reread the question. The final price is almost always smaller than the original. **Mistake 2: Adding instead of subtracting.** Under exam pressure, tired brains sometimes add the discount, turning a decrease into an increase. *Fix:* Remember the balloon — decrease means the number must SHRINK. If your answer grew, you added by mistake. **Mistake 3: Muddling the percentage of the wrong number.** In multi-step questions, pupils sometimes find the percentage of the *new* price instead of the original. *Fix:* Always take the percentage of the number stated in that step, and label each number clearly. 🧙 And now, my #1 power tip for exam day: **always use the multiplier method to check.** Turn the decrease into 'what remains' (100% minus the decrease), then multiply. If 'find and subtract' and 'multiply the remainder' give the same answer, you are certainly correct. Two spells agreeing means victory is guaranteed. Go forth, brave apprentice — the castle is yours! 🏆

Common mistakes

Frequently asked questions

Why do I need to learn percentage decrease?

Because sale signs are everywhere! Understanding decrease means you always know the real price and never get tricked into overpaying. It's a superpower for shopping — and for exams too. You've got this! ⭐

What if I forget the method during the test?

Just remember 'find it, then subtract it'. Find the percentage as an actual amount, then take it away from the original. If your answer is smaller, you're on the right track. Keep calm and shrink! 🧙

What's the difference between the discount and the final price?

The discount is the money you SAVE. The final price is what you actually PAY — the original minus the discount. Always reread the question to see which one it wants. You're thinking like a champion!

Why is the multiplier method faster?

Instead of two steps (find, then subtract), you do one! If 20% comes off, 80% stays, so just find 80% of the number straight away. It's a brilliant time-saver — and a great way to double-check. Try it!

Can I add two decreases together, like 20% and 10%?

No — that's a sneaky trap! Apply each decrease one at a time to the new amount. 20% then 10% is NOT 30% off. Watch out for this and you'll beat the hardest questions! 🏆

How do I work out awkward percentages like 15%?

Break them into friendly chunks! 15% = 10% + 5%. Find 10% (divide by 10), then halve it for 5%, and add them. Awkward numbers become easy this way. Clever, right? Keep practising!