OjasaLearn

🧙 The Wizard's Growing Gold Spell

Master percentage increase — grow prices, prices and recipes bigger using percentages, just like a real 11+ champion!

🧙 Welcome, young apprentice, to the highest tower of Maths Castle! Today the Maths Wizard will teach you one of the most useful spells in the whole kingdom: the **percentage increase** spell. Here's a surprising fact — nearly everything you buy has been made bigger by a percentage at some point. When a shop adds **VAT** (a tax) of 20%, when your savings grow with **interest** at the bank, when a football stadium reports that ticket sales rose by 15%, or when a video game's player numbers jump by 40% — all of these use percentage increase! Imagine you saved £100 in a magic vault, and each year it grew by 5%. After many years, it could grow into a small fortune, all thanks to this spell. Percentages are everywhere: in sports scores, phone battery levels, sale signs, and even the tip you leave at a restaurant. Learning to make numbers grow by a percentage means you will never be tricked by a clever shopkeeper again, and you'll fly through 11+ exam questions that leave others scratching their heads. So grab your wizard's hat, sharpen your pencil-wand, and let's learn the spell that turns small numbers into bigger ones. ⭐

So what exactly IS a **percentage increase**? A **percentage** simply means 'out of 100'. The little % sign is like a tiny label saying 'per hundred'. When we talk about a percentage increase, we mean making something **bigger** by a certain fraction of itself. Think of it like a balloon 🎈 — you start with a balloon of a certain size, and then you puff extra air into it. The extra puff is the increase. If you increase something by 100%, you double it — like blowing the balloon up to twice its size. If you increase by 50%, you add on half again — so £10 becomes £15. The tricky part is remembering that the increase is always worked out from the **original** amount, not from a random number. So 10% of £200 is different from 10% of £50. The bigger the starting number, the bigger the actual increase, even if the percentage looks the same. Picture two piggy banks: adding 10% to a full one gives more coins than adding 10% to an empty one. Once you see it as 'the original amount PLUS a slice on top', percentage increase becomes as easy as casting a friendly spell.

How does the spell actually **work**? There are two magical routes to the same answer. The **first route** is 'find and add'. You first find the **percentage of the original amount**, then you **add** it back on. For example, to increase £80 by 25%, you first find 25% of 80, which is 20, then add: 80 + 20 = £100. The **second route** is the wizard's favourite shortcut called the **multiplier method**. If you increase by 25%, the new amount is 100% + 25% = **125%** of the original. As a decimal, 125% is **1.25**. So you simply multiply: 80 × 1.25 = £100. Same answer, fewer steps! The key term here is the **multiplier**: for any increase, you add the percentage to 100 and turn it into a decimal. A 10% increase means multiply by **1.1**; a 20% increase means **1.2**; a 5% increase means **1.05**. Be careful with that last one — 5% is 1.05, NOT 1.5! The multiplier method is brilliant for exams because it works in one line and is perfect when you need to increase again and again, like money growing over several years.

Here is the exact **method** the Wizard wants you to follow every single time. **Step 1:** Find 10% of the original amount by dividing by 10. This is your handy building block. **Step 2:** Use that 10% to build the percentage you need — for example, 30% is three lots of 10%, and 5% is half of 10%. **Step 3:** Add your increase back onto the original amount. That's the 'find and add' route. If you prefer the shortcut, follow the **multiplier steps** instead: **Step 1:** Add your percentage to 100 (so a 15% increase gives 115). **Step 2:** Turn that number into a decimal by dividing by 100 (115 becomes 1.15). **Step 3:** Multiply the original amount by that decimal. Choose whichever route feels comfy — both are correct! In the exam, if the numbers are friendly, 'find and add' is safe and clear. If you must increase several times or the numbers are awkward, the multiplier method saves precious time. Always write down your working so you can check it, and always double-check whether the question wants the **final amount** or just the **size of the increase**.

Let's cast our first easy spell together. **Question: Increase £60 by 10%.** First, we find 10% of £60. To find 10%, we divide by 10: 60 ÷ 10 = **£6**. That £6 is our increase — the extra puff of air in the balloon. Now we add it back onto the original: 60 + 6 = **£66**. And that's our answer — £66! ⭐ Let's check it with the Wizard's shortcut to be sure. A 10% increase means a multiplier of 1.1 (because 100% + 10% = 110% = 1.1). So 60 × 1.1 = 66. The answers match perfectly, so we know we're right. Notice how quick and gentle this was: dividing by 10 is easy because you just move the digits along one place. A common wobble here is accidentally giving £6 as the final answer — but £6 is only the increase, not the new total. Always remember to add it back on! Picture the balloon: £6 was the extra air, but the whole balloon is now worth £66. Well done, apprentice — you've cast your first percentage increase spell successfully.

Now for a trickier, two-step spell. **Question: A jacket costs £40. In a sale the price first rises by 20%, then the shop adds another 5%. What is the final price?** Beware — this is a trap for hasty wizards who add 20% and 5% to get 25%! That does NOT work, because the second increase is worked out from the NEW price, not the original. Let's do it properly, one step at a time. **First increase:** 20% of £40 is 40 ÷ 10 × 2 = £8. New price: 40 + 8 = **£48**. **Second increase:** now we take 5% of £48, not £40. 10% of 48 is 4.80, so 5% is half of that: **£2.40**. Final price: 48 + 2.40 = **£50.40**. So the answer is £50.40. If you had wrongly added 25% to £40, you'd get £50 — close, but wrong, and that's exactly the tempting distractor the examiners love! The safe rule is: **each new increase starts from the most recent amount.** Using the multiplier method, you could write 40 × 1.2 × 1.05 = 48 × 1.05 = 50.40 — same answer, beautifully quick. Take your time and never merge two separate percentages into one.

Here's how this appears in a real **GL or CEM exam**. **Question: A train ticket costs £25. The price increases by 12%. What is the new price?** Options: **A) £3** **B) £28** **C) £28.50** **D) £280**. Let's work it out carefully. 10% of £25 is 25 ÷ 10 = £2.50. We need 12%, so we also need 2%, which is 25 ÷ 100 × 2 = £0.50. Add them: 12% = 2.50 + 0.50 = **£3**. That £3 is the increase. Now add it on: 25 + 3 = **£28.50**. So the correct answer is **C) £28.50**. ✅ Now let's see why the wrong options are tempting. **A) £3** is the size of the increase only — a pupil who forgets to add it back on picks this. **B) £28** comes from rounding 12% down to 10% (£2.50) and sloppily calling it £3 or £28 — a careless slip. **D) £280** comes from a decimal-point disaster, multiplying by 10 by mistake. Each wrong answer is a real mistake a rushing student makes, which is why you must slow down, find the increase, and always add it back onto the original. The examiners are testing whether you know the difference between the increase and the final total.

Finally, the Wizard's warnings — the **three most common mistakes** and how to defeat them. **Mistake 1: Giving the increase instead of the final amount.** This happens because you work so hard finding the percentage that you forget the last step. Fix: always ask yourself, 'Have I ADDED it back on?' The balloon must include its extra air! **Mistake 2: Adding two percentages together in multi-step questions.** Increasing by 20% then 10% is NOT a 30% increase, because the second increase grows from a bigger number. Fix: do each step separately, one after the other, using the new amount each time. **Mistake 3: Muddling the decimal multiplier.** Pupils write 1.5 for a 5% increase when it should be 1.05. Fix: remember 100% is always there first, so 100 + 5 = 105 = **1.05**. Say it aloud: 'one point zero five'. 🧙 The Wizard's #1 power tip for exam day: **always find 10% first by dividing by 10** — it's your golden building block. From 10% you can quickly make 5% (halve it), 20% (double it), or 1% (divide by 10 again). Build any percentage you need, add it on, and check with the multiplier. Do this and no percentage question can defeat you! 🏆

Common mistakes

Frequently asked questions

Why do we have to learn percentage increase?

Because it's everywhere in real life! Sale prices, VAT, bank savings, and even game scores all use it. Learning it means shops can never trick you. You're building a super-useful skill — well done! 🌟

What if I forget the multiplier trick?

No worries at all! Just use the 'find and add' method: find the percentage of the original amount, then add it on. Both routes give the same answer. Pick whichever feels comfy for you. 🧙

Why can't I just add 20% and 10% together?

Because the second increase grows from a bigger number, not the original. Always do each step separately, using the new amount each time. Take it slowly and you'll always be right! ⭐

How do I find 10% quickly?

Just divide the number by 10 — move each digit one place to the right. So 10% of £70 is £7. It's your golden building block for making any percentage. Easy magic! 🎯

What's the difference between the increase and the final amount?

The increase is the extra bit you add on. The final amount is the original plus that extra bit. Exams love testing this, so always ask: 'Have I added it back?' You've got this! 🏆

Why is a 5% increase 1.05 and not 1.5?

Because you always start with 100% (the whole amount). Add 5% to get 105%, which as a decimal is 1.05. Say it aloud: 'one point zero five'. Great question, apprentice! 🧠