🎮 The Percentage Change Quest

Master how to calculate price rises, drops and discounts in just 15 minutes!

Paragraph 1 — 🧙‍♂️ The Maths Wizard greets you at the grand entrance of Maths Castle. Imagine you’ve saved up for the latest video game, but when you get to the shop the price tag says it’s on sale! Suddenly the cost drops from £80 to £68. How much have you really saved? Or think about your school trip: the bus ride was £12 yesterday, but today the driver says the fare is £15. How much more are you paying? These everyday moments are all about **percentage change**, a magic spell that tells you how big a jump or dip is compared to where you started. Knowing this helps you spot the best bargains, plan travel budgets, and even understand how fast your favourite sports team improves. The wizard will show you the secret formula, and by the end you’ll be able to whisper the answer before anyone else even finishes their shopping list. 🌟

Paragraph 2 — **What is percentage change?** It is the amount something grows or shrinks, expressed as a part of 100 of the original amount. Think of the original price as a whole pizza. If the pizza shrinks, the missing slice shows how much you’ve lost. If it grows, the extra slice shows your gain. In maths language, we write it as a **percentage** because we compare the change to a base of 100. For example, if a bike’s price goes from £200 to £250, the increase is £50. That £50 is compared to the original £200, giving a change of 25 %. This tells you the price grew by a quarter of its original size. The concept works the same whether the number gets bigger, smaller, or even flips sign – a negative percentage means a drop. 📉

Paragraph 3 — **How does it work?** The wizard’s formula is simple: **% change = (new value − original value) ÷ original value × 100**. First, find the difference between the new amount and the old amount. Then, divide that difference by the original amount to see what fraction of the original the change represents. Finally, multiply by 100 to turn that fraction into a percentage. Let’s try it with a real‑world case: a concert ticket costs £45 now, but last year it was £36. Difference = £45 − £36 = £9. Fraction of original = £9 ÷ £36 = 0.25. Multiply by 100 → 25 %. So the ticket price increased by **25 %**. Each step uses basic operations you already know, and the wizard’s bolded terms remind you what to do at each stage.

Paragraph 4 — **The Method** you can follow every time: 1️⃣ **Find the difference** – subtract the original amount from the new amount. (New − Original) → this tells you how much has changed. 2️⃣ **Divide by the original** – put the difference over the original amount to get a decimal fraction. 3️⃣ **Convert to a percentage** – multiply the fraction by 100 and add the % sign. If the result is negative, the change is a decrease; if it’s positive, it’s an increase. Remember to keep the order of subtraction correct – swapping the numbers would flip the sign and give the opposite answer! ✅

Paragraph 5 — **Simple worked example** – A school uniform costs £80, but today it’s on sale for £60. How much percent cheaper is the sale price? Step 1: Difference = £60 − £80 = ‑£20 (a drop). Step 2: Divide by original: ‑£20 ÷ £80 = ‑0.25. Step 3: Multiply by 100 → ‑25 %. The negative sign tells us the price fell by **25 %**. If we only need the size of the discount, we can drop the sign and say “a 25 % discount”. This example shows why it’s important to subtract the new price from the original (not the other way round) and why a negative result signals a decrease. 🎉

Paragraph 6 — **Medium worked example** – You want a new board game that costs £60. The shop offers a 15 % discount, then adds 20 % VAT to the reduced price. First, find the discount: 15 % of £60 = 0.15 × £60 = £9. New price after discount = £60 ‑ £9 = £51. Next, calculate VAT: 20 % of £51 = 0.20 × £51 = £10.20. Final price = £51 + £10.20 = £61.20. To see the overall percentage change from the original £60 to £61.20, use the formula: Difference = £61.20 ‑ £60 = £1.20. Divide by original: £1.20 ÷ £60 = 0.02. Multiply by 100 → **2 % increase**. Even though you got a discount, the VAT pushed the price slightly higher than the original. This two‑step process is common in real shopping, so keep each part tidy and check your work at the end.

Paragraph 7 — **Exam‑level example** – *GL Assessment, Year 6, Question 12*: "A laptop’s price fell from £500 to £425. What was the percentage decrease?" A) 12 % B) 13 % C) 15 % D) 17 % Solution: Difference = £425 ‑ £500 = ‑£75. Divide by original: ‑£75 ÷ £500 = ‑0.15. Multiply by 100 → ‑15 %. The negative sign shows a decrease, so the percentage decrease is **15 %**. The correct answer is **C**. Why the other options look tempting: - A (12 %) comes from mistakenly using £75 ÷ 625 (adding the difference to the new price) – a common slip. - B (13 %) might result from rounding 0.15 to 0.13 if you forget to move the decimal correctly. - D (17 %) could appear if you divide the discount (£75) by the new price (£425) instead of the original. Understanding the order of the formula prevents these traps. This question mirrors the exact steps you’ll use in the exam, so practise it until it feels automatic. 🌟

Paragraph 8 — **Common mistakes & power tips** – 1️⃣ *Reversing subtraction*: Subtracting the original from the new gives a positive number for a decrease. Always do **new − original** first. 2️⃣ *Dividing by the new value*: The denominator must be the original amount; using the new amount flips the percentage. 3️⃣ *Forgetting the sign*: A negative result means a drop, but many students drop the sign and claim a positive percentage. **Power tip** from the Maths Wizard: Write the three‑step formula on a sticky note and say it out loud – “difference, divide, multiply”. This verbal cue keeps the order clear, even under pressure. Keep practising, and you’ll turn every percentage change into a piece of cake! 🎂

Common mistakes

• Wrong: A shirt costs £30 and is reduced to £24. Claim: 20 % discount because 6 ÷ 30 = 0.2. — Right: Correct: Difference = £24 ‑ £30 = ‑£6. ÷ 30 = ‑0.2 → 20 % discount.. Make sure to subtract new from original, not the other way round.
• Wrong: A bike price rises from £120 to £150. Student says 25 % increase because 30 ÷ 120 = 0.25. — Right: Correct: Difference = £150 ‑ £120 = £30. ÷ 120 = 0.25 → 25 % increase.. Check the difference first; the percent comes from dividing by the original.
• Wrong: Discount 10 % on £80 gives £8 off, student writes final price £72 then adds 5 % tax on £80. — Right: Correct: £80 ‑ £8 = £72. Tax = 5 % of £72 = £3.60. Final price = £75.60.. Always apply tax to the reduced price, not the original.
• Wrong: A game costs £50, 20 % off, then 10 % VAT. Student calculates VAT on £50, not on £40. — Right: Correct: Discount = £10 → £40. VAT = 10 % of £40 = £4. Final = £44.. VAT follows the discount; use the new subtotal.
• Wrong: Exam question: Price falls from £200 to £150. Student answers 25 % because 50 ÷ 200 = 0.25, but the question asked for increase. — Right: Correct: It's a 25 % decrease, not increase. Answer: 25 % decrease.. Read the question carefully – it may ask for increase or decrease.

Frequently asked questions

Why do we need to use the original amount and not the new amount?

Because the original amount is the baseline we’re comparing to. Using it keeps the percentage meaningful. Keep practicing – you’ll remember! 🌟

What if the new price is the same as the old price?

Then the difference is zero, so the percentage change is 0 %. It means nothing has changed. Great question! 👍

Can a percentage change be more than 100 %?

Yes! If something more than doubles, the increase is over 100 %. For example, £30 to £70 is a 133 % rise. You’ve got this! 🚀

Why do we sometimes get a negative answer?

A negative sign tells you the value got smaller – a decrease or discount. Think of it as “downward” change. Well done! 😊

How can I quickly check my work in an exam?

Re‑run the steps: difference, divide, multiply. If the answer feels too big or small, double‑check the subtraction order. You’re on the right track! 🏆

What if I forget the formula during a test?

Remember the three‑word cue: **Difference, Divide, Multiply**. Whisper it to yourself and the steps come back. Keep believing in yourself! 🌈