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🧙 Maths Castle: Multiply Near Multiples of 10

Master mental multiplication by adjusting near‑10 numbers, turning 9×12 into 10×12−12 and similar shortcuts.

🧙 **Welcome to Maths Castle!** Imagine you’re at a bustling market buying 9 packs of stickers, each pack costs 14 gold coins. You could add 14 nine times, but the wizard knows a faster spell: think of 9 as **10 − 1**. Multiply 10 × 14 = 140, then subtract one group of 14 → 126 coins. That’s the power of **multiplying near multiples of 10** – a mental‑maths shortcut that turns a long addition into two tiny steps. In the 11+ exam you’ll meet questions like “What is 19 × 12?” or “Calculate 21 × 18 quickly.” Knowing this trick saves precious seconds, reduces careless errors, and lets you tackle harder problems (like scaling recipes or working out journey times) with confidence. The wizard’s secret is simply the distributive law, but dressed up as a friendly castle adventure so you’ll remember it forever. Ready to learn the spell? Grab your wand – the first gate awaits! ⭐

**What is it?** Multiplying near multiples of 10 means you replace a factor that is close to 10, 20, 30, … with that round number, then **adjust** by adding or subtracting the missing (or extra) groups. For example, 9 is one less than 10, 11 is one more than 10, 19 is one less than 20, and 21 is one more than 20. The **core idea**: use the easy multiplication with the round number, then correct the answer by the **difference** multiplied by the other factor. This works because of the distributive property: a × (b + c) = a × b + a × c. When you think of 9 as (10 − 1), you are really doing 9 × 14 = (10 − 1) × 14 = 10 × 14 − 1 × 14. The same logic applies to any near‑multiple – 29 × 6 = (30 − 1) × 6 = 30 × 6 − 6. Once you recognise the pattern, every “awkward” multiplication becomes a pair of simple sums. 🎯

**How does it work?** Let’s break the spell into its magical ingredients. Suppose you need **11 × 23**. Step 1: Spot the nearest round multiple – 11 is **10 + 1**. Step 2: Multiply the round part: 10 × 23 = **230** (easy, just add a zero). Step 3: Multiply the adjustment: the “+1” means **one extra group of 23**, so 1 × 23 = **23**. Step 4: Combine – because the adjustment was **+**, you **add** the extra group: 230 + 23 = **253**. If the factor were 9 (10 − 1), step 3 would be 1 × 23 = 23 and step 4 would **subtract** → 230 − 23 = 207. The same steps work for 19 × 12 (20 − 1), 31 × 7 (30 + 1), even 49 × 32 (50 − 1). The wizard’s rule: **Round → Multiply → Adjust → Combine**. Notice the adjustment is always **the difference × the other factor**, never just the difference alone. 🧠

**The Method – step‑by‑step** 1️⃣ **Identify** the factor that is close to a multiple of 10 (10, 20, 30…). 2️⃣ **Write** it as that multiple **plus** or **minus** a small number (the *difference*). 3️⃣ **Multiply** the round multiple by the other factor – this is usually a “add‑a‑zero” job. 4️⃣ **Multiply** the *difference* by the other factor – this gives the *adjustment amount*. 5️⃣ **Add** the adjustment if the original factor was **higher** than the round number, **subtract** if it was **lower**. 6️⃣ **Check** your answer with a quick estimate (e.g., 9 × 14 ≈ 10 × 14 = 140, so answer should be a bit less). Follow these six tiny steps every time and the castle gates will swing open for you! ✅

**Simple Worked Example – 9 × 14** 1️⃣ Identify: 9 is near **10** (difference = −1). 2️⃣ Write: 9 = 10 − 1. 3️⃣ Multiply round part: 10 × 14 = **140**. 4️⃣ Multiply difference: 1 × 14 = **14**. 5️⃣ Because 9 is **lower** than 10, **subtract** the adjustment: 140 − 14 = **126**. 6️⃣ Estimate check: 9 × 14 ≈ 10 × 14 = 140 → answer a little less → 126 ✔️. All steps are tiny, each doable in your head. Practice a few and you’ll cast the spell without writing anything down! 🎮

**Medium Worked Example – 19 × 12** (two‑step wrinkle) 1️⃣ Identify: 19 is near **20** (difference = −1). 2️⃣ Write: 19 = 20 − 1. 3️⃣ Round multiplication: 20 × 12 = **240** (double 12 → 24, add zero). 4️⃣ Adjustment: 1 × 12 = **12**. 5️⃣ 19 is **lower** than 20, so **subtract**: 240 − 12 = **228**. 6️⃣ Estimate: 20 × 12 = 240, so answer a bit less → 228 ✔️. **Where students pause:** they sometimes forget to multiply the difference by the *other* factor (they just subtract 1). Remember: the adjustment is **difference × other factor**, not just the difference. Keep the wizard’s chant: “Round, multiply, adjust, combine!” 🏆

**Exam‑Level Example (GL style)** *Question:* Which of the following equals **21 × 18**? A) 378 B) 368 C) 398 D) 358 *Wizard’s walkthrough:* - 21 = 20 + 1 (difference = +1). - 20 × 18 = **360**. - Adjustment: 1 × 18 = **18**. - 21 is higher → **add**: 360 + 18 = **378** → **Option A**. *Why the distractors tempt:* B) 368 = 360 + 8 (forgets to multiply the 1 by 18). C) 398 = 360 + 38 (adds 20 instead of 18). D) 358 = 360 − 2 (subtracts instead of adds). Spotting the correct adjustment pattern eliminates the traps instantly. 🎯

**Common Mistakes & Power Tips** 1️⃣ **Mistake:** *Adjusting by the difference only* (e.g., 9 × 14 → 140 − 1 = 139). *Why:* brain treats “−1” as “minus one” not “minus one group”. *Fix:* whisper “**times the other number**” every time you adjust. 2️⃣ **Mistake:** *Wrong rounding direction* (using 10 for 11, then subtracting). *Why:* confusing “near” with “nearest lower”. *Fix:* draw a tiny number line: 10 ← 11 → 20 – see that 11 is **above** 10. 3️⃣ **Mistake:** *Forgetting the sign* (adding when you should subtract). *Why:* rushing the final combine step. *Fix:* use a colour code – **green +** for higher, **red −** for lower. 🧙 **Wizard’s #1 Power Tip:** *Before the exam, practise 10 rapid‑fire near‑multiple questions in 60 seconds. Speed + accuracy = the golden key to the top grammar schools!* ⭐

Common mistakes

Frequently asked questions

Why do we need this trick if we can just use a calculator?

Exams like the 11+ don’t allow calculators, and mental speed builds number sense for harder maths later. 🌟

What if the factor is 2 away from the multiple, like 28?

Use 30 − 2: 30 × other − 2 × other. The same steps work for any small difference. 🎯

Can I use this for division too?

Not directly, but the same thinking (splitting numbers) helps with mental division shortcuts. 🧠

What if I forget whether to add or subtract?

Ask: is my factor higher or lower than the round multiple? Higher → add, lower → subtract. 🏆

Do I have to write every step down?

In the exam you’ll do it mentally; writing helps while you’re learning. Practice until it’s automatic! ⚡

Is there a limit to how big the numbers can be?

The method works for any size as long as one factor is close to a multiple of 10. Bigger numbers just mean bigger round‑multiple products. 🚀