# Speed Math Tricks — 15 Tricks for Faster Math TL;DR Speed math tricks are arithmetic shortcuts that let your child compute mentally — multiplying near 100, squaring numbers ending in 5, finding percentages without long arithmetic. The 15 tricks below come with the algebra that powers each one, because a trick understood transfers to other math; a trick memorised does not. ## The Reframe — Tricks With Understanding, Not Stage Magic Speed math tricks have a reputation problem. Marketing for Vedic math and abacus programs promises that "in 6 weeks your child will multiply two-digit numbers in seconds" — and the promise is technically true. The problem is what it teaches. A child who memorises that 97×103=9991 via a trick — without understanding _why_ — has gained a parlour skill. The trick does not transfer to algebra, geometry, or word problems. It does not even transfer to similar-looking arithmetic. A child who learns the same trick _along with_ the algebra that powers it — (100−3)(100+3)=1002−9 — has gained two things: the trick and a piece of algebra they will use in Grade 8. The right frame for speed math tricks: each trick is a window into a piece of algebra. Teach the trick _and_ the window. The fluency comes either way; the understanding only comes when you teach both. ## How to Use the Tricks Below Each trick has three parts: the _trick_ (the shortcut), the _why_ (the algebra), and the _try it_ (a problem your child can practise). Skip the why and the trick becomes rote. Skip the trick and the why is abstract algebra without an entry point. One trick a week is plenty. Twelve weeks and your child has fifteen mental-math tools and an early understanding of algebraic identities — which is exactly the right shape for a Grade 5 or Grade 6 student. ## Multiplication Tricks (1–5) ### Trick 1 — Multiply by 11 (Two-Digit Numbers) **The trick.** For any two-digit number ab, ab×11=a(a+b)b. If a+b>9, carry the 1. _Examples._ 35×11=3(3+5)5=385, 72×11=7(7+2)2=792, 86×11=8(8+6)6=946 (carry the 1). **The why.** ab×11=ab×(10+1)=ab×10+ab. The first part shifts the digits one place left; adding ab to it gives a(a+b)b when there is no carry. **Try it.** 47×11, 93×11, 58×11. ### Trick 2 — Multiply Two Numbers Near 100 **The trick.** For two numbers near 100, say 97 and 96: compute the deficits (3 and 4), multiply them (12), and add 100 minus the deficit-sum to get the front digits. 97×96=(100−3)(100−4)=100−3−4=93, and 3×4=12. Answer: 9312. **The why.** (100−a)(100−b)=10000−100a−100b+ab=100⋅(100−a−b)+ab. **Try it.** 98×97, 99×95, 96×94. ### Trick 3 — Multiply by 5 **The trick.** Multiplying by 5 is "multiply by 10, then halve." 47×5=470/2=235. **The why.** 5=10/2, so n×5=n×10/2. **Try it.** 36×5, 84×5, 127×5. ### Trick 4 — Multiply by 9 with Fingers **The trick.** Hold up ten fingers. To compute 7×9, fold down the 7th finger. The fingers to the left of the fold (6) are the tens; the fingers to the right (3) are the ones. Answer: 63. **The why.** n×9=n×(10−1)=10n−n. **Try it.** 8×9, 4×9, 6×9. ### Trick 5 — Multiply by 25 **The trick.** Multiplying by 25 is "multiply by 100, then divide by 4." 36×25=3600/4=900. **The why.** 25=100/4. **Try it.** 48×25, 20×25, 13×25. ## Squaring Tricks (6–9) ### Trick 6 — Squaring Numbers Ending in 5 **The trick.** For any number n5, (n5)²=n×(n+1)⋅100+25. _Examples._ 35²=3×4⋅100+25=1225, 65²=6×7⋅100+25=4225, 85²=8×9⋅100+25=7225. **The why.** (10n+5)²=100n²+100n+25=100 n(n+1)+25. **Try it.** 45², 75², 95², 105². ### Trick 7 — Squaring Numbers Near 100 **The trick.** For a number near 100, say 97: (97)²=(97−3)⋅100+3²=9400+9=9409. For 103: (103)²=(103+3)⋅100+3²=10600+9=10609. **The why.** (100−a)²=10000−200a+a²=100⋅(100−2a)+a². **Try it.** 96², 104², 98². ### Trick 8 — Square Then Use Difference of Squares **The trick.** 97×103=(100−3)(100+3)=100²−9=9991. **The why.** (a−b)(a+b)=a²−b². **Try it.** 48×52, 95×105, 19×21. ### Trick 9 — Squaring with Nearby Round Number **The trick.** 47²: Round to 50. 50²=2500. The difference is 3, so subtract 2×50×3−3²=291. Answer: 2500−291=2209. **The why.** (a−b)²=a²−2ab+b². **Try it.** 48², 52², 39². ## Percentage Tricks (10–12) ### Trick 10 — 10% and 1% Anchors **The trick.** Find 10% of any number by moving the decimal one place left. Find 1% by moving it two places. Then add up. _Example._ 15% of 80? 10% is 8, 5% is 4 (half of 10%), total 12. **The why.** Percent means "per hundred." Moving the decimal divides by 100; 10% is dividing by 10. **Try it.** 15% of 60. 25% of 80. 35% of 200. ### Trick 11 — Reverse the Percentage **The trick.** _What is 8% of 25?_ Hard to do directly. Reverse it: _25% of 8._ That is 8/4=2. **The why.** Percent multiplication is commutative. **Try it.** 4% of 75. 12% of 50. 18% of 50. ### Trick 12 — Percent Increase / Decrease **The trick.** A 20% increase on 80 is 80 + 16 = 96. _Or:_ 80×1.20=96. **The why.** A 20% increase means new value = old × 1.20. **Try it.** 15% increase on 200. 30% decrease on 200. 12% tip on $45. ## Other Tricks (13–15) ### Trick 13 — Divide by 5 **The trick.** Dividing by 5 is "multiply by 2, then divide by 10." 235/5=235×2/10=47. **The why.** 5=10/2, so dividing by 5 is multiplying by 2/10. **Try it.** 145/5, 320/5, 87/5. ### Trick 14 — Add a Long Column with Cumulative Estimation **The trick.** Adding 87 + 53 + 41 + 67? Round each to nearest 10: 90 + 50 + 40 + 70 = 250. Adjust: −3+3+1−3=−2. Final: 250−2=248. **The why.** Sums distribute. **Try it.** 43+78+56+62. 91+29+47+33. ### Trick 15 — The Casting-Out-Nines Check **The trick.** To check 235×47=11045: add the digits of each number. 235→2+3+5=10→1, 47→4+7=11→2. 1×2=2. Now check the answer: 11045→1+1+0+4+5=11→2. **The why.** Casting out nines works because 10≡1(mod9). **Try it.** Use casting-out-nines to check 128×37. ## Where Most Parents Try the Wrong Order The instinct is to start with the _coolest_ trick. The right order is to start with the easiest trick (Multiply by 11), explain the why immediately, let the child try a few, then move to the next. ## Where Speed Tricks Go Sideways Four traps: - Memorising without understanding. - Using tricks where the standard method is faster. - Treating tricks as a substitute for fluency. - Showing off. ## When to Bring in Outside Help Speed math tricks are not a tutoring need by themselves. If your child is struggling with school math conceptually, speed tricks are not the right intervention — conceptual help is. ## How Bhanzu Approaches This At Bhanzu, speed math tricks are introduced from Grade 5 onwards as a _finishing layer_ on top of conceptual fluency. Trainers do not introduce speed tricks before the conceptual foundation is in place.