Speed Math Tricks — 15 Tricks for Faster Math

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:

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.