Speed & Vedic Maths Tricks
23 real mental-maths shortcuts, each with the method, worked examples, the algebra that proves why it works — and a “try it” box plus a timed sprint so the trick actually sticks.
To multiply a two-digit number by 11, add its two digits and put the total in the middle: 45 × 11 becomes 4, (4+5), 5 = 495. Carry over when the total reaches 10 or more, so 78 × 11 becomes 7, (15), 8 = 858. This page explains 23 such shortcuts with the algebra behind every one.
All 23 tricks
A green tick appears once you get 3 right in the “try it” box.
Trick
Try it yourself
Questions of exactly this type, made fresh each time. Type the answer and press Enter.
Set up your sprint
Choose the tricks you want to practise and race the clock.
Your personal bests
Most correct answers in a sprint, saved on this device.
How the sprint works
- Questions are drawn at random from the tricks you ticked.
- Type with the keypad or your keyboard — a correct answer moves on at once.
- A wrong answer shows the right one for a moment, then carries on.
- At the end you see your speed in questions per minute and your accuracy.
Keyboard: 0–9 type · Enter check · Backspace delete · Esc stop
Time’s up!
Answers to look at again
Each one is shown with the trick’s working.
Prove it to yourself: before vs after
Do 10 questions the long way first (paper and pencil allowed, no trick). Then do 10 more using the trick. The clock will show you exactly how much the trick is worth.
Your result
Round 1 — the long way
Round 2 — with the trick
Tricks cheat sheet
All 23 shortcuts on one page — print it and stick it inside your maths notebook.
Speed & Vedic Maths — Cheat Sheet
23 mental-maths shortcuts · ClassHud Tools · classhud.com
Fast maths is understood, not memorised
Every shortcut on this page is ordinary algebra wearing a disguise. Once you can see the algebra you will never forget the trick — and you will know exactly when it applies and when it does not.
Read the method
Three or four short steps, with the exact numbers worked out beside them.
Check why it works
The algebra behind every trick, so it is a tool you understand, not magic.
Practise in the box
Fresh questions of exactly that type, with instant checking and full working.
Beat the clock
A 60-second or 2-minute sprint, and a before-vs-after test that proves the gain.
The one idea behind half the tricks
Almost every multiplication shortcut comes from one identity:
(B + x)(B + y) = B(B + x + y) + xy
Choose B as a round number (10, 100, 1000) and the hard multiplication becomes one easy multiplication by B plus a tiny product. That single line gives you squares near a base, products near a base, and the special case 43 × 47.
Difference of two squares
(m − d)(m + d) = m² − d²
Any two numbers can be written this way: m is their average and d is half their difference. 48 × 52 → m = 50, d = 2 → 2500 − 4 = 2496. It is quickest when the average is a round number.
Why digit sums catch mistakes
10 leaves remainder 1 when divided by 9, and so does 100, 1000 and every power of 10. That makes every number leave the same remainder as the sum of its digits.
So if the digit roots of your two factors multiply to a different digit root from your answer, the answer is certainly wrong. (A match is not a proof — swapping two digits keeps the same sum — but it catches most slips.)
Squares you should simply know
Every shortcut gets faster if these are automatic:
| n | n² | n | n² | n | n² |
|---|---|---|---|---|---|
| 11 | 121 | 16 | 256 | 21 | 441 |
| 12 | 144 | 17 | 289 | 22 | 484 |
| 13 | 169 | 18 | 324 | 23 | 529 |
| 14 | 196 | 19 | 361 | 24 | 576 |
| 15 | 225 | 20 | 400 | 25 | 625 |
When not to use a trick
A shortcut that does not fit wastes more time than long multiplication. Check the conditions first:
- The base method needs both numbers close to the same base — 87 × 34 is not a job for it.
- “Units adding to 10” needs the same tens digit as well.
- The unit-digit square-root method only works on a perfect square.
- When nothing fits, criss-cross multiplication always works — it is simply long multiplication written in one line.
Where these come from
The sixteen sutras of Vedic mathematics were set out by Bharati Krishna Tirthaji in his 1965 book. The two you will meet most are Nikhilam (“all from 9 and the last from 10”) and Urdhva-Tiryagbhyam (“vertically and crosswise”).
They are not a different mathematics — they are clever orderings of the same arithmetic, chosen so that the hard steps happen on small numbers.
Speed & Vedic Maths Tricks — your questions
What is the trick to multiply any number by 11?
For a two-digit number, add the two digits and drop the total between them: 45 × 11 gives 4, (4+5), 5 = 495. If the total is 10 or more, carry one to the left: 78 × 11 gives 7, (15), 8, which becomes 858. For longer numbers, add each neighbouring pair of digits working from the right.
How do I square a number ending in 5?
Take the digits before the 5, multiply them by the next whole number up, and write 25 after the answer. For 35², take 3 × 4 = 12, then write 25 to get 1225. For 85², take 8 × 9 = 72 to get 7225. It works because (10a + 5)² = 100a(a + 1) + 25.
What is the one idea behind most Vedic multiplication tricks?
Almost every multiplication shortcut comes from the identity (B + x)(B + y) = B(B + x + y) + xy. Choose B as a round number such as 10, 100 or 1000 and a hard multiplication becomes one easy multiplication by B plus a tiny product. That single line gives you squares near a base, products near a base and the special cases.
How do I multiply numbers like 48 and 52 quickly?
Use the difference of two squares: (m − d)(m + d) = m² − d², where m is the average of the two numbers and d is half their difference. For 48 × 52, m is 50 and d is 2, so the answer is 2500 − 4 = 2496. It is quickest whenever the average lands on a round number.
How does the digit-sum check catch mistakes?
Every power of 10 leaves remainder 1 when divided by 9, so a number leaves the same remainder as the sum of its digits. If the digit roots of your two factors do not multiply to the digit root of your answer, the answer is certainly wrong. A match is not a proof, since swapping two digits keeps the same sum, but it catches most slips.
Is Vedic maths actually faster than the normal method?
For the numbers a trick is designed for, yes — often two or three times faster. For other numbers it can be slower, because you spend time deciding whether the trick applies. The before-and-after test on this page times you doing ten questions the long way and ten with the trick, so you can see the real gain for yourself.
Which squares should I simply know by heart?
Every shortcut gets faster when the squares from 11 to 25 are automatic: 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576 and 625. Knowing these also lets you spot the difference-of-squares and near-a-base methods quickly during a timed paper.