Vedic maths tricks for kids: eight tricks for fast calculation with worked examples, the age for each one, and the practice that makes them stick

Vedic maths tricks for kids are worth teaching for one reason: a child who can multiply 43 by 11 in their head in two seconds starts to believe that numbers are on their side. That belief is worth more than the trick. This post gives eight tricks, each with a worked example, the age it suits, and the reason it works, because a trick without the reason is a magic act and a trick with the reason is mathematics. It ends with the ten-minute practice plan our students use. The tricks come from the sixteen sutras published by Bharati Krishna Tirthaji in 1965; where the two systems overlap, the Trachtenberg comparison shows the same sums done both ways.

Before any trick: the tables

Every trick below assumes the times tables to 12 are automatic, meaning the child says 7 × 8 = 56 without a pause. If that is not true yet, ten minutes a day for a term on the tables comes first. A trick learned on top of missing tables is the one thing in this post that does harm.

Trick 1: multiply by 11 (age 7 and up)

Write the two digits with their sum in the middle.

• 43 × 11: 4, then 4 + 3 = 7, then 3: 473.
• 62 × 11: 6, 8, 2: 682.
• When the sum is more than 9, carry: 78 × 11: 7, 7 + 8 = 15, 8 → write 5, carry 1 to the 7: 858.

Why it works: 11 = 10 + 1, so 43 × 11 = 430 + 43; the tens digit gets the sum of the neighbours.

Trick 2: square a number ending in 5 (age 8 and up)

Multiply the first digit by one more than itself, then write 25.

• 35²: 3 × 4 = 12, then 25: 1 225.
• 65²: 6 × 7 = 42, then 25: 4 225.
• 105²: 10 × 11 = 110, then 25: 11 025.

Why it works: (10a + 5)² = 100a(a + 1) + 25. Show a 10-year-old the algebra; it is the first time algebra looks useful.

Trick 3: multiply two numbers near 100 (age 9 and up)

Write how far each number is below 100. Subtract one number's deficit from the other number for the left part; multiply the deficits for the right part (two digits).

• 97 × 96: deficits 3 and 4. Left: 97 − 4 = 93. Right: 3 × 4 = 12. Answer 9 312.
• 94 × 98: deficits 6 and 2. Left: 94 − 2 = 92. Right: 6 × 2 = 12. Answer 9 212.
• 91 × 89: deficits 9 and 11. Left: 91 − 11 = 80. Right: 9 × 11 = 99. Answer 8 099.

Works the same for numbers just above 100 with surpluses added instead: 103 × 104: 103 + 4 = 107, 3 × 4 = 12, 10 712.

Why it works: (100 − a)(100 − b) = 100(100 − a − b) + ab.

Trick 4: vertically and crosswise for two-digit numbers (age 10 and up)

For 23 × 41: right column, cross, left column.

• Right: 3 × 1 = 3.
• Cross: 2 × 1 + 3 × 4 = 2 + 12 = 14, write 4, carry 1.
• Left: 2 × 4 = 8, plus the carry = 9.
• Answer: 943.

Try 34 × 52: right 4 × 2 = 8; cross 3 × 2 + 4 × 5 = 26, write 6 carry 2; left 3 × 5 = 15 + 2 = 17; answer 1 768.

Why it works: (10a + b)(10c + d) = 100ac + 10(ad + bc) + bd. This is long multiplication with the columns done in one pass, and a child who learns it alongside the school method sees they are the same thing.

Trick 5: doubling and halving (age 8 and up)

Halve one number and double the other until the sum is easy.

• 16 × 35 = 8 × 70 = 4 × 140 = 560.
• 25 × 24 = 50 × 12 = 100 × 6 = 600.
• 14 × 45 = 7 × 90 = 630.

Why it works: multiplication does not change when one factor is halved and the other doubled. This trick teaches number sense more than any other.

Trick 6: multiply by 5, 25 and 50 (age 8 and up)

• By 5: halve, then times 10. 48 × 5: 24 × 10 = 240. 37 × 5: 18.5 × 10 = 185.
• By 25: quarter, then times 100. 36 × 25: 9 × 100 = 900. 18 × 25: 4.5 × 100 = 450.
• By 50: halve, then times 100. 46 × 50: 23 × 100 = 2 300.

Why: 5 is 10 ÷ 2, 25 is 100 ÷ 4, 50 is 100 ÷ 2.

Trick 7: subtract from 1 000 (age 8 and up)

All from 9 and the last from 10.

• 1 000 − 357: 9 − 3 = 6, 9 − 5 = 4, 10 − 7 = 3: 643.
• 1 000 − 481: 5, 1, 9: 519.
• 10 000 − 2 736: 7, 2, 6, 4: 7 264.

Why: 1 000 = 999 + 1; subtracting from 999 never needs borrowing, and the extra 1 is added back to the last digit. This is the trick that ends borrowing mistakes in money change questions.

Trick 8: check the answer with digit sums (age 9 and up)

Add the digits of each number until one digit is left; the operation on the digit sums must match the digit sum of the answer.

• Check 23 × 41 = 943. Digit sums: 2 + 3 = 5; 4 + 1 = 5; 5 × 5 = 25 → 2 + 5 = 7. Answer: 9 + 4 + 3 = 16 → 1 + 6 = 7. Matches.
• Check 97 × 96 = 9 312. Sums: 16 → 7; 15 → 6; 7 × 6 = 42 → 6. Answer: 9 + 3 + 1 + 2 = 15 → 6. Matches.

Why it works: the digit sum is the remainder on dividing by 9, and remainders multiply. A mismatch means a mistake; a match means probably right (it misses errors that are multiples of 9, which is rare). Children who check with digit sums stop handing in wrong answers.

Which trick when

The ten-minute plan

One trick a week. Day one, the trick with the reason, five examples together. Days two to five, five sums a day with the trick, checked with digit sums, two minutes. Day six, the same five sums with the school method, to see they agree. Day seven, the child teaches the trick to a parent, which is where it becomes permanent. After eight weeks the child has eight tricks and, more importantly, a habit of looking at a sum before doing it.

What we do

In our maths classes the tricks are taught inside the school curriculum, at the point where they help, with the reason every time, and never in place of the method the school tests. If your child has seen the videos and wants the tricks, bring them to a free 30-minute class and we start with the one that fits the age.

Questions parents ask

See how we teach this, 1-on-1 online →