Speed Math Tricks - SpeedMath

Number	Rule
2	Last digit is even (0, 2, 4, 6, 8).
3	Sum of digits is divisible by 3.
4	Number formed by last two digits is divisible by 4.
5	Last digit is 0 or 5.
6	Divisible by both 2 and 3.
7	Double the last digit and subtract from the remaining number; repeat. If result is divisible by 7, the original is too.
8	Number formed by last three digits is divisible by 8.
9	Sum of digits is divisible by 9.
10	Last digit is 0.

Number	Rule
11	Difference of (sum of digits in odd places) and (sum of digits in even places) is 0 or a multiple of 11.
12	Divisible by both 3 and 4.
13	Multiply last digit by 4 and add to remaining number; repeat until small. If result is divisible by 13, so is the original.
14	Divisible by both 2 and 7.
15	Divisible by both 3 and 5.
16	Number formed by last four digits is divisible by 16.
18	Divisible by both 2 and 9.
20	Last digit is 0 and tens digit is even, or last two digits form a multiple of 20.

Type	Vedic shortcut
Multiply by 11	For a two‑digit number ab, answer is a (a + b) b (carry if a + b ≥ 10). Example: 34 × 11 ⇒ 3 (3 + 4) 4 = 374.
Both near 10	If x and y are close to 10 with offsets a and b (10 + a, 10 + b or 10 − a, 10 − b): Left part = 10 + (a + b); right part = a·b. Example: 13 × 12 ⇒ (10 + 3, 10 + 2) ⇒ left 15, right 06 ⇒ 156.
Both near 100	If x = 100 − a and y = 100 − b, then x·y = (100 − a − b) \| (ab). Example: 97 × 94 ⇒ a = 3, b = 6 ⇒ 100 − 3 − 6 = 91 and 3×6 = 18 ⇒ 9118.
Square ending in 5	For n5, square is n(n + 1) \| 25. Example: 35² ⇒ 3×4 = 12 ⇒ 1225; 85² ⇒ 8×9 = 72 ⇒ 7225.
Vertical & crosswise (2‑digit)	For (a b) × (c d): 1) Units = b·d. 2) Middle = a·d + b·c. 3) Tens = a·c. Carry as needed to form final three‑digit answer.
Square of 2‑digit	For ab: 1) Units = b². 2) Middle = 2ab. 3) Left = a². Combine with carries. Example: 23² ⇒ left 4, middle 12, units 9 ⇒ 529.
Multiply by 5 / 25	×5: multiply by 10 then halve. ×25: divide by 4 (if divisible) and append "00".

Operation	Shortcut idea
Fast addition	Group to 10s or 100s: pair numbers whose last digits sum to 10. Example: 37 + 29 + 43 + 21 ⇒ (37 + 43) + (29 + 21) = 80 + 50 = 130.
Left‑to‑right addition	Add from most significant side: 468 + 357 ⇒ (400 + 300) = 700, (60 + 50) = 110, (8 + 7) = 15 ⇒ 700 + 110 + 15 = 825.
Subtraction using complements	To compute 1000 − N, subtract each digit from 9 and last digit from 10. Example: 1000 − 673 ⇒ (9−6)(9−7)(10−3) = 327.
Borrow‑free subtraction	When subtracting, add 10 to a smaller digit and increase subtrahend next digit by 1 instead of traditional borrowing, working left‑to‑right for fewer mistakes.
Division by 5	Multiply number by 2, then divide by 10 (move decimal one place left). Example: 345 ÷ 5 ⇒ 690 ÷ 10 = 69.
Division by 9 or 11 (estimate)	Use digit‑sum idea: if N is close to multiple of 9 or 11, replace numerator and divisor by nearby convenient pair, adjust mentally for the small difference.
Recurring decimals from simple fractions	Memorise key pairs: 1/3 = 0.333…, 2/3 = 0.666…, 1/7 ≈ 0.142857…, 1/9 = 0.111…, 1/11 ≈ 0.09, 0.18, 0.27 pattern etc., then scale up for bigger numerators.
Checking with 9‑sum	Replace each number by sum of its digits reduced modulo 9, perform the operation, and compare with 9‑sum of exact answer to quickly detect possible errors.