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πŸ’‘ Tangyuan's Math Tips

Six mental-math tricks for two-digit multiplication. Every trick has conditions β€” when they don't match, fall back to splitting the number.

1. Split one number (the basic move)

Break any two-digit number into β€œtens + ones”, multiply step by step, then add. This is the foundation β€” every trick below is a special case of it.

24 Γ— 13 = 24 Γ— 10 + 24 Γ— 3 = 240 + 72 = 312

2. Same tens, units add to 10

When the tens digits match and the units add up to 10: multiply tens Γ— (tens + 1) for the front, units Γ— units for the back. Pad the back with a 0 if it's a single digit.

23 Γ— 27 β†’ front: 2 Γ— 3 = 6, back: 3 Γ— 7 = 21 β†’ 621
45 Γ— 45 β†’ front: 4 Γ— 5 = 20, back: 5 Γ— 5 = 25 β†’ 2025

3. Same units, tens add to 10

When the units match and the tens add up to 10: the front is tens Γ— tens + units, the back is units Γ— units (pad to two digits).

32 Γ— 72 β†’ front: 3 Γ— 7 + 2 = 23, back: 2 Γ— 2 = 04 β†’ 2304
41 Γ— 61 β†’ front: 4 Γ— 6 + 1 = 25, back: 1 Γ— 1 = 01 β†’ 2501

4. Near 100? Use a base number

Write numbers as β€œ(round Β± difference)” and expand. See 25, look for 4; see 5, look for 2.

98 Γ— 96 = (100βˆ’2)(100βˆ’6) = 10000 βˆ’ 800 + 12 = 9408
25 Γ— 24 = 25 Γ— 4 Γ— 6 = 100 Γ— 6 = 600

5. Multiplying by 11 or 99

Γ— 11: pull the two ends apart, add them for the middle (carry if needed). Γ— 99: multiply by 100, then subtract the number itself.

34 Γ— 11 β†’ 3 (3+4) 4 = 374
57 Γ— 11 β†’ 5 (12) 7 β†’ carry β†’ 627
23 Γ— 99 = 2300 βˆ’ 23 = 2277

6. Cross multiplication (for anything else)

The mental version of long multiplication: units Γ— units for the ones digit, cross-sum for the tens, tens Γ— tens for the top β€” watch the carries.

34 Γ— 56:
units 4Γ—6 = 24 β†’ write 4 carry 2
cross 3Γ—6 + 4Γ—5 = 38, +2 = 40 β†’ write 0 carry 4
tens 3Γ—5 = 15, +4 = 19 β†’ 1904

Want to try them? Practice with Tangyuan β†’