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Cheat Sheet
🔮 Squaring tricks
Ends-in-5²:
n = AB5 → (AB)(AB+1) then append 25
e.g. 35² → 3×4=12 →
1225
Near-anchor (d²):
d² = (d+x)(d−x) + x²
e.g. 43² → pick x=3 → 40×46 + 9 = 1840+9 =
1849
⚡ Multiply by 11
2-digit AB×11:
A _ B, middle = A+B
e.g. 45×11 → 4_(4+5)_5 =
495
If sum ≥ 10, carry into left digit.
⚡ Double & Halve
Keep halving one factor, doubling the other
until one becomes a round number.
e.g. 35×12 → 70×6 → 140×3 =
420
⚡ Anchor Factoring
Break one number into easy factors.
e.g. 16×25 → 4×4×25 → 4×100 =
400
e.g. 18×15 → 18×(30÷2) → 540÷2 =
270
🧮 Rule of 72
Years to double = 72 ÷ annual return %
8% → 72÷8 =
9 years
6% → 72÷6 =
12 years
🧮 Salary decoder
Annual ÷ 2000 = hourly (40hr/50wk)
$60k ÷ 2000 =
$30/hr
Hourly × 2000 = annual
🧮 Tip shortcuts
10%:
move decimal left
15%:
10% + half of 10%
20%:
10% × 2
e.g. $84 → 10%=$8.40 → 15%=$12.60
⚡ Give & Take subtraction
Round the subtrahend to nearest 10,
then compensate.
84−39 → 84−40+1 =
45
73−28 → 73−30+2 =
45
⚡ Left-to-Right addition
Work from biggest place to smallest.
57+36: 57+30=87, 87+6 =
93
423+258: 400+200=600, 20+50=70,
3+8=11 →
681
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