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Cheat Sheet
🔮 Ends-in-5 Square
n²:
tens digit T → T×(T+1), append 25
35² → 3×4=12 →
1225
· 85² → 8×9=72 →
7225
🔮 Near-anchor squaring
d² = (d−x)(d+x) + x² (x = distance to nearest 10)
43² → x=3 → 40×46+9 = 1840+9 =
1849
🔮 ×11 sandwich
AB×11 → A_(A+B)_B (carry if A+B≥10)
45×11 → 4_9_5 =
495
· 78×11 → 8_5_8 =
858
🔮 Double & Halve
Halve one, double the other until round.
35×12 → 70×6 → 140×3 =
420
🔮 Anchor factoring
16×25 = 4×(4×25) = 4×100 =
400
8×125 =
1000
· 4×125 =
500
— memorise!
🧮 Rule of 72
Years to double = 72 ÷ annual % return
6%→12yr · 8%→9yr · 12%→6yr
🧮 Salary decoder
Hourly × 2000 ≈ annual (40hr/wk, 50wks)
$30/hr × 2000 =
$60k/yr
🧮 Tip shortcuts
10%:
move decimal ·
15%:
10%+5% ·
20%:
10%×2
$84 → 10%=$8.40 → 15%=
$12.60
⚡ Give & Take sub
Round subtrahend up, compensate after.
84−39 → 84−40+1 =
45
⚡ Left-to-right add
Work biggest place first.
57+36: 57+30=87, +6 =
93
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