- Middle school🔢Arithmetic🧮
Powers of 2 to memorize (up to 1024)
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024… A short list that unlocks tons of mental math — and all of computing.
- Middle school🔢Arithmetic🧩
Find the GCD without a single division
Euclid's algorithm, mental version: subtract the small from the big until you get the same value. That's the GCD.
- Middle school🔢Arithmetic🔟
Divisibility by 3 and 9: add up the digits
A number is divisible by 3 (or 9) if the sum of its digits is. Mind-blowing test, works for all integers.
- Middle school🔢Arithmetic⚖️
Are two fractions equal? The cross-product decides
$\dfrac{a}{b} = \dfrac{c}{d}$ if and only if $ad = bc$. A foolproof test, no common denominator needed.
- Middle school🔢Arithmetic➕
Adding two fractions: the common denominator without hunting
$\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}$. A simple formula that skips the search for the least common multiple.
