Shortcuts, checks, and contest gems — each one with a worked example and the reason it works. Learn the trick, understand the trick, then use it with confidence.
✦ The Chen Math Academy Way — what makes this different
Other websites hand you a trick and move on. Here, every trick is taught the way Mr. Chen teaches: with literacy, precision, and accuracy; with attention to detail, dedication, and discipline; and with integrity. Students learn the shortcut and why it works, when it works, and how to check it — the high-level thinking that turns a trick into real problem-solving skill. That is why parents choose this academy over the rest.
Math literacy
Students understand what the numbers mean — not just memorize steps. A trick is only taught once the idea behind it is clear.
Precision
Every trick is shown with exact steps. No hand-waving, no “just trust it” — each move is stated and checked.
Accuracy
Every trick on this page is verified, and every trick comes with a way to check the answer. Being fast never excuses being wrong.
Attention to detail
The small cases matter: carries, edge cases, and exactly where a trick stops working are all spelled out.
Dedication
Tricks are practiced until they are automatic — not watched once and forgotten. Speed comes from repetition with understanding.
Discipline
Check every answer before moving on: digit sums, estimates, and last digits. Good habits are part of the lesson, not an afterthought.
Integrity
No gimmicks that only work sometimes. Every trick here states exactly when it works and when it does not.
High-level thinking
Tricks are taught as reasoning, not magic. Students learn why a shortcut works — so they can invent their own.
Lightning Multiplication
Multiply faster than a calculator, with pen and paper.
⚡ Multiply by 11
For a two-digit number ab: write a, then a + b, then b. Carry if a + b is 10 or more.
34 × 11: 3, then 3 + 4 = 7, then 4 → 374.
67 × 11: 6, then 6 + 7 = 13 — carry the 1: 6 + 1 = 7, then 3, then 7 → 737.
Why it works: 11n = 10n + n, so the middle digit is the sum of the two digits.
Answer: 34 × 11 = 374; 67 × 11 = 737
⚡ Squares ending in 5
Take the tens digit n, compute n(n + 1), then write 25 after it.
65²: 6 × 7 = 42, then 25 → 4225.
105²: 10 × 11 = 110, then 25 → 11025.
Why it works: (10n + 5)² = 100n(n + 1) + 25.
Answer: 65² = 4225; 105² = 11025
⚡ Difference of squares
If two numbers sit equally far from a round number m: (m − d)(m + d) = m² − d².
29 × 31: both are 1 away from 30, so 30² − 1² = 900 − 1.
48 × 52: both are 2 away from 50, so 50² − 2² = 2500 − 4.
Why it works: The cross terms cancel: (m − d)(m + d) = m² − d².
Answer: 29 × 31 = 899; 48 × 52 = 2496
⚡ Multiply by 5
Halve the number, then multiply by 10.
86 × 5: half of 86 is 43, times 10 is 430.
Works the other way too: 5 × 248 = 124 × 10 = 1240.
Why it works: Multiplying by 5 is the same as multiplying by 10 and dividing by 2.
Answer: 86 × 5 = 430
⚡ Numbers near 100
97 × 93: write both as distances from 100, then combine.