Fast Mental Arithmetic: Core Techniques & Shortcuts
Competitive mental calculators do not compute like computers; they exploit arithmetic symmetry. Select a technique below to view the visual step-by-step lesson, or jump straight into the trainer to build lightning reflexes.
Multiplying by 5 (Append 0 & Halve)
To multiply by 5 quickly in your head, do not do long multiplication. Instead, use the fact that 5 = 10 / 2. Divide the number by 2 (halve it), then multiply by 10 (append 0 or shift decimal).
Multiplying by 11 (Split & Insert Sum)
To multiply any two-digit number by 11, separate the two digits and drop their sum into the space between them. If the sum is 10 or greater, simply carry 1 into the hundreds place.
Squaring Numbers Ending in 5 (N5²)
Any integer ending in 5 has a square that always ends in 25. The leading digits are found by taking the tens digit N and multiplying it by the next integer (N + 1).
Multiplying by 9 and 99 (Rounding & Compensation)
Numbers adjacent to round powers of ten (9, 99, 999) are easiest to calculate by overshooting to the clean power of ten and compensating backwards.
Fast Division by 5 (Double & Shift Decimal)
Dividing in your head is mentally taxing. Instead, invert the operation: double the number (multiply by 2) and divide by 10 (shift the decimal left by one place).
Divisibility (3, 9, 11) & Multiplication Sanity Check
To test divisibility or find remainders quickly, sum the digits (for 3 and 9) or alternate digit signs (for 11). To check large 3-digit multiplication A × B = C, multiply the remainders of A and B: they MUST equal the remainder of C! If remainders differ, the answer is guaranteed wrong in 5 seconds.
Practice Speed Math & IQ on Android
Download the official BoostIQ Android app to practice mental arithmetic and cognitive reasoning tests offline.
