Advanced Techniques Summary

Mental Math · Axiom Academy

Master the most powerful mental math strategies for lightning-fast calculations and complex problem solving. Cross-Multiplication: Ancient technique for two-digit multiplication. Split numbers into tens and units, then cross-multiply systematically. Base Method: Choose a convenient base (10, 100, 1000) close to your numbers. Work with differences from the base for faster calculation. Vertically and Crosswise: Universal method applicable to multiplication, division, and even algebraic operations. Duplex Method: Elegant squaring technique that works by doubling and adding products of digits systematically. Reciprocal Method: For dividing by numbers near powers of 10, use reciprocals. where you estimate . Factorization Trick: Break divisors into factors. Complement Division: For numbers close to 100, use complements to simplify the calculation process. Scaling Technique: Multiply both dividend and divisor by the same factor to create easier numbers. Numbers Ending in 5: For n5^2 , use n(n+1) then append 25. Example: Near 50 Method: Find difference from 50, square it, then adjust: 48^2 = 2500 - 200 + 4 = 2304 Difference of Squares: n^2 = (n-k)(n+k) + k^2 where k makes calculation easier. Digital Root Checking: Verify squares using sum of digits (modulo 9) for instant error detection. Near-Base Method: For numbers near 100: (100-a)(100-b) = 100(100-a-b) + ab Partition Strategy: Split larger numbers into manageable parts, multiply sections, then combine results efficiently.

This is the written version of the interactive lesson above. See the full Mental Math course.