Technique guides · 技
Mental math techniques
In-depth guides to calculating in your head, with worked examples, common mistakes and practice problems. Read a guide, then train the technique in the dojo.
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How to Divide Large Numbers in Your Head
Six mental division techniques with worked examples: split the dividend, halve and halve again, think in multiplication, cancel zeros, split the divisor and divide by 5 or 25.
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Mental Addition with Big Numbers
Add large numbers in your head: left-to-right addition, rounding and compensation, friendly pairs, splitting and adding long lists. Worked examples and practice.
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Mental Subtraction Tricks
Subtract in your head without borrowing: count up, round and compensate, shift both numbers, subtract from 1 000 and work left to right. Worked examples and practice.
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Mental Multiplication of Large Numbers
Multiply big numbers in your head: split into parts, the 11 trick, times 5 and 25, squaring numbers ending in 5 and the difference of squares. Worked examples.
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Multiplying Decimals in Your Head
Multiply decimals mentally: ignore the point and place it afterwards, estimate first, use fractions like 0.5 and 0.25, and multiply by 0.1 or 0.01. Worked examples.
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Percentages in Your Head
Calculate percentages mentally: 10 % and 1 % building blocks, flip the percentage, fraction equivalents, percent increase and decrease, and turning fractions into percent.
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Derivatives in Your Head
Find derivatives mentally: the power rule, constants and sums, standard functions, the chain rule and the product rule, each with a worked example and quick checks.
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Modulo Made Simple
Understand modulo through clock arithmetic: remainders, last-digit tricks, divisibility rules for 3, 9 and 11, and reducing large numbers before you calculate.
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How to Solve Equations in Your Head
Five mental techniques for equations: work backwards, keep the balance, clear fractions, use the zero product rule and spot quadratic factors, all with worked examples.
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Powers and Square Roots in Your Head
Square numbers ending in 5, square numbers near a round number, estimate square roots, find exact roots of perfect squares and use the power laws, all in your head.
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Fractions and Simplifying in Your Head
Add, multiply, divide and simplify fractions mentally: find the common denominator, cross multiply, cancel before multiplying, flip and multiply, and convert to decimals.
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Integrals and Areas in Your Head
Mental integration: reverse the power rule, read integrals as areas of triangles and trapezoids, use symmetry for odd and even functions, and estimate definite integrals quickly.
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Order of Operations: Why Viral Math Puzzles Fool Everyone
Five rules that solve the viral puzzles flooding social media: powers first, multiply and divide before add and subtract, left to right for equal ranks, brackets, and the hidden bracket of the fraction bar.
Read guideLooking for shorter tricks? Browse the Secret Scrolls.