Round and correct
Definition · Level 13 · Interview mechanics
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Replace one factor by a nearby round number, multiply, then add or subtract the difference times the other factor.
Example
17 × 24 = 17 × 25 − 17 = 425 − 17 = 408.
Where Tradecraft teaches it
Level 13 · Interview mechanics, in the lesson “Mental math: products, squares and fractions”: Shortcuts for products, squares and percentages, and a fraction table: the two-step recall behind fast answers.
Related terms
- Difference of squares(a + b)(a − b) = a² − b²: a product of two numbers equally far from a round number becomes that round number squared, minus a small square.
- EighthsSteps of 12.5%: 1/8 = 12.5%, 3/8 = 37.5%, 5/8 = 62.5%, 7/8 = 87.5%.
- Near-100 product(100 − a)(100 − b) = 100 × (100 − a − b) + ab: take both shortfalls off 100 to get the hundreds, then add the product of the shortfalls.
- Ninths & eleventhsFor fractions below 1: over 9, the numerator repeats (4/9 = 0.444…); over 11, nine times the numerator repeats (3/11 = 0.2727…, 7/11 = 0.6363…).
- Percentages multiplySuccessive percentage changes combine by multiplying their factors, not by adding the percentages.
- Quick percentages10% is the number with its decimal point moved one place; 5% is half of that; 15% is both added.