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Math blog

Techniques explained carefully, with worked examples step by step, from mental math to college.

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  1. How to calculate percentages in your head: 10%, 1% and growth factors

    Calculate percentages mentally with 10%, 5% and 1%, handle increases and discounts with a multiplier, and chain successive changes, with worked examples.

    • 2 min read
    • Middle school

  2. The rule of three: direct, inverse and compound proportion with examples

    Tell whether quantities are directly or inversely proportional, set up a simple or compound rule of three without memorizing arrows, and check it with worked examples.

    • 2 min read
    • Entrance exams

  3. Simple vs. compound interest: the difference, formulas and examples

    See the difference between simple and compound interest, the formulas I = P·r·t and A = P(1 + r)^t, equivalent rates and worked examples step by step.

    • 2 min read
    • Entrance exams

  4. How to solve quadratic equations: the quadratic formula and sum and product

    Solve quadratic equations with the quadratic formula, the discriminant, sum and product of roots, and factoring for incomplete equations, step by step.

    • 1 min read
    • High school

  5. Fractions: how to add, subtract, multiply and divide, with examples

    Add and subtract fractions with a common denominator, multiply by cross-canceling and divide by the reciprocal. Mixed numbers and worked examples included.

    • 1 min read
    • Middle school

  6. LCM and GCD: fast methods (prime factorization, ladder and Euclid)

    Find the LCM and GCD by prime factorization, by the ladder method and with the Euclidean algorithm, use lcm · gcd = a · b and solve the classic word problems.

    • 2 min read
    • Middle school

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