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Tutorial articles on the Math Mental blog, with worked examples solved step by step.

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

    To find x% of a value, multiply the value by x/100. In your head, start from 10% (divide by 10) and 1% (divide by 100) and combine them: 15% = 10% + 5%. For increases and discounts, multiply by the factor: +20% is ×1.2 and −20% is ×0.8.

    • Tutorial
    • 2 min read

  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.

    • Tutorial
    • 3 min read

  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.

    • Tutorial
    • 2 min read

  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.

    • Tutorial
    • 2 min read

  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.

    • Tutorial
    • 2 min read

  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.

    • Tutorial
    • 2 min read

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