https://math.jhonatasfender.com/en/blog Math articles with step-by-step worked examples: percentages, the rule of three, interest, quadratic equations, fractions, LCM and GCD, logarithms and statistics. en Thu, 17 Sep 2026 00:00:00 GMT https://math.jhonatasfender.com/en/blog/how-to-calculate-percentages-in-your-head https://math.jhonatasfender.com/en/blog/how-to-calculate-percentages-in-your-head 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. Thu, 17 Sep 2026 00:00:00 GMT percentages mental math personal finance exam prep https://math.jhonatasfender.com/en/blog/rule-of-three-direct-inverse-and-compound https://math.jhonatasfender.com/en/blog/rule-of-three-direct-inverse-and-compound The rule of three solves problems with proportional quantities. If they are directly proportional, their ratio is constant; if inversely proportional, their product is constant. In a compound rule of three, the unknown equals the known value times one ratio per quantity, inverted when the relationship is inverse. Wed, 16 Sep 2026 00:00:00 GMT rule of three proportion ratio exam prep https://math.jhonatasfender.com/en/blog/simple-vs-compound-interest https://math.jhonatasfender.com/en/blog/simple-vs-compound-interest With simple interest, each period's interest is charged only on the initial principal: A = P(1 + r·t), linear growth. With compound interest, it is charged on the accumulated amount: A = P(1 + r)^t, exponential growth. At the same rate, compound interest yields more from the second period on. Tue, 15 Sep 2026 00:00:00 GMT interest personal finance percentages exam prep https://math.jhonatasfender.com/en/blog/how-to-solve-quadratic-equations https://math.jhonatasfender.com/en/blog/how-to-solve-quadratic-equations An equation ax² + bx + c = 0 with a ≠ 0 has roots x = (−b ± √Δ)/(2a), where Δ = b² − 4ac. If Δ > 0 there are two real roots, if Δ = 0 one double root, and if Δ < 0 no real roots. The roots add up to −b/a and multiply to c/a, which lets you find integer roots mentally. Mon, 14 Sep 2026 00:00:00 GMT quadratic equations quadratic formula algebra exam prep https://math.jhonatasfender.com/en/blog/fractions-add-subtract-multiply-divide https://math.jhonatasfender.com/en/blog/fractions-add-subtract-multiply-divide To add or subtract fractions, rewrite them over the same denominator (ideally the least common multiple) and combine the numerators. To multiply, multiply numerators together and denominators together. To divide, multiply the first fraction by the reciprocal of the second. Simplify at the end or, better, before multiplying. Sun, 13 Sep 2026 00:00:00 GMT fractions LCM arithmetic mental math https://math.jhonatasfender.com/en/blog/lcm-and-gcd-fast-methods https://math.jhonatasfender.com/en/blog/lcm-and-gcd-fast-methods The GCD is the greatest common divisor and the LCM the least positive common multiple. With prime factorization, the GCD takes the shared primes with the smallest exponent and the LCM takes every prime with the largest exponent. For two numbers, lcm(a, b) · gcd(a, b) = a · b, and the Euclidean algorithm finds the GCD without factoring. Sat, 12 Sep 2026 00:00:00 GMT LCM GCD prime numbers divisibility https://math.jhonatasfender.com/en/blog/logarithms-definition-and-properties https://math.jhonatasfender.com/en/blog/logarithms-definition-and-properties The logarithm of a in base b is the exponent x such that b^x = a, with b > 0, b ≠ 1 and a > 0. The key rules are log(xy) = log x + log y, log(x/y) = log x − log y, log(xⁿ) = n · log x and the change of base log_b a = log a / log b. Logarithms turn exponential equations into linear ones. Fri, 11 Sep 2026 00:00:00 GMT logarithms exponential functions algebra exam prep https://math.jhonatasfender.com/en/blog/mean-median-and-mode https://math.jhonatasfender.com/en/blog/mean-median-and-mode The mean adds the values and divides by how many there are; it is sensitive to outliers. The median is the middle value of the sorted data; it resists outliers and better describes skewed distributions such as salaries. The mode is the most frequent value and the only one that works for categorical data. Thu, 10 Sep 2026 00:00:00 GMT statistics mean median mode exam prep