Ristvõrrandi

Ristvõrrandi, often translated as cross-multiplication, is a mathematical technique used to solve proportions or find an unknown value in an equation where two ratios are equal. It is a fundamental concept in arithmetic and algebra, particularly useful when dealing with fractions and their relationships.

The principle of ristvõrrandi is derived from the property of equality in proportions. If we have a proportion in the form a/b = c/d, then cross-multiplication states that ad = bc. This means that the product of the numerator of the first fraction and the denominator of the second fraction is equal to the product of the denominator of the first fraction and the numerator of the second fraction.

To apply ristvõrrandi, one multiplies the "outer" terms (numerators and opposite denominators) and sets them equal to the product of the "inner" terms (denominators and opposite numerators). If one of the values in the proportion is unknown, this equality allows us to isolate and solve for that unknown. For example, in the proportion x/5 = 3/10, cross-multiplication yields 10x = 5 * 3, which simplifies to 10x = 15. Dividing both sides by 10 gives x = 1.5. This method is widely used in various applications, including solving word problems involving rates, percentages, and scaling.