Keresztmultiplikációt

Keresztmultiplikációt, often translated as cross-multiplication, is a method used to solve proportions or equations involving fractions. It is a fundamental technique in algebra and arithmetic.

The principle of cross-multiplication is based on the property of equality. If two ratios are equal, such as a/b = c/d, then the product of the numerator of the first ratio and the denominator of the second ratio must be equal to the product of the denominator of the first ratio and the numerator of the second ratio. Mathematically, this is expressed as a * d = b * c.

This method is particularly useful for solving for an unknown variable when it appears in a proportion. For example, if you have the equation x/5 = 3/10, you can use cross-multiplication to find x. Multiplying across gives 10x = 5 * 3, which simplifies to 10x = 15. Dividing both sides by 10 yields x = 1.5.

Cross-multiplication is also employed in various applications, including converting units, scaling recipes, and solving problems in geometry and physics where proportional relationships exist. Its simplicity and directness make it a widely used mathematical tool. It's important to ensure that the fractions being cross-multiplied are indeed equal for the method to yield a correct result.