Cross multiplication rule

Cross multiplication rule is a rule used in geometry and algebra when working with equal ratios. It is used when two fractions or ratios are set equal to each o

Cross multiplication rule is a rule used in geometry and algebra when working with equal ratios. It is used when two fractions or ratios are set equal to each other. This rule helps to find unknown values by changing a proportion into a multiplication problem.[1] It is based on a simple idea: when two ratios are equal, the product of the means is equal to the product of the extremes. This statement is often used as a justification in geometry and algebra problems. It explains why cross multiplication works. In a proportion, there are two fractions that are equal. Each fraction has a numerator and a denominator. When it is used, the numbers are multiplied across the equal sign. This means one number from the top of one fraction is multiplied by the bottom number of the other fraction. The rule can be written in words as: the product of the means equals the product of the extremes.[2] The “means” are the two numbers in the middle of the proportion, and the “extremes” are the two numbers on the outside. When these products are equal, the proportion is true. It is often used in geometry problems involving similar triangles. It is also used when working with proportional relationships, such as those found in the Side Splitter Theorem. In these cases, ratios are set equal, and cross multiplication is used to solve for missing side lengths. For example, if two ratios are equal, like a/b = c/d,[3] then the rule says that a × d = b × c.[2] This shows how the values are connected through multiplication. This method helps find missing values when one part of the proportion is unknown.[2] It is important because it turns a ratio problem into a multiplication problem, which is easier to solve. It is used in many geometry situations where proportions appear, especially when comparing lengths of sides in triangles.

References

  1. ↑ "CK12-Foundation". flexbooks.ck12.org. Retrieved 2026-06-19.
  2. ↑ 2.0 2.1 2.2 "6.3: Introduction to Proportion". Mathematics LibreTexts. 2019-08-05. Retrieved 2026-06-19.
  3. ↑ https://www.hawaii.edu/hawaiicc/math/Courses/Math025/Notes/Lesson33.pdf

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