Solve proportions and ratio problems instantly. Find missing values in proportions using cross multiplication and get step-by-step solutions for ratio equations.
A proportion is a mathematical statement that two ratios are equal. Written as a/b = c/d, it expresses that the ratio of a to b is the same as the ratio of c to d. Proportions are fundamental in mathematics, science, and everyday problem-solving, from cooking recipes to architectural scaling.
Cross multiplication is the primary method for solving proportions. If a/b = c/d, then a × d = b × c. This technique transforms the proportion into a simple equation that can be solved for any unknown variable, making it an essential tool in algebra and applied mathematics.
A ratio compares two quantities (like 3:4 or 3/4), while a proportion states that two ratios are equal (like 3/4 = 6/8). Ratios can be expressed as fractions, decimals, or using colon notation, and they represent the relative size or amount of different quantities.
Proportions appear everywhere: map scales, recipe adjustments, currency conversion, speed calculations, and percentage problems. Understanding proportions helps solve practical problems involving scaling, similarity, and direct variation relationships.
When one quantity increases, the other increases proportionally. Examples include distance and time at constant speed, or ingredients in recipes when scaling up or down.
When one quantity increases, the other decreases proportionally. Examples include speed and travel time for a fixed distance, or the number of workers and time to complete a job.
Involving multiple variables changing simultaneously. Used in complex real-world scenarios like calculating work rates with varying numbers of workers and different time periods.
You can also solve proportions by finding the scale factor (multiplier) between corresponding terms, or by converting ratios to decimals and comparing them directly.
Always label your variables clearly, check units for consistency, and verify your answer makes sense in the context of the problem. Practice with different types of proportion problems to build confidence.