Introduction to Ratios and Proportions
A ratio is a mathematical comparison of two or more numbers, representing their relative sizes. It is commonly written with a colon, such as \(A:B\), or as a fraction \(A/B\). Ratios are fundamental in everyday life: they describe recipe ingredients (e.g., 2 cups of flour to 1 cup of sugar), map scales (e.g., 1 inch to 10 miles), business profit shares, and financial asset allocations.
A proportion is an equation stating that two ratios are equal, written as \(A:B = C:D\) or \(\frac{A}{B} = \frac{C}{D}\). Solving a proportion involves finding a missing value when the other three are known. This is most commonly solved using cross-multiplication, where the product of the extremes equals the product of the means (\(A \cdot D = B \cdot C\)).
This calculator simplifies and solves ratios and proportions. By selecting between ratio simplification, proportion variable solving, or total partition dividing, the user can solve algebraic equations and view proportional distributions on a stacked bar chart.