Solve proportions

Learning Objectives Define a proportion and identify its parts (means and extremes). Set up a proportion correctly from a given word problem or scenario. Solve for an unknown variable in a proportion using the cross-product property. Solve proportions that include binomial expressions, requiring use of the distributive property. Apply proportional reasoning to solve real-world problems involving scaling, similar figures, and rates. Verify the solution of a proportion by substitution. Ever wonder how architects create tiny scale models of giant skyscrapers? They use the power of proportions to make sure every part is perfectly scaled! 🏙️ This tutorial will guide you through the process of solving proportions. You will learn how to set up and solve these powerful equations, w...

TermDefinitionExample RatioA comparison of two quantities by division. It can be written in three ways: a to b, a:b, or as a fraction a/b.The ratio of 3 apples to 5 oranges is 3:5 or 3/5. ProportionAn equation that states that two ratios are equivalent.The equation \frac{1}{2} = \frac{4}{8} is a proportion because both ratios represent the same value. Cross-ProductsIn a proportion \frac{a}{b} = \frac{c}{d}, the cross-products are the product of the numerator of the first ratio and the denominator of the second (a*d), and the product of the denominator of the first ratio and the numerator of the second (b*c).In the proportion \frac{2}{3} = \frac{4}{6}, the cross-products are 2 * 6 and 3 * 4. Both equal 12. ExtremesIn a proportion written as a:b = c:d, the extremes are the first and last te...

The Proportion Equation \frac{a}{b} = \frac{c}{d} This is the fundamental structure of a proportion, where two ratios are set equal to each other. The values b and d cannot be zero. The Cross-Product Property If \frac{a}{b} = \frac{c}{d}, then a \cdot d = b \cdot c This property is the primary method for solving proportions. It states that the product of the means equals the product of the extremes. This converts the proportion into a linear equation that can be solved for an unknown variable.