Solve proportions (In Steps)

Learning Objectives Define ratio and proportion. Identify when two ratios form a proportion. Set up proportions correctly from word problems. Apply the cross-multiplication property to solve proportions. Solve for an unknown variable in a proportion. Check the solution to a proportion. Ever wondered how chefs scale recipes or how maps represent real distances? 🗺️ It's all thanks to proportions! In this lesson, you'll learn what proportions are and how to use a powerful tool called cross-multiplication to solve them. Understanding proportions will help you solve many real-world problems where quantities are related. Real-World Applications Scaling recipes for more or fewer servings Calculating distances on maps or blueprints Determining ingredient amounts f...

TermDefinitionExample RatioA comparison of two quantities by division. It can be written as a:b, a/b, or 'a to b'.The ratio of 3 apples to 5 bananas is 3:5 or 3/5. ProportionAn equation stating that two ratios are equivalent (equal).The equation 1/2 = 2/4 is a proportion because both ratios are equal to 0.5. Equivalent RatiosRatios that represent the same relationship or have the same value when simplified.The ratios 1/2 and 3/6 are equivalent because both simplify to 1/2. Cross-MultiplicationA method used to check if two ratios form a proportion or to solve for an unknown in a proportion. You multiply the numerator of one ratio by the denominator of the other.In the proportion 1/2 = 3/6, cross-multiplication gives 1 * 6 = 2 * 3, which simplifies to 6 = 6. VariableA symbol, usua...

Definition of a Proportion \frac{a}{b} = \frac{c}{d} This rule states that a proportion is an equation where two ratios, a/b and c/d, are equal. Here, b and d cannot be zero. Cross-Multiplication Property If \frac{a}{b} = \frac{c}{d}, then ad = bc This property is fundamental for solving proportions. It states that if two ratios are equal, then the product of the 'extremes' (a and d) is equal to the product of the 'means' (b and c). This allows you to convert a proportion into a simpler linear equation.