Equivalent ratios: word problems

Learning Objectives Define and identify equivalent ratios. Set up ratios from real-world word problems. Use multiplication or division to find equivalent ratios. Set up and solve proportions to find unknown quantities in equivalent ratio word problems. Apply unit rates to solve equivalent ratio word problems. Check the reasonableness of their answers in the context of the word problem. Ever wondered how chefs adjust recipes for more guests, or how map scales help us navigate? 🗺️ It's all about equivalent ratios! In this lesson, you'll learn how to understand and solve word problems involving equivalent ratios. This skill is crucial for making fair comparisons, scaling recipes, and solving many everyday challenges where quantities are related proportionally. Real-...

TermDefinitionExample RatioA comparison of two quantities by division. It can be written as a:b, a/b, or 'a to b'.If there are 3 red apples and 2 green apples, the ratio of red to green apples is 3:2. Equivalent RatiosRatios that express the same relationship between two quantities, even if the numbers themselves are different. They simplify to the same basic ratio.The ratio 1:2 is equivalent to 2:4 and 5:10 because they all represent the same proportional relationship. Simplest Form (of a Ratio)A ratio is in simplest form when its terms (the numbers in the ratio) have no common factors other than 1.The ratio 6:9 in simplest form is 2:3 (dividing both by 3). ProportionAn equation that states that two ratios are equivalent.$rac{1}{2} = rac{2}{4}$ is a proportion. Unit RateA rat...

Finding Equivalent Ratios by Scaling To find an equivalent ratio, multiply or divide both quantities in the ratio by the same non-zero number $k$. $rac{a}{b} = rac{a \times k}{b \times k}$ or $rac{a}{b} = rac{a \div k}{b \div k}$ This rule allows you to create ratios that represent the same proportional relationship but with different absolute values. Use multiplication to 'scale up' and division to 'scale down' or simplify. Solving Proportions using Cross-Multiplication If two ratios are equivalent, then their cross products are equal. If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$. This is a powerful method to solve for an unknown quantity in a proportion. Set up the two equivalent ratios, then multiply the numerator of one by the denominator of...