Equivalent ratios

Learning Objectives Define what a ratio is and what makes two ratios equivalent. Identify if two given ratios are equivalent using various methods. Generate equivalent ratios by scaling up (multiplication). Generate equivalent ratios by scaling down (division) to simplify. Apply the concept of equivalent ratios to solve real-world problems. Express ratios in their simplest form. Have you ever followed a recipe and needed to double it, or cut it in half? 🧑‍🍳 That's exactly when you use equivalent ratios without even realizing it! In this lesson, we'll explore what equivalent ratios are and how they represent the same relationship between quantities, even if the numbers look different. Understanding equivalent ratios is crucial for solving problems involving scali...

TermDefinitionExample RatioA ratio is a comparison of two quantities by division. It can be written as a:b, a/b, or 'a to b'.If there are 3 apples and 5 oranges, the ratio of apples to oranges is 3:5. Equivalent RatiosEquivalent ratios are ratios that express the same relationship between two quantities. They look different but have the same value when simplified.The ratio 1:2 is equivalent to 2:4 because both simplify to 1:2. Simplest Form of a RatioA ratio is in its simplest form when its terms (the numbers in the ratio) have no common factors other than 1. It's like simplifying a fraction.The ratio 6:9 simplifies to 2:3, which is its simplest form. Scaling UpScaling up a ratio means multiplying both terms of the ratio by the same non-zero number to get an equivalent rati...

Generating Equivalent Ratios (Multiplication) $a:b = (a \times k) : (b \times k)$ To find an equivalent ratio, multiply both terms of the original ratio by the same non-zero number ($k$). This is called scaling up. Generating Equivalent Ratios (Division/Simplifying) $a:b = (a \div k) : (b \div k)$ To find an equivalent ratio or simplify a ratio, divide both terms of the original ratio by the same non-zero common factor ($k$). This is called scaling down. To find the simplest form, divide by the Greatest Common Factor (GCF). Checking Equivalence using Cross-Products If $a:b$ and $c:d$ are equivalent ratios, then $a \times d = b \times c$. This rule, often used for proportions, states that if two ratios are equivalent, the product of the 'outer' terms (extrem...