Equivalent ratios

Learning Objectives Define what an equivalent ratio is. Identify if two given ratios are equivalent. Generate equivalent ratios by multiplying both terms by the same non-zero number. Generate equivalent ratios by dividing both terms by the same non-zero number. Express a ratio in its simplest form. Solve real-world problems involving equivalent ratios. Have you ever followed a recipe and needed to double it? 🍳 Or perhaps you've seen different sized maps, but they all show the same places? These situations often involve equivalent ratios! In this lesson, you'll discover 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 scaling recipes, compa...

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 apples and 2 bananas, the ratio of apples to bananas is 3:2. Equivalent RatiosRatios that express the same relationship between two quantities, even though the numbers themselves might be different. They simplify to the same basic ratio.The ratios 1:2 and 2:4 are equivalent because they both represent the same proportional relationship. Simplest Form (of a Ratio)A ratio is in its simplest form when the two quantities (terms) have no common factors other than 1. It's like simplifying a fraction.The ratio 6:9 in simplest form is 2:3, because both 6 and 9 can be divided by their greatest common factor, 3. Scaling Up RatiosCreating an equivalent ratio...

Generating Equivalent Ratios (Multiplication) If $a:b$ is a ratio, then $a \times c : b \times c$ is an equivalent ratio, where $c$ is any non-zero number. To find an equivalent ratio with larger numbers, multiply both parts of the ratio by the same non-zero number. This is called 'scaling up'. Generating Equivalent Ratios (Division) If $a:b$ is a ratio, then $a \div c : b \div c$ is an equivalent ratio, where $c$ is any common non-zero factor of $a$ and $b$. To find an equivalent ratio with smaller numbers or to simplify a ratio, divide both parts of the ratio by the same common non-zero factor. This is called 'scaling down'. Checking for Equivalence (Cross-Multiplication) Two ratios $a:b$ and $c:d$ are equivalent if and only if $a \times d = b \ti...