Equivalent ratios

Learning Objectives Define what a ratio is and what equivalent ratios mean. Identify whether two given ratios are equivalent. Generate equivalent ratios by multiplying or dividing both terms by the same non-zero number. Simplify ratios to their simplest form. Solve real-world problems involving equivalent ratios. Explain the relationship between equivalent ratios and fractions. Have you ever followed a recipe and needed to make more or less of it? 🧑‍🍳 That's where equivalent ratios come in handy! In this lesson, you'll learn what equivalent ratios are and how to find them. Understanding equivalent ratios helps us compare quantities fairly and adjust recipes, scale maps, and even mix colors correctly. Real-World Applications Adjusting ingredients in a recipe...

TermDefinitionExample RatioA comparison of two quantities. 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 represent the same proportion.The ratio 1:2 is equivalent to 2:4 because both represent 'half'. Simplest Form (of a ratio)A ratio where the two numbers have no common factors other than 1. It's like a fraction in its lowest terms.The simplest form of the ratio 6:9 is 2:3, because both 6 and 9 can be divided by 3. Scaling Up (ratios)Creating an equivalent ratio by multiplying both parts of the ratio by the same whole number greater than 1.To scale...

Rule for Scaling Up Ratios To find an equivalent ratio by scaling up, multiply both parts of the ratio by the same non-zero number $n$. `\frac{a}{b} = \frac{a \times n}{b \times n}` Use this rule when you want to find a ratio with larger numbers that still represents the same relationship, for example, when increasing a recipe. Rule for Scaling Down Ratios To find an equivalent ratio by scaling down, divide both parts of the ratio by the same common non-zero factor $n$. `\frac{a}{b} = \frac{a \div n}{b \div n}` Use this rule to simplify a ratio to its simplest form or to find a ratio with smaller numbers that represents the same relationship. Rule for Checking Equivalence Two ratios are equivalent if they can both be simplified to the same simplest form, or if one ca...