Equivalent ratios: word problems

Learning Objectives Define what an equivalent ratio is. Identify ratios within word problems. Determine the scaling factor between two equivalent ratios. Use multiplication or division to find missing values in equivalent ratio word problems. Apply equivalent ratios to solve real-world scenarios presented as word problems. Explain their reasoning when solving equivalent ratio word problems. Have you ever followed a recipe and needed to make more or less of it? 🧑‍🍳 That's exactly when you use equivalent ratios without even realizing it! In this lesson, you'll learn how to understand and solve word problems that involve equivalent ratios. We'll explore how to scale ratios up or down to find missing information, which is a super useful skill for everyday life....

TermDefinitionExample RatioA comparison of two quantities by division. It shows how much of one thing there is compared to another.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. They look different but represent the same comparison.The ratio 1:2 is equivalent to 2:4 because both represent 'half'. Term (of a Ratio)Each number in a ratio is called a term. For example, in the ratio 3:5, 3 is the first term and 5 is the second term.In the ratio 4 to 7 (4:7), the terms are 4 and 7. Scaling UpMultiplying both terms of a ratio by the same number to get an equivalent ratio with larger terms.Scaling up 1:3 by multiplying by 2 gives 2:6. Scaling DownDividing both term...

Finding Equivalent Ratios by Multiplication $$a:b = (a \times k) : (b \times k)$$ To find an equivalent ratio, you can multiply both terms of the original ratio by the same non-zero number (the scaling factor, 'k'). This is useful for scaling up. Finding Equivalent Ratios by Division $$a:b = (a \div k) : (b \div k)$$ To find an equivalent ratio, you can divide both terms of the original ratio by the same non-zero number (the scaling factor, 'k'). This is useful for scaling down or simplifying ratios. Setting up a Proportion for Word Problems $$\frac{\text{Quantity 1A}}{\text{Quantity 1B}} = \frac{\text{Quantity 2A}}{\text{Quantity 2B}}$$ or $$A:B = C:D$$ When solving word problems, set up two ratios that are equivalent. Make sure the corresponding...