Ratios: word problems

Learning Objectives Identify and extract ratio information from word problems. Write ratios in different forms (a:b, a/b, a to b) based on word problem descriptions. Determine if two ratios are equivalent by scaling or simplifying. Solve for unknown quantities in ratio word problems using multiplication or division. Distinguish between part-to-part and part-to-whole ratios in context. Apply ratio concepts to solve real-world problems presented as word problems. Have you ever looked at a recipe and seen '2 cups of flour for every 1 cup of sugar'? 🍪 That's a ratio! It tells you how much of one thing there is compared to another. In this lesson, you'll learn how to read, understand, and solve word problems that involve ratios. Mastering ratios will help yo...

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. Term (of a Ratio)Each number in a ratio is called a term. For example, in the ratio 3:2, '3' is the first term and '2' is the second term.In the ratio 5 to 7, the terms are 5 and 7. Forms of RatiosRatios can be written in three ways: using a colon (a:b), as a fraction (a/b), or using the word 'to' (a to b).The ratio of 4 boys to 5 girls can be written as 4:5, 4/5, or 4 to 5. Equivalent RatiosRatios that represent the same comparison or relationship between quantities, even if the numbers are different. They are like equivalent fractions.The rati...

Writing Ratios from Word Problems If a word problem compares quantity 'A' to quantity 'B', the ratio should be written in that order: $A:B$, $A/B$, or $A \text{ to } B$. Always pay attention to the order of the quantities mentioned in the problem, as reversing them changes the meaning of the ratio. Finding Equivalent Ratios To find an equivalent ratio, multiply or divide both terms of the ratio by the same non-zero number. If $a:b$ is a ratio, then $k \cdot a : k \cdot b$ (where $k \neq 0$) is an equivalent ratio. This rule is crucial for scaling ratios up or down to solve for unknown quantities in word problems. It's similar to finding equivalent fractions. Solving for Unknowns in Ratio Problems Set up the given ratio and the ratio with the un...