SAT Math — Problem Solving & Data Analysis ✨

Lesson Chunk

Ratios, Proportions, and Percentages

Understanding ratios, proportions, and percentages is essential in mathematics, as these concepts allow us to compare different quantities and analyze relationships effectively. Let's start with ratios. A ratio is a way to express the relationship between two quantities. For example, if you have 3 cats and 5 dogs, you can express this relationship as a ratio of 3:5 or as a fraction 3/5. This means that for every 3 cats, there are 5 dogs. Next, we have proportions. A proportion is an equation that states that two ratios are equal. This can be written in the form a/b = c/d, where a and b are the first ratio, and c and d are the second ratio. To solve for unknowns in proportions, we often use a method called cross-multiplication. This means you multiply the numbers diagonally across the equal sign, leading to the equation ad = bc. This technique is very useful for finding missing values in proportional relationships. Now, let’s talk about percentages. The term 'percent' literally means 'per hundred.' This means that when we talk about percentages, we are referring to a part of a whole that is divided into 100 equal parts. For example, to find 15% of 200, you would multiply 200 by 0.15, which gives you 30. This tells you that 15% of 200 is 30. Additionally, understanding how to calculate percentage change is crucial. The formula for percentage change is ((new value - old value) / old value) × 100. For instance, if the price of an item increases from $40 to $50, you would calculate the percentage increase as follows: ((50 - 40) / 40) × 100, which results in a 25% increase. The SAT often includes multi-step problems involving percentages, so it’s vital to carefully identify the base quantity, which is the 'of' quantity in these problems. Mastering these concepts will not only help you on the SAT but also in real-life situations where you need to compare and analyze data effectively. Context recap: Understanding ratios, proportions, and percentages is essential in mathematics, as these concepts allow us to compare different quantities and analyze relationships effectively. Let's start with ratios. A ratio is a way to express the relationship between two quantities. For example, if you have 3 cats and 5 dogs, you can express this relationship as a ratio of 3:5 or as a fraction 3/5. Why this matters: Ratios, Proportions, and Percentages helps learners in Exam Prep connect ideas from SAT Prep Foundations to decisions they make during practice and assessment. Highlight tradeoffs, assumptions, and verification. Step-by-step approach: (1) define the goal in one sentence, (2) identify evidence that supports the goal, (3) explain how each piece of evidence changes your conclusion, and (4) verify the final answer against the original goal and constraints.