Percentages - SAT Math SAT Study Notes
Overview
Imagine you're sharing a pizza with friends. How do you make sure everyone gets a fair slice? Or maybe you're at a store, and they announce a big '50% off!' sale. How much money do you actually save? That's where percentages come in! They help us understand parts of a whole in a super easy, standardized way. Percentages are everywhere in real life: from calculating discounts and tips to understanding statistics in the news, like '70% of people prefer chocolate ice cream.' On the SAT, percentages are a big deal because they test your ability to think about numbers in different ways and solve practical problems. Mastering percentages means you'll be able to tackle word problems with confidence, understand financial math, and even impress your friends with your quick mental math skills when splitting a bill. It's a fundamental math tool that you'll use far beyond the SAT!
What Is This? (The Simple Version)
Think of a percentage like a special fraction where the bottom number (the denominator) is always 100. It's a way to show a part of a whole, but instead of saying 'half a pizza,' you say '50% of the pizza.' The word 'percent' literally means 'per hundred' or 'out of every hundred.'
Imagine you have 100 little squares in a grid. If you color in 25 of them, you've colored in 25% (read as 'twenty-five percent') of the squares. It's a universal language for comparing parts of different things. For example, if your friend ate 1/4 of a cake and you ate 25% of a cake, you both ate the same amount!
Key idea: Percentages are just fractions with a secret denominator of 100. So, 75% is the same as 75/100, which can be simplified to 3/4. And 100% means the whole thing, like eating the entire pizza!
Real-World Example
Let's say you want to buy a cool new video game that costs $40. The store announces a special sale: 20% off! How much money do you save, and what's the new price?
- Understand the discount: '20% off' means you save 20 out of every 100 dollars. Since the game is $40, we need to find 20% of $40.
- Convert percentage to a decimal: To do math with percentages, it's usually easiest to change them into a decimal (a number with a point, like 0.25). To do this, just divide the percentage by 100. So, 20% becomes 20 ÷ 100 = 0.20.
- Calculate the savings: Multiply the original price by the decimal. $40 * 0.20 = $8. This means you save $8!
- Find the new price: Subtract the savings from the original price. $40 - $8 = $32. So, the new price for your game is $32. Awesome!
How It Works (Step by Step)
Let's learn how to find a percentage of a number, like finding 15% of 60. 1. **Convert the percentage to a decimal:** Divide the percentage by 100. (Example: 15% becomes 0.15). 2. **Multiply the decimal by the number:** This gives you the 'part' you're looking for. (Example: 0.15 * 60). 3. **Cal...
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Key Concepts
- Percentage: A way to express a number as a fraction of 100, meaning 'per hundred'.
- Decimal: A number that includes a decimal point, used to represent fractions or percentages in calculations.
- Fraction: A way to represent a part of a whole, written as one number over another (e.g., 1/2).
- Original Amount: The starting value or base number before any change occurs.
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Exam Tips
- →Convert percentages to decimals (divide by 100) or fractions (put over 100 and simplify) before doing calculations; it's usually easier.
- →For percentage change problems, always divide by the **original amount** (the starting number) to find the correct percentage.
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