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Basic Math and Pre-Algebra - Percents

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    Study Guide Basic Math and Pre - Algebra – Percents 1. Applica Ɵ ons of Percents Percents are used everywhere — in shopping, money, grades, statistics, and more. In this lesson, you’ll learn the most common ways percents are used and how to solve these problems step by step. 1.1 Finding a Percent of a Number To find a percent of a number: 1. Change the percent to a decimal or fraction . 2. Multiply. 3. Remember: the word “of” means multiply . Example 1: What is 20% of 80? Using fractions: Using decimals: So, 20% of 80 is 16.

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    Study Guide Example 2: What is 15% of 50? Using fractions: Using decimals: So, 15% of 50 is 7.5. Example 3: What is ½% of 18? First, convert ½% to a fraction: Or using decimals: So, ½% of 18 is 0.09. Example 4: What is 70% of 20? So, 70% of 20 is 14.

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    Study Guide 1.2 What Percent Is One Number of Another? Now let’s reverse the question. Instead of finding a part, we find the percent . Division Method To find what percent one number is of another: 1. Divide the part by the whole. 2. Change the decimal to a percent. Example 4: 20 is what percent of 50? So, 20 is 40% of 50. Example 5: 27 is what percent of 90? So, 27 is 30% of 90. 1.3 Using the Equa Ɵ on Method Another way to solve percent problems is to turn the words into an equation. Here’s how: • “What” → use x • “Is” → use = • “Of” → use × • Change percent to decimal or fraction

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    Study Guide Example 6: 10 is what percent of 50? Write the equation: Divide both sides by 50: So, 10 is 20% of 50. Example 7: 15 is what percent of 60? So, 15 is 25% of 60. Finding the Whole from a Percent Sometimes in math, you know a percent of a number , but you don’t know the original number. Your job is to find the whole . Let’s learn how to do that step by step.

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    Study Guide Example 8: 15 is 50% of what number? Step 1: Turn the percent into a decimal. 50% = 0.50 Step 2: Write an equation. If 15 is 50% of a number, we can write: Here, x is the number we’re trying to find. Step 3: Solve the equation. Divide both sides by 0.50: [ Another way to think about it: 50% = 1/2 So: Dividing by 1/2 is the same as multiplying by 2: ࿨ ࿩ ࿪ Answer: 30 So, 15 is 50% of 30.

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    Study Guide Example 9: 20 is 40% of what number? Step 1: Convert the percent to a decimal. 40% = 0.40 Step 2: Write the equation. Step 3: Solve. Divide both sides by 0.40: ࿨ ࿩ ࿪ Answer: 50 So, 20 is 40% of 50. Quick Tip: The Shortcut “___ is ___% of what number?” You can use this formula: 1.4 Finding the Whole When You Know the Percent Sometimes you know the percent and the part, but not the whole. Example 10: 30 is 20% of what number? Write the equation:

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    Study Guide Divide both sides by 0.20: So, 30 is 20% of 150. Example 11: 40 is 80% of what number? So, 40 is 80% of 50. 1.5 The Propor Ɵ on (Is/Of) Method You can also use a proportion. This works for all three types of percent problems. Set it up like this: • The percent always goes over 100. • The number after “of” goes on the bottom. • The number next to “is” goes on the top. Example 12: 30 is what percent of 50? So, 30 is 60% of 50.

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    Study Guide Example 13: 40 is what percent of 200? So, 40 is 20% of 200. Example 14: 60 is 20% of what number? So, 60 is 20% of 300. Example 15: What number is 15% of 30? So, 4.5 is 15% of 30. 1.6 Percent Change (Increase or Decrease) To find percent change, use this formula:

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    Study Guide Example 16: What is the percent decrease from $500 to $400? Step 1: Find the change. Step 2: Divide by starting amount. Step 3: Convert to percent. So, there is a 20% decrease. Example 17 : Jon’s salary increases from $150 to $200. Step 1: Find the change. Step 2: Divide by starting amount. Step 3: Convert to percent. So, Jon’s salary increased by 33 ⅓ %. Example 18: What is the percent change from 2,100 to 1,890? Step 1: Find the change.

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    Study Guide Step 2: Divide by starting amount. Step 3: Convert to percent. So, the percent change is 10% (a decrease). Final Reminder The terms: • Percent increase • Percent decrease • Percent rise • Percentage difference • Percent change all refer to the same basic idea: how much something changes compared to where it started. Summary There are three main types of percent problems: 1. Find the part (percent of a number) 2. Find the percent (what percent is one number of another) 3. Find the whole (when you know the percent and the part) Choose the method that feels easiest: • Multiply • Divide • Write an equation • Use a proportion The math stays the same — only the setup changes.

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