Basic Math and Pre-Algebra - Percents - Quick Guides | Mathematics

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Study GuideBasic Math and Pre-Algebra–Percents1. ApplicaƟons of PercentsPercents 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.1.1Finding a Percent of a NumberTo find a percentofa number:1.Change the percent to adecimal 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 GuideExample 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 Guide1.2What Percent Is One Number of Another?Now let’s reverse the question.Instead of finding a part, we find thepercent.Division MethodTo 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 90.1.3Using the EquaƟon MethodAnother way to solve percent problems is to turn the words into an equation.Here’s how:•“What”→usex•“Is”→use=•“Of”→use×•Change percent to decimal or fraction

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Study GuideExample 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 PercentSometimes in math, you know apercent of a number, but you don’t know the original number.Your job is to find thewhole.Let’s learn how to do that step by step.

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Study GuideExample 8:15 is 50% of what number?Step 1: Turn the percent into a decimal.50% =0.50Step 2: Write an equation.If 15 is 50% of a number, we can write:Here,xis 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% = 1/2So:Dividing by 1/2 is the same as multiplying by 2:࿨࿩࿪Answer: 30So,15 is 50% of 30.

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Study GuideExample 9:20 is 40% of what number?Step 1: Convert the percent to a decimal.40% =0.40Step 2: Write the equation.Step 3: Solve.Divide both sides by 0.40:࿨࿩࿪Answer: 50So,20 is 40% of 50.Quick Tip: The Shortcut“___ is ___% of what number?”You can use this formula:1.4Finding the Whole When You Know the PercentSometimes 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 GuideDivide both sides by 0.20:So,30 is 20% of 150.Example 11:40 is 80% of what number?So,40 is 80% of 50.1.5The ProporƟon (Is/Of) MethodYou 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 GuideExample 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 30.1.6Percent Change (Increase or Decrease)To find percent change, use this formula:

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Study GuideExample 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 a20% decrease.Example17: 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 by33⅓%.Example 18:What is the percent change from 2,100 to 1,890?Step 1: Find the change.

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Study GuideStep 2: Divide by starting amount.Step 3: Convert to percent.So, the percent change is10% (a decrease).Final ReminderThe terms:•Percent increase•Percent decrease•Percent rise•Percentage difference•Percent changeall refer to the same basic idea: how much something changes compared to where it started.SummaryThere 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 proportionThe math stays the same—only the setup changes.

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