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NY Regents Exam - Integrated Algebra: Help and Review25 chapters | 272 lessons | 12 flashcard sets

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Learn how understanding and being able to calculate percentages can help you when shopping and when reading test scores. Also learn how to easily convert a decimal into a percentage and vice versa.

An easy way to think about percentages is to break down the word 'percent' into 'per' and 'cent.' Think about the word 'cent' for a moment. How many cents does it take to make a dollar? 100, right? So **percentage** literally means 'per 100.' For example, if I said 75% of that bin is made up of apples, it means that there are 75 apples for every 100 items in the bin. This can also be written as 75/100. In school, 100% means a perfect score, meaning you got all the answers right. If there were 100 questions, you got all 100 questions right. 75% in school means you got 75 questions right out of 100 questions.

Even though 100% seems to be the highest percentage you can go, it is possible to have 150%, 200%, and even 500%. What it means is that for every 100 of one particular item, there are 150, 200, or 500 of the other item. So, 200% can be written as 200/100; 150% as 150/100; and 500% as 500/100.

In real life, you will encounter the majority of your percentages when shopping. Most often, you will see signs at your favorite store saying things like 25% off, 10% off, and so on. If you had a set amount of cash on you, how would you know how much you can buy with these discounts? You would need to use your skills in calculating percentages.

Let's say you want to know how much something costs with a 25% discount. The original price is $14.99. So how do you figure out how much 25% is? To do this, you would multiply your original price by the percentage. Now remember that 'percentage' means 'per 100' or 'out of a hundred,' so in our calculation we have to include that.

Our discount is $3.75. We would end up paying $14.99 - $3.75 = $11.24 for our item. But wait, we have to include sales tax too. Let's say our sales tax is 8%. We would do a similar calculation to figure out how much tax we would have to pay.

Looks like our sales tax is $0.90, and so our final total is $11.24 + $0.90 = $12.14. We have $15 in our wallet so, yes, we have enough, and with a couple dollars and change left!

Now let's say you want to figure out what the percentage is of something. Let's say you want to know the percentage of wasted food at your restaurant. If you had to throw away $200 worth of food at the end of the day but you made $995 that day, how can you calculate your percentage of waste that day? To do this, you would take what you lost and divide it by your total for the day.

When you make the division, you get a decimal number. Remember, again, that 'percentage' means 'out of a hundred,' so to figure the percentage you have to do the reverse of what we did above and multiply by 100.

The formula for figuring out the percentage is this.

When using percentages in equations and mathematical operations, you need to use the decimal form. It is easy to convert any percentage to decimal form. To make the conversion, you simply divide by 100 or move the decimal point two places to the left.

Notice how the decimal point moves two places to the left when you divide by 100? Remember this step and you won't have to manually divide by 100 each time.

To change from a decimal back to a percentage is easy too. Instead of dividing, you would multiply by a 100 or move the decimal two places to the right.

When you multiply by 100, it moves the decimal point two spaces to the right. Remember that so you won't have to multiply by 100 each time.

Let's review. **Percentages** are useful in shopping and when reading test scores. 'Percentage' means 'out of 100,' so 50% on a test means that 50 out of 100 answers are correct. To calculate a shopping discount or how much a percentage is of something, you would multiply the original by the percentage to calculate how much of a discount you get. Converting from percentage to decimal means you shift the decimal point two spaces to the left. Converting from decimal to percentage means you move the decimal point two spaces to the right.

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NY Regents Exam - Integrated Algebra: Help and Review25 chapters | 272 lessons | 12 flashcard sets

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