Math Homework Helper: Percentages and Finding Percents

Percentages are used in lots of areas, including statistics, science and finance. In politics, percentages are even used to decide who wins elections. Read this article to learn what a percentage is, and how to calculate one!

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Homework Help for Percentages

A percentage represents a fraction with 100 as the denominator. Percentages are written using the percent sign (%). For instance, the fraction 50/100 is written as 50%, and the fraction 8/100 is written as 8%. Here are a few more examples:

  • 15/100 = 15%
  • 75/100 = 75%
  • 110/100 = 110%

Writing Fractions as Percentages

Most of the time, the fractions that we want to turn into percentages don't have 100 as the denominator. For example, if you got 17 questions right on a test with 20 questions, you might want to figure out what percentage 17/20 is equal to. To write fractions as percentages, we have to find an equivalent fraction with a denominator of 100. The fraction 17/20 is equal to 85/100, which is equal to 85%. This means that you got 85% of your test questions correct. Here are some other examples:

  • 2/5 = 40/100 = 40%
  • 1/25 = 4/100 = 4%
  • 18/50 = 36/100 = 36%

Sometimes, when you try to turn a fraction into a percentage, you'll find that it doesn't have an equivalent fraction with a denominator of 100. The fractions 5/24 and 7/8 are examples of this. Here's how you handle this situation:

  1. Change the fraction to a decimal by dividing the numerator by the denominator. You can do this by hand or with a calculator. For instance, 7/8 = 0.875.
  2. Multiply the resulting decimal by 100. This will tell you what percentage the original fraction is equal to. For example, 0.875 x 100 = 87.5, so 7/8 = 87.5%.

Finding the Percentage of a Quantity

Now that you can turn fractions into percentages, it's time to work backwards. Often, you'll need to find a certain percentage of something. For example, if you have to pay a 5% tax on your grocery bill, or you earn a 10% commission for every candy bar you sell, you'll need to calculate the amount of money those percentages represent.

Calculating Taxes and Tips

One way to do this is to change the percentage into a fraction out of 100, and then multiply it by the amount you're finding the percentage of. For instance, if your grocery bill is $50.00, you can calculate 5% of it by multiplying 50/1 x 5/100. This equals 250/100, which simplifies to 5/2. To get the final amount of tax in dollars, convert 5/2 to a decimal by dividing the numerator by the denominator. Since 5 ÷ 2 = 2.5, the tax on your grocery bill is $2.50. You would use the same steps to figure out the amount of a tip.

Tip: Read percentage problems carefully. In this problem, we were finding the amount of the tax, which was $2.50. Some problems will ask you to find the amount of the total bill with tax, so you would add $2.50 to $50.00 to get $52.50 as your answer.

Calculating Commissions

Let's try another example: Sandra earns a 10% commission for each candy bar she sells, and each candy bar costs $3.00. If she sells 30 candy bars, how much commission will she earn?

The first step is to determine the total value of all of the candy bars sold by multiplying $3.00 by 30. Since $3.00 x 30 = $90.00, Sandra's commission will be equal to 10% of that amount. To calculate the commission, we have to write 10% as the fraction 10/100, and multiply it by $90.00 (10/100 x 90/1). The result is the fraction 900/100, which can be simplified to 9/1. Since 9 ÷ 1 = 9, Sandra's commission will be $9.00.

Tip: If you have a calculator handy, you can change the percentage into a decimal, and multiply the total amount by the decimal to get your answer. For example, 10/100 = 0.1, and $90.00 x 0.1 = $9.00.

How to Practice Percentages

There are tons of opportunities to practice percentage problems in daily life. You can ask your parents to let you calculate the server's tip when you go to a restaurant, or you can calculate the sales tax when you go shopping. You can also survey your friends about their likes and dislikes, and report the results using percentages.

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