1. Percentages Lesson 2.05

2. After completing this lesson, you will be able to say: I can define a percentage as a ratio of a number to 100. I can calculate a percent of a number as a rate per 100. I can solve a variety of problems involving percentages.

3. What is a Percentage?

4. Percentage A part-to-whole ratio that compares a number to 100; percentages are written with the percent symbol (%).

5. When the ratio becomes a percentage, the second term is always 100. When you record a percentage, write the first term in the ratio, followed by the percent sign (%). The table below will show how you can take a ratio from a situation, create a ratio, and write the percent: In wordsWritten as a RatioWritten as a percent 26 out of 10026:10026% 26 for every 10026 to 100

6. In the world of 100 people, there are 8 seniors. How is this expressed as a ratio and a percentage? In wordsWritten as a RatioWritten as a percent

7. In the world of 100 people, there are 8 seniors. How is this expressed as a ratio and a percentage? In wordsWritten as a RatioWritten as a percent 8 out of 1008:1008% 8 for every 1008 to 100 Check your work

8. Finding Percentages What if the part-to-whole ratio was not out of 100? Fractions also represent part-to-whole relationships, which means that all fractions can be written as a percent. For this reason, it will be best to write all ratios in fraction form when working with percentages.

9. Finding Percentages Sofia went to the bakery and bought 20 cookies. Out of the 20 cookies, she has 5 sugar cookies. What is the percentage of sugar cookies? CCCCCCCCCCCCCCCCCCCC 10% Since you know that 5 are sugar cookies, the first 5 are colored

10. So if 5 out of 20 cookies are sugar, that means 25% of them are sugar cookies. In other words, if Sofia had 100 cookies, 25 of them would be sugar cookies.

11. Using equivalent fractions StepFractionExplanation 1 To set up the equivalent ratios, the first fraction will be the ratio of sugar cookies to total number of cookies. Then set it equal to another ratio, with a denominator of 100. Since you are trying to find the percent, the ratio needs to be out of 100. 2100 ÷ 20 = 5Next determine which number times 20 would give you 100. 3Multiply both terms by the value. So every 5 out of 20 is equal to 25 out of 100. This means 25% of the cookies were sugar cookies.

12. Try It A cookie jar has 20 cookies: 6 oatmeal cookies, 9 chocolate chip cookies, and 5 sugar cookies. Determine the percentage for oatmeal cookies. StepFractionExplanation 1 2 3

13. Check your work A cookie jar has 20 cookies: 6 oatmeal cookies, 9 chocolate chip cookies, and 5 sugar cookies. Determine the percentage for oatmeal cookies. Determine the percentage for chocolate chip cookies. StepFractionExplanation 1 To set up the equivalent ratios, the first fraction will be the ratio of sugar cookies to total number of cookies. Then set it equal to another ratio, with a denominator of 100. Since you are trying to find the percent, the ratio needs to be out of 100. 2100 ÷ 20 = 5Next determine which number times 20 would give you 100. 3Multiply both terms by the value. The percent of oatmeal cookies is 30%.

14. Using Percentages What if you know the percent but need to determine the part or the whole? In the morning, the local grocery story had 130 tubs of ice cream. By the end of the day, they sold 55%. How many tubs of ice cream did they sell? What is 55% of 130? Method 1: Since 55% of 130 tells you part of a whole, to find the answer you multiply the percent (35%) by the total amount (130). Change the percent to a decimal. To change the percent to a decimal, divide by 100. 55% ÷100 = 0.55 Multiply the decimal by the whole, which is 130. 0.55 × 130 = 71.5 Therefore, 55% of 130 is 71.5.

17. Now that you completed this lesson, you should be able to say: I can determine the appropriate conversion factor when converting units. I can convert units between metric and customary systems.