So far we have discussed fractions and decimals and how to convert between each of them. Now it is time to introduce the third, percents.

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1 Unit 3.7: Fractions, Decimals and Percent Lesson: Relating Fractions Decimals and Percents Objectives: Students will review where they have seen percents and to discuss where and how they are applied in society. Students will review how fractions, decimals and percents are related and convert between the three. Procedure: So far we have discussed fractions and decimals and how to convert between each of them. Now it is time to introduce the third, percents. When we first introduced the concepts of decimals, fractions and percents we found that they were the same thing written in different ways. Review: For example: In the table above there are 3 out of 6 boxes shaded, so as a fraction this is 3, this can be 6 simplified by reducing to 1. As a decimal, there are 0.5 of the boxes shaded. (1 divided by 2 2). As a percent this can be expressed, as 50% of the boxes are shaded. As you can see, fractions, decimals and percents are all different ways of expressing the same number. So what is a percent? A percent is a comparison to the number 100. We usually say that it is a number out of 100. We use percents to compare numbers in the same way so that understanding is easier. For example: It is easier to think of 30% off rather than 3/10 s off. It is easier to think of a test mark of 64% rather than 16/25. It is easier to think of 12% improvement, rather than 0.12:1 improvement. 1

2 Where have you seen percents in your life? Some examples are; shopping, weight gain and loss; business profits; etc. Percents Percent is a number that is out of 100, so if we think of it as a box with 100 cells, we can create fractions out of 100. The following box has 100 squares. What fraction is shaded? What is this as a decimal? = 0.5 Since percent is out of 100, that means that this must have 50% shaded. So, and must all be the same. Lets break this down into smaller parts: Fraction to Percent: To convert a fraction to a percent there are two methods, which can be used. Since percent is out of 100, you can convert the fraction to an equivalent fraction with a denominator of 100. (Percent is out of 100). 3 is what percent? Convert this fraction to an equivalent fraction that has a denominator 4 of = , multiply by 20. So multiply 3 by 20 to get an equivalent fraction 3 75 (3 20) = (4 20) 2

3 Since percent is always out of 100, 3 4 is 75%. There is another way that some people find easier, we can convert 3 4 into a decimal and then multiply by % 4 = = = convert multiply to by decimal 100 Why do we multiply by 100, well it is simple really. All numbers have a denominator of 1, so when you divide the fraction out, you get Now convert that into an equivalent 1 fraction with a denominator of ( ) = (1 100) Since all decimals can be treated as if they have a denominator of 1, we can simply multiply by 100 each time. Lets try another example; 7 8 is what percent? Convert to a decimal: Multiply by 100: 3

4 13 20 is what percent? Convert to a decimal: Multiply by 100: Bob received a mark of 7 out of 35 on his math test. What percent is this? Solution: Write as a fraction first gives us. Now convert this to decimal: Finally convert the decimal to percent by multiplying by 100. Bob received a mark of on his math test. It is 217 km from Sedgewick to Bobs Farm near Edmonton. If Bob has driven 144 km on the way to his farm, what percent of the distance has he traveled so far? Round your answer to the nearest percent. Write as a fraction: Convert to a decimal: Convert to a percent:. Round to nearest percent Bob has driven of the way to his farm. 4

5 Bob wants to grow to be 2 metres tall. He is 1.45 metres now, what percent of the way is he so far? Round your answer to the nearest tenth. Create a fraction: Create a decimal: Convert to a percent: Bob is of the way to his goal of 2 metres tall. Converting Percent to decimals and fractions: Since a percent is always out of a 100, creating a fraction is simply a matter of writing the percent over 100 to create a fraction and then reducing the fraction. What is 20 percent as a fraction? Written as a fraction: Now reduce by dividing the top and bottom by the same number until reduced to simplest form = Bob received a mark of 40 percent on his math test. What fraction of the questions did he get correct? Write as a fraction out of 100: Now reduce to lowest form: Bob got of the questions correct. 5

6 Write the following percents as a fraction with a denominator of 100. a) 24% b) 16% c) 76% Converting Percents to Decimals To convert a percent to a decimal, we need to think of what a percent is. It is a number out of 100, so we need to divide by % is what number as a decimal? Since 75% is out of 100, you can think of it as 75. This can be converted to a decimal by 100 dividing = 0.75 You can do this without writing the fraction down, if you can remember that a percent is always out of 100. What is 60% as a decimal? Write the following percents as a decimal. a) 24% b) 16% c) 76% 6

7 Converting Decimals to Percents To get a percent from a decimal, all we have to do is reverse what we just did. To go from a percent to a decimal, we divided by 100. So to go from a decimal to a percent, reverse this and multiply by 100. What is 0.75 as a percent? (multiply by 100) What is as a percent? Write the following decimals as percents. a) 0.54 b) c) Josh got 47 out of 59 on his test. Marcie stated that she received 80% on her test. Who received the higher mark and by how many percent? Josh s percent: Since Marcie got 80%, she received the higher mark. How much higher was her mark? Her mark was higher than Josh s. Complete Page 112#1,2,3,4 7

8 Homework Book Pages 66#1,2,3,4,5,6 first table only, 7,8,9, 8