LESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to:

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1 LESSON PLANS FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Lesson Purpose: The students will be able to: 1. Change fractions to decimals. 2. Change decimals to fractions. 3. Change percents to decimals. 4. Change decimals to percents. 5. Change fractions to percents. 6. Change percents to fractions. 7. Find a percent of a given number. 8. Find what percent a given number is of another number. 9. Ordering fractions, decimals and percents. Terms: 1. fraction: a number in the form a/b where b is 0. The numerator is the part of the whole and the denominator is the whole. So, 5/8 means there are 5 parts to the whole of 8. The denominator is also known as the base. 2. percent: a ratio whose denominator is 100; The symbol is %. 3. decimal: a number written using the base-ten place value system where a decimal point separates the ones and the tenths digits. 4. proportion: an equation stating that two statements are equivalent. 1. Change fractions to decimals: Like a fraction, a decimal represents a part of a whole. Whatever is to the right of the decimal point tells what the part, if any, is between the two wholes tells us that there are 3 wholes and 44/100 th parts. To convert a fraction into a decimal, it s numerator denominator. How many places into the decimal one should go, depends on the situation. Remind the students about decimal places: whole tenth 100 th 1000 th 10,000 th 100,000 th 1,000,000 th 10,000,000 th 100,000,000 th Example 1: ¼ = 1 4 or 0.25 In this case, the decimal ends in the 100 th place. Example:2: 1/3 = 1 3 or Here, you have a repeating decimal and it is usually preferable to cut it off after the second 3. (0.33) Example:3: 2/3 = 2 3 or Here, you have a repeating decimal and it is usually preferable to cut it off after the second 6, but since the next digit is also a 6, round up so it s Change decimals to fractions: The entire number will be the numerator, and whatever the place that the last number to the furthest right after the decimal is located will be the Page 1

2 denominator. Reduce if necessary. Example 1: 0.4 = 4/10 because the last number to the right (4) is in the tenth place, 10 will be the denominator. 4/10 can be reduced to 2/5. Example 2: = 43221/ because the last number to the right (1) is in the 100,000 th place, will be the denominator. Example 3: = 2/ because the last number to the right (2) is in the 1,000,000 th (millionth) place, 1, will be the denominator. Example 4: 3.5 = 3 and 5/10 because the last number to the right (5) is in the tenth place, so 10 will be the denominator. However, since there is a whole number to the left of the decimal, that will be represented as a whole number within the fraction., it will be 3 and 5/10 or reduced, 3 ½. If you wish to keep the entire value as a fraction, the same rule applies: the denominator is still 10 since the number furthest to the right after the decimal is in the tenth place. 35/10 or, reduced, 7/2. 3. Change percents to decimals. Move the decimal point two places to the left. You are really dividing it by 100. Example 1: 45% becomes 0.45 Example 2: 45.36% becomes Example 3: % becomes Change decimals to percents: Move the decimal point two places to the left. You are multiplying it by 100. Example 1: 0.63 becomes 63% Example 2: becomes 43.33% Example 3: becomes % 5. Change fractions to percents: The same procedure is used as for changing a fraction to a decimal except there is one further step move the decimal point two places to the right. Example 1: ¼ = 1 4 or 0.25 Move the decimal two places to the right: 25%. Example:2: 1/3 = 1 3 or Move the decimal two places to the right: In this case, since there are trailing 3 s, they can be used as decimals to the point where they are needed. 33.3% or 33.33% (NOTE: In many case, when using percents, it is desirable to cut the decimals off after either the tenth or the hundredth place. Page 2

3 Example 3: 2¼ = 2 plus 1 4 or 0.25 Move the decimal two places to the right: 225%. A whole number represents 100%, so for every whole number, it is multiplied by 100 (%) and added to the percent (200% + 25% = 225%). 6. Change percents to fractions. a) change the percent to a fraction by placing to over 100. b) reduce, if needed Example 1: a) 45% = 45/100 b) 45/100 is reduced to 9/20 Example 2: a) 45.5% = 455/1000 for every number to the right of the decimal point, add a zero to the denominator. In this case, denominator will be b) 455/1000 is reduced to 91/200 Example 3: a) 45.55% = 4555/10000 for every number to the right of the decimal point, add a zero to the denominator. In this case, denominator will be b) 4555/10000 is reduced to 911/2000 Example 4: a) 455% = 455/100 b) 455/100 is reduced to 4 and 91/20 7. Find a percent of a given number: When you need to find a percent of a number, simply convert the percent into a decimal and multiply by the base (80). Example 1:What is 70% of 80: a) Convert the percent into a decimal and multiply by the base (90). 0.7 x 80 = b) Move the decimal two places to the right to convert it back to the number: 0.56 = 56 Example 2:What is 25% of 90: a) Convert the percent into a decimal and multiply by the base (90) x 90 = b) Move the decimal two places to the right to convert it back to the number: = 22.5 Example 3:What is 150% of 600: a) Convert the percent into a decimal and multiply by the base (90) x 600 = 9. b) Move the decimal two places to the right to convert it back to the number: Page 3

4 9 = 900 Note: if there are no numbers as you move the decimal to the right, plug in zeroes for every time you move the decimal place. 8. Find what percent a given number is of another number: In this case, it becomes a fraction. The given number that you need to know what percent it is becomes the part or the numerator and the while the other number becomes the whole (also known as the base becomes the denominator. You then divide denominator into numerator, and your answer will be a decimal. To change a decimal into a percent, move the decimal two places the right. Example 1: 60 is what percent of 80? a) Turn it into a fraction 60/80 b) Turn it into a decimal by dividing the numerator by the denominator: = 0.75 c) Turn it into a percent by moving the decimal two places to the right 0.75 = 75% Example 2: 36 is what percent of 60? a) Turn it into a fraction 36/60 b) Turn it into a decimal by dividing the numerator by the denominator: = 0.6 c) Turn it into a percent by moving the decimal two places to the right 0.6 = 60% Example 3: 150 is what percent of 50? a) Turn it into a fraction 150/50 b) Turn it into a decimal by dividing the numerator by the denominator: = 3 c) Turn it into a percent by moving the decimal two places to the right 3 = 300% 9. Ordering fractions, decimals and percents: When given a group of fractions, decimals and percents to be put in size order, always convert them all to decimals and then list them from greatest to smallest or vice versa as requested. NOTE: It is always a good idea to make sure all the values have the same number of to the right of the decimal so as not to confuse 0.6 with 0.606, etc. So, adjust the shorter values to fit with the longest of the group. Example 1: List the following from greatest to smallest: 45% 4/ a) 45% = (move decimal two places to the right) Note: add a zero to this one so it also has three values to the right of the decimal as the other two. b) 4/9 = (divide 4 by 9) c) (already a decimal) Solution: 1. 45% (0.450) 2. 4/9 (0.444) (0.443) Example 2: List the following from greatest to smallest: 60% 6/ , 80% of 70 a) 60% = (move decimal two places to the right) b) 6/11 = (divide 6 by 11) c) (already a decimal) d) 80% of 70 = x 70 = Page 4

5 Solution: 1. 60% = (0.6000) 2. 80% of 70 = (0.5600) = (0.5570) 4. 6/11 = (0.5454) Example 3: List the following from least to greatest: 28% 4/ , 41% of 70 a) 28% = (move decimal two places to the right) b) 4/11 = (divide 4 by 11) c) (already a decimal) d) 41% of 70 = 0.41 x 70 = Solution: 1. 4/11 = (0.2720) = (0.5710) 3. 28% = (0.2800) 4. 41% of 70 = (0.2870) Lesson/Classroom Activities: The following are problem solving exercises the students can solve, individually, or in groups for you to review with them: 1. Convert the following: a) 5/12 to a decimal b) 1.24 to a fraction c) 5/8 to a percent d) 58% to a fraction e) 60.6% to a decimal f) to a percent Solutions: a) 5/12 = 5 12 = or b) 1.24 to a fraction = 124/100 = 31/25 c) 5/8 to a percent = = 62.5% d) 58% to a fraction = 58/100 = 29/50 e) 60.6% to a decimal = f) to a percent = 100.4% 2. Find the following values (round to the nearest 100 th ): a) 60% of 30 b) 120% of 50 c) 85% of 85 d) 2% of 1200 e) 500% of 50 f) 2/5 of 90 Solutions: a) 60% of 30 = 0.6 x 30 = 0.18 = 18 b) 120% of 50 = 1.20 x 50 = 0.60 = 60 c) 85% of 85 = 0.85 x 85 = = d) 2% of 1200 = 0.02 x 1200 = 0.24 = 24 Page 5

6 e) 500% of 50 = 5 x 50 = 2.5 = 250 f) 2/5 of 90 = 2/5 = 40% = 0.4 x 90 = 0.36 = a) 42 is what percent of 70? b) 150 is what percent of 60? c) 3 is what percent of 150? d) 600 is what percent of 50? Solutions: a) 42 is what percent of 70? = 0.60 = 60% b) 150 is what percent of 60? = 2.5 = 250% c) 3 is what percent of 150? = 0.01 = 1% d) 600 is what percent of 50? = 12 = 1200% 4. List the following from greatest to smallest: 54% 6/ Solution: 1. 6/11 = (0.5454) 2. 0,544 = (0.5440) 3. 54% = (0,5400) 5. List the following from least to greatest: 31% 4/ , 38% of 80 Solution: = (0.3003) of 80% = (0.3040) 3. 31% = (0.3100) 4. 4/12 = (0.3333) Page 6

7 EXAM/WORKSHEET FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING Name Date Change the following from fraction to decimal (round up to the nearest 100 th ): 1. _8_ 2. _5_ Change the following from decimal to fraction (Reduce & Answer in mixed fraction if necessary): Change the following from percent to decimal: 5. 59% % Change the following from decimal to percent: Change the following from fraction to percents: Change the following from percent to fraction % % Find the following values: % of % of 30 Find the following percents: 15: 72 is what percent of 300? is what percent of 14? Page 7

8 Order the following from greatest to least: 17: 48%, 48, %, 16% of 90, 1, Order the following from least to greatest: 19: 11%, 11, , 130% of 90, 13, 121% Page 8

9 ANSWER KEY FOR PERCENTAGES, FRACTIONS, DECIMALS, AND ORDERING 1. ( ) (3.125) % % % % 11. _ % % 17: 48 = ( ) = = ( ) = %, = ( ) 24% = : = % 0f 90 = % = = = = % = Page 9