1. FRACTIONS DECIMALS PERCENTS Shelby Blackwood

2. The student will be able to convert fractions, decimals, and percentages. This lesson will meet the following standards for Oklahoma 6 th grade mathematics curriculum:  PASS – Strand 2N, Standard 2.1 Number Sense: Convert compare, and order decimals, fractions, and percents using a variety of methods.  Common Core – RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent. Shelby Blackwood

3. Decimals, fractions, and percentages are just different ways of showing the same value. The following presentation will show you different procedures to convert these numbers. Shelby Blackwood *Source: www.mathisfun.com

4. How to change fractions to decimals Method 1-Use a proportion  Step 1 – Rename the fraction as an equivalent fraction with 100 as the denominator. We can multiply 5 by 20 to get 100. You must multiply the numerator by 20 also. 1 x 20 20 5 x 20 100 = Shelby Blackwood

5. Method 1-Use a proportion (continued)  Step 2 – 20/100 is 20 divided by 100. A quick way to divide by 100 is to move the decimal two places from the right. Write the numerator with two decimal places from the right.  So, 1/5 =.20 or.2 as a decimal! =.20 20 100 =.20 Shelby Blackwood

6. Easy, right? But there’s a problem. What do you do when you have a fraction, such as 1/7, that has a denominator that is not a factor of 100? You would use the long division method. It will always work! Shelby Blackwood

7. How to change fractions to decimals  Step 1 – First, you should realize that 1/7 is the same thing as 1 divided by 7. In order to change this fraction to a decimal, you will use division. Follow the algorithm on the next slide. Shelby Blackwood Method 2- Use a long division algorithm

8. 17  Step 1 – 7 will not go into 1, so add a decimal and a 0 to the right of the 1.0  Step 2 – Bring the decimal straight up.  Step 3 – Divide 7 into 10. It goes 1 time, so place a 1 above the 0 1  Step 4 – Multiply 1 times 7 and subtract it from 10. 7 3  Step 5 – You get 3. Seven will not go into 3, so you can add another 0 and bring it down. Shelby Blackwood 0 0

9.  Step 6 – Now divide 7 into 30. It will go 4 times, so place a 4 next to the one. 17.0. 1 7 3 0 0 4  Step 7 – 7 times 4 is 28, so place the 28 under the 30 and subtract. You get 2. 2 8 2  Step 8 – Add another 0 to the dividend and bring it down. 0 0  Step 9 – Divide 7 into 20. It will go 2 times, so place a 2 next to the 4 and multiply 2 times 7. Place 14 under the 20 and subtract. You get 6. 1 4 2 6 Shelby Blackwood

10.  Step 10 – You can stop here. This is a non-terminating, non- repeating decimal and would go on forever. 17.0. 1 7 3 0 0 4 2 8 2 0 0 1 4 2 6  Step 11 – Since it is a non-terminating, non-repeating decimal, we will round it to two decimal places to get an approximate value. Shelby Blackwood The result would be.14, so 1/7 is approximately.14 as a decimal.

11. How to change fractions to a percent  Step 1 – After changing 1/5 to a decimal,.20, you will multiply by 100 to change it to a percent..20 x 100 = 20% shortcut: when multiplying by 100, you move the decimal two places to the right 1/5 =.20 = 20% Shelby Blackwood

12. Resource Page Follow these links for more help changing fractions to decimals and percents. http://www.youtube.com/watch?v=VlqhVldVces http://www.mathplayground.com/howto_perfracdec.html http://www.quia.com/cb/34887.html When you are ready to practice what you’ve learned, follow this link to play a Jeopardy! game using fractions, decimals, and percents. Shelby Blackwood

13. Why Convert Decimals to Percents One use for decimals is in working with percents, which are commonplace in everyday life: Discounts on Sale Items Counting Money, ETC. The word percent means per one hundred. The symbol % is used for percent. The % symbol can be traded for a factor of 100. A factor of 100 can be traded for a % symbol. This simple idea is the key to success with percents. Jessica Thompson

14. How to Change Decimals to Percents Jessica Thompson From DecimalTo Percent move the decimal point 2 places to the right, and add the "%" sign. To convert from decimal to percent: multiply by 100, and add a "%" sign. The easiest way to multiply by 100 is to move the decimal point 2 places to the right. So:

15. Converting Decimals to Percents is as Easy as Sliding the Decimal 2 Places to the Right and Adding a % Sign It must be noted that “Sliding the Decimal” is only allowed because it is the same as multiplying the original number by 100. WWW.KHANACADEMY.COMWWW.KHANACADEMY.COM Web Link http://s3.amazonaws.com/KA-youtube-converted/5z568fLBQyQ.mp4/5z568fLBQyQ.mp4 EXAMPLES: 0.25 = 25% 3.75 = 375% 7.0683 = 706.83% Here's the idea that makes this work: 0.25 = 25/100 = 25 x 1/100 =.25% Notice that the 1/100 gets traded in for the percent symbol. Jessica Thompson

16. http://www.aaastudy.com/dec71dx2.htm Websites to Practice Converting Decimals to Percents http://www.math-play.com/Decimals-and-Percents/Decimals- and-Percents.html http://s3.amazonaws.com/KA-youtube- converted/5z568fLBQyQ.mp4/5z568fLBQyQ.mp4 Video Link to Khan Academy to Learn How to Convert Decimals to Percents Jessica Thompson

17. How to Change Decimals to Fractions Jessica Thompson Step 1: Write down the decimal divided by 1, like this: decimal / 1 Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.) Step 3: Simplify/Reduce the fraction To Convert a Decimal to a Fraction Follow These Steps:

18. Jessica Thompson

21. Websites to Practice Converting Decimals to Fractions Video Link to Khan Academy to Learn How to Convert Decimals to Percents http://www.mathplayground.com/percent04.html http://www.aaastudy.com/fra71bx2.htm http://www.khanacademy.org/math/arithmetic/decimals/v/converting- decimals-to-fractions-1--ex-1

22. Converting Percents to Fractions and Decimals Jill Porter

23. Things to remember when converting a percent to a fraction The % Sign means (Per 100) Ex. 25% is 25/100 When converting a percent to a fraction fractions must always be reduced to lowest terms. 25 /25 = 1 100 /25 = 4 So the reduced version of 25/100 is 1/4 Jill Porter

24. Example Problems 15% 15 /5 = 3 27% _ 27 100 / 5 = 20 100 NOTE nothing will go 22% 22 /2 = 11into both 27 and 100 100 /2 = 50evenly so 27/100 is lowest terms 60% 60 /20 = 375% _75 /25 = 3 100/20 = 5 100 /25 = 4 Jill Porter

25. Working with Percentages that include decimals When you have a Percent that includes a decimal you must get rid of the decimal before you can convert the percent into a fraction. Move decimal to the right until it is at the end of the number. If there is one decimal place this would be the same as multiplying by 10 Remember if you multiply the numerator by 10 you must multiply the denominator by 10 as well Jill Porter

26. Example Problems 5.5% 5.5 X 10 = __55 /5 = 11 100.0 X 10 = 1000 /5 = 200 25.5% 25.5 X 10 = 255 /5 =_ 51 100.0 X 10 = 1000/5 = 200 85.5% 85.5 X 10 = 855 /5 = 171 100.0 X 10 =1000/5 = 200 Jill Porter

27. Things to Remember When Converting Percents to Decimals Percent means per 100 So to change a number from a percent into a decimal just remove the percent sign and divide by 100 37% 37/100 = 0.37 Simply move the decimal two places to the left Repeat same process even if the percent has a decimal in it such as 8.5% Jill Porter

28. Example Problems 5% 5/100 = 0.05 15.3% 15.3/100 = 0.153 25% 25/100 = 0.25 50.7% 50.7/100 = 0.507 Practice moving decimal places 2 spaces to the left 77% 77. = 0.77 83% 83. = 0.83 115% 115. = 1.15 Jill Porter

29. Resource page For extra explanations and practice you can visit http://www.youtube.com/watch?v=04eEAxkc4bk http://www.math-salamanders.com/convert-percent- to-fraction.html Jill Porter