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Lesson 27 PERCENTS ARE RATIOSThe very first Lesson on Percent is Lesson 3. Now every statement of percent can be expressed verbally in this way: "One number is some percent of another number." For example, 8 is 50% of 16. Every statement of percent therefore involves three numbers. 8 is called the Amount. 50% is the Percent. 16 is called the Base. The Base always follows "of." As for the ratio of two numbers,it is their relationship in which a larger number is so many times a smaller, while a smaller number is a certain part or parts of a larger. (Lesson 16) This Lesson is a review of ratio in the language of percent. 



What ratio does each of the following express? 50% Half. Because 50 is half of 100. 25% A quarter, or a fourth. Because 25 is a quarter of 100.
200% Two times, or twice as much. Because 200 is two times 100. 250% Two and a half times. Because 250 is two and a half times 100. (Lesson 17, Question 6.) 1000% Ten times. Because 1000 is ten times 100. Whatever ratio the percent has to 100 percent, that is the ratio we mean. The Amount Example 1. How much is 100% of 12? Answer. 12. 100% is the whole thing. Example 2. How much is 200% of 12? Answer. 24. 200% is twice as much as 100%. Example 3. How much is 300% of 12? Answer. 36. 300% is three times 100%. Example 4. How much is 50% of 12? Answer. Translate immediately into the language of ratio: "How much is half of 12?" Answer: 6.
Translate: "How much is a third of 12?" A third of 12 is 4. Example 6. How much is 350% of 12? Translate: "How much is a three and a half times 12?" (350% = 300% + 50%: Three times plus half.) Three times 12 is 36. Half of 12 is 6. 36 + 6 = 42. We see that more than 100% of 12 is more than 12, while less than 100% will be less. Example 7. How much is 1% of $512? Translate: "How much is a hundredth of $512?" (1% means a hundredth, because 1 is the hundredth part of 100.) To find a hundredth of a number, divide it by 100. To divide a whole number by 100, separate two decimal places (Lesson 3, Question 5): $512 ÷ 100 = $5.12. Example 8. How much is 2% of $512? Answer. 2% is twice as much as 1%. 1% of $512 is $5.12. Therefore 2% is 2 × $5.12 = $10.24. Example 9. How much is 10% of $434? Translate: "How much is a a tenth of $475?" (10% means a tenth, because 10 is a tenth of 100.) To find a tenth of a number, divide it by 10. To divide a whole number by 10, separate one decimal place: $434 ÷ 10 = $43.4 Money however is written with two decimal places. Therefore report the answer as $43.40. Example 10. How much is 20% of $142? Answer. 20% is twice as much as 10%. 10% is $14.20. Therefore 20% is $28.40. The Base Example 11. 7 is 25% of _?_ Answer. The Base  the number that follows of  is missing. "7 is a quarter of what number?" 7 is a quarter of 28. Example 12. 10 is 20% of _?_ Translate: "10 is the fifth part of what number?" (20% means the fifth part, because 20 is the fifth part of 100.) 10 is the fifth part of 50. Example 13. 15 is 300% of _?_ Translate: "15 is the three times what number?" 15 is three times 5. Example 14. 280 is 1000% of _?_ Translate: "280 is the ten times what number?" 280 is ten times 28. The Percent Example 15. 48 is what percent of 48? Answer. 100%. 100% is the whole thing! Example 16. 9 is what percent of 36? Answer. To ask 9 is what percent of 36? is the same as asking 9 has what ratio to 36? Percents are ratios. Now, 9 is a fourth of 36. Therefore, 9 is 25% of 36. 25% means a fourth, or a quarter. Example 17. 35 is what percent of 7? Translate: "35 has what ratio to 7?" 35 is five times 7. The percent, then, will be five times 100: 35 is 500% of 7. In every case, The percent has that same ratio to 100. Example 18. $2.50 is what percent of $250? Answer. "$2.50 is which part of $250?" The digits are the same: 2, 5, 0. But $2.50 has two decimal places. It is $250 divided by 100: 2.50 = 250 ÷ 100. Therefore, $2.50 is 1% of $250. (Example 7 above.) At this point, please "turn" the page and do some Problems. or Continue on to the next Section. Introduction  Home  Table of Contents Please make a donation to keep TheMathPage online. Copyright © 20012007 Lawrence Spector Questions or comments? Email: themathpage@nyc.rr.com 