73 73% = % = 100. n % = n

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1 HFCC Math Lab Arithmetic 0 PERCENT PROBLEMS The meaning of the word percent should be familiar to you. If you score 85% on a test, you know that you scored 85 points out of a possible 00 points. That is, the word percent mean parts per hundred. In general: Percent is a part out of 00. CHANGING A PERCENT TO A FRACTION: We can use the idea of percent being part out of 00 to change a percent to a fraction. 3 3% % 00 or or 73 73% 00 n n % n 00 To write a percent as a fraction, use the rule:. That is, parts per hundred. Remember: After changing a percent to a fraction, always reduce the fraction to lowest terms if possible.. Change each of the following percents to a fraction reduced to lowest terms. 5 5% % % (Remember that a fraction bar means division) % %

2 EXERCISE : Change each of the following percents to a fraction reduced to lowest terms:. 0% 2. 20% 3. 30% 4. 40% 5. 50% 6. 60% 7. 70% 8. 80% 9. 90% 0. 00%. 25% 2. 75% % % 5. 2 % % % 87 2 % NOTE: You should be able to mentally convert between the percents and fractions in Exercise above. 2 For example, when you see 40%, you should automatically know that it is equal to the fraction When you see the fraction, you should automatically know that it is equal to 66 %. 3 3 Check your answers to Exercise on the answer pages at the end of this handout before memorizing the results. CHANGING A PERCENT TO A DECIMAL: 7 7% % % Note: From the examples above, notice that in changing a percent to a decimal, the digits in the number stayed the same. However, the decimal point moved 2 places to the left. To change a percent to a decimal, move the decimal point 2 places to the left and drop the % symbol -2-

3 Change the following percents to decimals:. 38% % %.5% %.00 Note: This means that 00% is all of some quantity. One means the entire quantity. CHANGING A DECIMAL TO A PERCENT: To change a decimal to a percent, move the decimal point 2 places to the right and write the % symbol. Change the following decimals to percents:. 0.35% 35% % % CHANGING A FRACTION TO A PERCENT: In order to change a fraction to a percent, we must first be able to change a fraction to a decimal. Remember: To change a fraction to a decimal, divide the numerator by the denominator. Change each of the following fractions to a decimal To change a fraction to a percent, change the fraction to a decimal, then change the decimal to a percent

4 Change each of the following fractions to a percent % % % % % change a decimal to a percent, we must move the decimal point two places to the Note: When we divide by 3, we get a repeating decimal. ( Try it. ) right. Therefore, when the fraction equals a repeating decimal, stop dividing when you have two decimal places and convert the remainder to a fraction. To This shows that % SOLVING BASIC PERCENT PROBLEMS: - 4-

5 There are two methods that can be used to solve basic percent problems similar to the following: What number is 25% of 20? 40 is 65.5% of what number? 5 is what percent of 25? Method I: Translating to an Equation to Solve a Percent Problem To solve a percent problem:. Translate the sentence to an equation Note: 2. Solve the equation. When translating words to an equation, remember that: is means of usually means to multiply 2. We will let the letter n stand for what number or what percent. 3. Before multiplying by a percent, we need to change the percent to a decimal or a fraction. Translate to an equation and find the number.. What number is 25% of 20? n n 30 Answer: 30 is 25% of % of 24 is what number? n 7.8 n Answer: 32.5% of 24 is

6 3. What number is 25% of 340? n n 425 Answer: 425 is 25% of 340. Translate to an equation and find the number. 6 is 50% of what number? 6.50 n n n Answer: 6 is 50% of % of what number is 2.73?.042 n n n 65 Answer: 4.2% of 65 is is 325% of what number? n n n Note: is rounded off. Answer: 240 is 325% of

7 Translate to an equation and find the percent.. 5 is what percent of 25? 5 n n n and.6 60% Answer: 5 is 60% of What percent of 90 is 60? n n n and % 3 3 Answer: 66 2 of 90 is 60 3 % 3. 2 is what percent of 8? 2 n 8 2 n n and.5 50% Answer: 2 is 50% of

8 Method II: Use a Proportion to Solve a Percent Problem To solve a percent problem, set up the following proportion, then solve for the unknown quantity. The Percent The Part 00 The Whole Note:. Percent is a part out of 00. Therefore, in the proportion above, the percent corresponds to the part, and 00 corresponds to the whole. 2. The words or quantity that follows of is the whole. 3. If you don t remember how to set up or solve a proportion, see the Learning Lab Handouts: Arithmetic 7 Ratio and Proportion Arithmetic 8 Proportion Word Problems Translate to a proportion and find the number.. What number is 8% of 35? Given: The Percent 8 The Whole 35 Find: The Part Let n The Part Set up the proportion: The Percent 00 The Part The Whole 8 00 n 35 Solve the proportion: 00 n n 630 Answer: 6.3 is 28% of n n

9 2. 25% of 484 is what number? Given: The Percent 25 The Whole 484 Find: The Part Let n The Part Set up the proportion: The Percent The Part 00 The Whole 25 n Solve the proportion: 00 n Answer: 25% of 484 is is 40% of what number? Given: The Part 25 The Percent n n 00 n Find: The Whole Let n The Whole Set up the proportion: The Percent The Part 00 The Whole n Solve the proportion: 40 n n 2500 Answer: 25 is 40% of n n

10 % of what number is 03.32? Given: The Percent 24.6 The Part Find: The Whole Let n The Whole Set up the proportion: The Percent The Part 00 The Whole n Solve the proportion: 24.6 n n n n 420 Answer: 24.6% of 420 is Translate to a proportion and find the percent.. 36 is what percent of 72? Given: The Part 36 The Whole 72 Find: The Percent Let n The Percent Set up the proportion: The Percent The Part 00 The Whole n Solve the proportion: 72 n n Answer: 36 is 50% of n n n 50-0-

11 Note: When you use the Proportion Method to find a percent, you do NOT need to move the decimal point in your answer. This is because the variable represents the percent already. 2. What percent of 35.8 is 4.475? Given: The Whole 35.8 The Part Find: The Percent Let n The Percent n Set up the proportion: The Percent The Part 00 The Whole n Solve the proportion: n Answer: 2.5% of 35.8 is What percent of 250 is 500? Given: The Whole 250 The Part 500 n n n 2.5 Find: The Percent Let n The Percent Set up the proportion: The Percent The Part 00 The Whole n Solve the proportion: n n Answer: 200% of 250 is 500. n n

12 Note: With practice, you should be able to use both methods to solve percent problems. EXERCISE 2: Translate to an equation and find the answer.. What is 26% of 250? is 20.5% of what number? is what percent of 29? is 220% of what number? 5. What is 96% of 75? EXERCISE 3: Translate to a proportion and find the answer. 6. What percent of 344 is 43? 7. What is 235% of 4.4? 8. 4 is 0.5% of what number? 9. What is 6.5% of 300? 0. 5 is what percent of 5000? EXERCISE 4: Find an answer in whichever way you choose.. 38 is what percent of 95? 2. 2 is 24% of what number? 3. What percent of 4 is 2? 4. What number is 20 % of 20? 5. 25% of what number is? Note: The answers and selected solutions to the Exercises are found on the following pages. -2-

13 Answers and selected solutions: EXERCISE : 0% % % % % % % % % % 00 25% % % % % % % % EXERCISE 2: n is 20.5% of 400 n is 26% of n n 29 3 n is 220% of is 300% of 29-3-

14 5. n n is 96% of 75 EXERCISE 3: % of 344 is n n n n n is 0.5% of is 235% of n n n n n is 0.3% of is 6.5% of 300. EXERCISE 4:. 38 is 40% of is 24% of % of 4 is is 20% of % of 44 is. -4-