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Fractions, Decimals and Percents…Oh My!! Fractions, decimals and percents all represent the same thing – a part of a whole amount. As much as we try to avoid them, they are in our everyday lives. We use percents when figuring sales tax, how much tip to leave or how much we are going to save when that pair of shoes goes on sale. We use fractions when we cook. We see decimals at the grocery store and on our bank statements. The following is a list of some common fractions and their decimal and percent equivalents. Fraction Decimal Percent Fraction Decimal Percent 1 5 1 0.10 10% 0.5 50% 10 10 2 1 6 3 0.125 12.5% 0.6 60% 8 10 5 1 5 16.67% 0.625 62.5% 0.16 6 8 2 1 2 0.2 20% 66.67% 0.6 10 5 3 7 2 1 .25 25% 0.7 70% 10 8 4 3 6 3 0.3 30% 0.75 75% 10 8 4 1 8 4 33.3% 0.8 80% 0.3 3 10 5 3 7 0.375 37.5% 0.875 87.5% 8 8 4 2 9 0.4 40% 0.9 90% 10 5 10 Problem #1: A class of 30 students took a Math test. Seven students made an A. What percentage of the class made an A? 7 30 To convert this fraction to a decimal, divide the top number by the bottom number. On your calculator, you will key in “7 30 =”. The result should be 0.23333… This is the decimal equivalent. You will then convert this decimal to a percent by moving the decimal two places to the right. So the percentage of the class that made an A is 23.3%. Solution: First set up a fraction - 7 out of 30 students made an A. Fraction: Rules: 1. To convert a fraction to a decimal: divide the numerator by the denominator. 2. To convert a decimal to a percent: move the decimal two places to the right. 3. To convert a percent to a decimal: move the decimal two places to the left. numerator denominator Problem #2: A poll of the students at Lakeside High School resulted in a finding that 77% of the population was involved in some sort of extra-curricular activity. If there are 1700 students at LHS, how many are involved in extra-curricular activities? Solution: First convert the percent to a decimal: The decimal equivalent of 77% is 0.77. Next multiply this by the number of students. 0.77 1700 = 1309. So 1,309 students are involved in extra- curricular activities at Lakeside. Problem #3: Your bill at the restaurant was $40.50. How much will your 15% tip be? Solution: 40.50 0.15 = 6.075. So you should leave at least $6.08. Don’t have a calculator or one of those “how much tip to leave” cards? Here is a neat trick for figuring 15%...You can figure 10% of anything by moving the decimal one place to the left. So 10% is about $4.00. Now the 5% you need is half of the 10% you just found. Half of $4 is 2$. So add the two numbers: 4 + 2 = 6. Your tip is roughly $6.00. Problem #4: You want to find one-fourth of 188. What can you multiply by? Divide by? Solution: One-fourth is 0.25, so you can multiply by the decimal equivalent of the fraction. You can also divide by 4. ADDING/SUBTRACTING FRACTIONS You must have a common denominator. 1 5 3 5 4 5 4 1 12 5 7 5 3 15 15 15 Note: Any fraction with the same numerator and denominator is equivalent to 1. 3 11 16 29 1 For example… 3 11 16 29 MULTIPLYING/DIVIDING FRACTIONS No common denominator is necessary when multiplying or dividing fractions. To multiply simply find the product of the numerators and the denominators. 2 4 8 For example: 3 7 21 Division requires that you multiply by the reciprocal: 2 1 2 2 4 × 5 2 5 1 5 When calculating complicated, multistep or lengthy problems that require you to give a decimal approximation, don’t clear out your calculator and round until the very end. You get a better – more exact answer when you wait! Math 2 – Fraction/Decimal/Percent Review PRACTICE Show your work and be able to explain the process you used in solving the problems. 1. Mr. Al Gebra took a survey of his class and 7 of the 28 students did not do their homework the night before. What percent of the students did do the homework? 2. Maggie’s family went out to eat and when the bill arrived it was $52.45. They plan on leaving a 15% gratuity. How much tip did they leave? Explain how you can quickly estimate the tip amount. 3. Twenty percent of the profits from a recent fundraiser went toward operating costs. What are two ways to compute 20% of $1200? 4. Mr. Reauber loves to cook! He wants to make his favorite recipe, but the recipe feeds 8 and he is only cooking for 2. What fraction should he use to cut the recipe down? It calls for 2 cups of milk. How much milk will he need? .