Transcript Fraction
Basics of Percent: Fractions Developed by Angela Lavine, PhD What you will learn…. How to convert between fractions, decimals, percents & mixed numbers Terms…. Fraction – a fractions is simply a part of a whole. For example: A child has a 10 slice pizza, she eats 2 slices. A fraction for this would be: 2/10 or 1/5 Percentage – A rate per 100. Parts of the whole. Using the example above, what percentage of the whole is eaten? 2 out of 10 slices = 20% of the pizza eaten Mixed Numbers – a whole number plus a fraction. Example: 1 ½ Explanation Why convert a fraction into a percentage? You may find it easier to compare two or more numbers by looking at them as a percentages than as fractions. Explanation To write a PERCENT as a FRACTION: 1.Write the percent as the numerator with a denominator of 100: 10% 10/100 2. Simplify (put in lowest possible terms – look for the GCF): 10/100 = 1/10 To find the Greatest Common Factor (GCF): List the factor of each… 10: 1, 2, 5, 10 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 10 is the GCF of both numbers Take that factor and divide numerator and denominator by it 10/10 = 1 100/10 = 10 Simplest form: 10 % = 1/10 Worked examples To write a PERCENT as a FRACTION: 42% 42/100 = (simplify * find the GCF) = 42: 1, 2, 3, 6, 7, 14, 21, 42 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 GCF: 2 42/2 = 21 100/2 = 50 42% = 21/50 Practice Problems Write 68% as a fraction. Write 25% as a fraction. Solutions 68% 25% 68/100 68: 1, 2, 4, 17, 34, 68 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 GCF: 4 68/4 = 17 100/4 = 25 68% = 17/25 25/100 25: 1, 25 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 GCF: 25 25/25 = 1 100/25 = 4 25% = 1/4 Explanation How to write a FRACTION as a PERCENT: 1.Divide the numerator by the denominator: 1/5 = .2 2.Multiply by 100 .2 * 100 = 20 1/5 = 20% Worked Examples Write the following FRACTIONS as PERCENTAGES: 3/5 = 3/5 = .6 .6 * 100 = 60 3/5 = 60% 21/43 = 21/43 = .49 .49 * 100 = 49 21/43 = 49% Practice Problems Write the following FRACTIONS as PERCENTAGES: 73/81 9/13 27/31 Solutions 73/81 73/81 = .9 .9 * 100 = 90 73/81 = 90% 9/13 9/13 = .69 .69 * 100 = 69 9/13 = 69% 27/31 27/31 = .87 .87 * 100 = 87 27/31 = 87% Explanation To write a FRACTION as a MIXED NUMBER: 1. When the NUMERATOR is larger than the DENOMINATOR, think of the problem as a division problem to get the mixed number: 5/2 = 5/2 = 2 with 1 remaining Put the remaining number over the original DENOMINATOR 5/2 = 2 ½ You now have a MIXED NUMBER. Practice Problems Write the following FRACTIONS as MIXED NUMBERS: 10/3 11/7 23/3 Solutions 10/3 10/3 = 3 with 1 remaining 10/3 = 3 1/3 11/7 11/7 = 1 with 4 remaining 11/7 = 1 4/7 23/3 23/3 = 7 with 2 remaining 23/3 = 7 2/3 Explanation To write a MIXED NUMBER as a PERCENTAGE: 1. Convert the MIXED NUMBER to an IMPROPER FRACTION: 2½= Multiple the DENOMINATOR by the WHOLE NUMBER 2*2=4 Add the NUMERATOR 4 + 1 = 5 Use the original DENOMANTOR: 5/2 You now have a an IMPROPER FRACTION. 2. Take your fraction and follow the steps to convert to a PERCENTAGE: 5/2 = 2.5 2.5 * 100 = 250 250% Practice Problems Write the following MIXED NUMBERS as PERCENTAGES: 3 1/3 1 4/7 Solutions 3 1/3 3*3=9 9 + 1 = 10 10/3 10/3 = 3.33 3.33 * 100 = 333 333% 1 4/7 7*1=7 7 + 4 = 11 11/7 11/7 = 1.57 1.57 * 100 = 157 157% Wrapping Up FRACTIONS can easily be converted in PERCENTAGES, DECIMALS & MIXED NUMBERS and vise versa. You can convert to make the numbers easiest for you to analyze and help you to complete any problems successfully. ***GOOD LUCK!***