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/ 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% 68/100 68: 1, 2, 4, 17, 34, : 1, 2, 4, 5, 10, 20, 25, 50, 100 GCF: 4 68/4 = /4 = 25 68% = 17/25  25% 25/100 25: 1, : 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 = 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 = * 100 = 49 21/43 = 49%

Practice Problems Write the following FRACTIONS as PERCENTAGES: 73/819/1327/31

Solutions 73/81 73/81 =.9.9 * 100 = 90 73/81 = 90% 9/13 9/13 = * 100 = 69 9/13 = 69% 27/31 27/31 = * 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: 10/311/723/3

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: 2 ½ = Multiple the DENOMINATOR by the WHOLE NUMBER 2 * 2 = 4 Add the NUMERATOR = 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: 2. Take your fraction and follow the steps to convert to a PERCENTAGE: 5/2 = * 100 = %

Practice Problems Write the following MIXED NUMBERS as PERCENTAGES: 3 1/3 1 4/7

Solutions 3 1/3 3 * 3 = = 10 10/3 10/3 = * 100 = % 1 4/7 7 * 1 = = 11 11/7 11/7 = * 100 = %

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!***