Fractions What you need to know S.O Grady
What is a fraction? A fraction is a part of a whole (). Fractions consist of two numbers, a numerator and a denominator. Top number How many parts we have Bottom number- How many parts the whole is divided into Example We have parts out of parts Equivalent Fractions Equivalent fractions are fractions that look different but show exactly the same amount. Simplifying Fractions We are often given fractions and asked to simplify them that is, change them to an equivalent fraction, using smaller numbers. To simplify fractions, we divide the numerator and the denominator by the same number. We say a fraction is in its simplest form when it is simplified as much as it can be. Example Write these fractions in their simplest form ) ) This is the simplest form of because there are no other numbers which will divide into both and. ) 0 ) 9 S.O Grady
Mixed and Top Heavy Fractions A mixed number contains both whole numbers and fractions, example, A top heavy (or improper) fraction is a fraction where the numerator is bigger than the denominator, example 9, Top number Bottom number To change from a mixed number to a top heavy fraction Example : Change to a top heavy fraction 0 (( x ) ) thirds 0 thirds There are thirds in every whole number, therefore there are ( x ) thirds in Example : (( x ) ) eights eights Change these mixed numbers to top heavy fractions: ) ) Add the thirds 9 0 ) To change from a top heavy fraction to a mixed number Example : Change to a mixed number remainder There are quarters in every whole number. will tell us how many whole numbers we have. Example : remainder Change these top heavy fractions into mixed numbers: ) ) 9 whole numbers and quarters (not enough to make any more whole numbers) S.O Grady )
Adding and Subtracting Fractions There is one simple rule that you must follow when adding or subtracting fractions: Example You can only add/subtract fractions if they have the same denominator Example Often referred to as a Common denominator These fractions have a common denominator Mixed numbers must first be changed to top heavy fractions Example 9 Example These fractions have a common denominator Now try for yourself: ) ) ) S.O Grady
LCM lowest number both numbers will divide evenly into Adding and Subtracting Harder Fractions Earlier we saw that: You can only add/subtract fractions if they have a common denominator The denominators are not always the same (common). In these cases we must create equivalent fractions (by multiplying top and bottom by the same number), so that the denominators are the same. Example The denominators (thirds and halves) are not the same/ not common Find the lowest common multiple (LCM) of and () Change and to sixths (by multiplying top and bottom by the same number) Example 0 0 0 0 0 Not equal to LCM of 0 and is 0 Now try for yourself: ) ) ) S.O Grady
Mixed numbers must first be changed to top heavy fractions Example 9 9 LCM of and is Now try for yourself: ) ) ) Summary: To add/subtract fractions Make all mixed numbers into top heavy fractions Find a common denominator (use the LCM) Add/subtract fractions Change back into a mixed number and simplify, if possible S.O Grady
Multiplying Fractions To multiply fractions Change all mixed fractions into top heavy fractions Multiply the numerators to get the new numerator Multiply the denominators to get the new denominator Change to a mixed number and simplify, if possible Example Example x x 0 x x Mixed numbers must first be changed to top heavy fractions Example Example 0 x x Make top heavy Change to mixed number Simplify 0 0 x x Multiply the fractions: ) ) ) ) 9 S.O Grady
Dividing Fractions To divide fractions Change all mixed fractions into top heavy fractions Invert (swap numerator and denominator) the number you are dividing by Only differences to multiplying Change the sign to a multiply Multiply the fractions Change to mixed number and simplify, if possible Example Example 9 9 Invert nd number and multiply 9 9 0 9 0 Invert nd number and multiply Mixed numbers must first be changed to top heavy fractions Example 0 Invert nd number and multiply Do the following: ) ) S.O Grady
Fractions and Decimals Fractions can be turned into decimals by dividing the numerator by the denominator. Here are some you should know: Fraction Calculation Decimal 0 00 0. 0. 0. 0. 0 0. 0. 0. 00 0.0 (this represents the whole) The values listed in the table above should be learned as they will help when doing other calculations. We would use a calculator to change more difficult fractions into decimals. Change the following fractions into decimals (round your answer to decimal places, where necessary): ) ) ) ) S.O Grady 9
Notes S.O Grady 0
I can Hillhead High School Explain what a fraction is Explain equivalent fractions Simplify fractions Change a top heavy fraction to a mixed number Change a mixed number to a top heavy fraction Add fractions with common denominators Add fractions with different denominators Subtract fractions with common denominators Subtract fractions with different denominators Multiply fractions Divide Fractions Change from a fraction to a decimal S.O Grady