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Academic Skills Advice Summary Fractions 2 3 2 3 means that something has been cut into 3 equal pieces and you have 2 of them. also means 2 ÷ 3 (written as 3 2.00 when you do the calculation) 2 If the top and bottom number are the same you have a whole one: 2 = 1 3 3 = 1 etc Finding Fractions of Numbers: ๐ ๐ ๐ ๐ To find ๐ of a number ÷ by 2, to find ๐ ÷ by 3, to find ๐ ÷ by 4, to find ๐ ÷ by 5, etc. Always divide by the bottom number, then multiply by the top number: x Answer 2 3 of 12 12 ÷ 3 = 4 4 x 2 = 8 (to find 1 third ÷3 then x2 to find 2 thirds). ÷ Equivalent Fractions: Some fractions are exactly the same size as each other. You can times (multiply) or divide the top and bottom numbers as long as you remember the rule of fractions: Always do the same to the top as the bottom Nb. When you divide make sure you use a number that you can divide both the top and the bottom by. This is called simplifying or cancelling. Improper Fractions & Mixed Numbers: An Improper fraction is top heavy (๐๐ 12 5 ). 2 A mixed number has both a whole number and a fraction (๐๐ 5 3 ). Converting from Improper to Mixed: Divide the bottom number into the top then write the remainder as the fraction. Example: 13 5 How many 5โs in 13 (2) how many left over? (3) = 2 3 5 Converting from Mixed to Improper: Multiply the whole number by the bottom number of the fraction then add on the top number of the fraction. Example: 4 2 3 4 x 3 = 12 then add the extra 2 on. You have 14 thirds = © H Jackson 2012 / ACADEMIC SKILLS 14 3 1 Multiplying Fractions: ๏ท ๏ท Cancel first (remember always to cancel a pair โ top & bottom) Multiply top by top and bottom by bottom 1 2 3 10 × 25 = 21 2 (1×2) The 3 (top) and the 21 (bottom) both divide by 3. 35 (5×7) The 10 (top) and the 25 (bottom) both divide by 5. 7 5 Dividing Fractions: ๏ท ๏ท ๏ท Change the divide sign into a multiplication sign. Turn the second fraction upside down. Multiply as above. 2 5 ÷ 3 7 = 2 3 × 7 = 5 14 (2×7) 15 (3×5) Second fraction is turned upside down. ÷ becomes x Adding & Subtracting Fractions: ๏ท ๏ท Make sure the denominators are the same (using equivalent fractions) Add or subtract the top numbers only. 2 5 + 1 3 2 Top & bottom x3 5 + 1 3 Top & bottom x5 6 5 15 15 Now we have: 6 5 11 + = (๐กโ๐ ๐๐๐๐๐ก๐๐๐๐ ๐๐๐ ๐๐ ๐๐๐๐๐ ๐๐ ๐กโ๐ ๐๐๐๐๐๐๐๐๐ก๐๐๐ ๐๐๐ ๐กโ๐ ๐ ๐๐๐) 15 15 15 Nb. Use exactly the same method for take away but subtract the top numbers instead of adding. 6 15 โ 5 15 = 1 15 © H Jackson 2012 / ACADEMIC SKILLS 2