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FRACTIONS WHAT IS A FRACTION? A fraction is part of a whole one. 2/5 means 2 parts of 5. The top number is the numerator; the bottom one is the denominator. A fraction like 2/5 is called a proper fraction. A fraction like 12/7 is called an improper fraction. A fraction like 14/9 is called a mixed number. (If the numerator and the denominator are the same, then it is a whole one, ie 5/5 = 1) Addition and Subtraction of Fractions The example shows the basic principles of adding and subtracting fractions. Example - Addition 1/8 +¾ First make the denominators the same 3 (x2) = 6 4 (X2) = 8 Replace ¾ with 6/8 so that the denominators are now the same. 1/8 + 6/8 = 7/8 Add the numerators 1 + 6 = 7 Do not add the denominators. The denominator stays the same. Example – Subtraction ¾ - 3/16 First make the denominators the same 3 (x4) = 12 4 (x4) = 16 ¾ is equivalent to 12/16. Replace ¾ with 12/16 12/16 – 3/16 Subtract the numerators but not the denominators The denominator stays the same. = 9/16 Page 1 of 3 FRACTIONS Fractions of a Quantity Example: In a class of 40 students, 2/5 of them are left-handed. How many are left-handed? Divide 40 by 5 to find 1/5 (one fifth) = 8 So to find 2/5 (two fifths) multiply the answer by 2….. 8 x 2= 16 So 16 are left handed Example: Out of 36 students 2/3 walk to college. How many is this? To find one third - divide 36 by 3 = 12 To find two thirds - multiply by 2, so 2 x 12 = 24 24 students walk to college Equivalent Fractions: Example: From the diagram it can be seen that ½ = 2/4 ½ 2 These are fractions that have the same value /4 Example: 7/9 = ?/27 Fractions can be changed into their equivalent by either multiplying or dividing the numerator and denominator by the same number. 7 (x3) 21 9 (x3) 27 Multiply the top and bottom by 3 35/50 = 7/? 35 (÷5) 7 50 (÷5) 10 Divide the top and bottom by 5 Simplifying Fractions Fractions can be simplified if the numerator and the denominator have a common factor. Example: Simplify 12/18 6 is the highest common factor of 12 and 18 Divide both the top and bottom number by 6 12 (÷6) = 2 18 (÷6) = 3 Page 2 of 3 FRACTIONS Multiplication and Division of Fractions When multiplying and dividing fractions, write out whole or mixed numbers as improper fractions before starting. (eg 21/2 as 5/2) Example: 4 x 2 = 8 Multiply the numerators together 7 11 77 Multiply the denominators together. For division, change it into a multiplication by turning the second fraction upside down, (taking the reciprocal) and multiply both fractions together. Example: 7 ÷ 12 9 18 Turn the 7 x 18 = 126 = 1 1 9 12 108 6 Page 3 of 3 12/18 upside down and multiply with 7/9 Rewrite back as a mixed number