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Multiply and Divide with Algebra Nelson Marlborough Institute of Technology TE WHARE WANANGA O TE TAU IHU These two operations are opposites. 63=2 and 3X2=6 How to recognise multiplication Usually shown by ( ). And by X. Often shown by parts of the term sitting next to each other. “4(2a)” means 4 times 2a. “5 X 6” means 5 times 6. “7ab” means 7 times a times b. Sometimes shown as a dot Sometimes with the words “expand” “7 . 6” means 7 times 6. “Expand 8(3a)” means 8 times 3a. How to multiply You MUST MULTIPLY all parts of the terms i) Multiply the signs If signs are different … answer is negative (-) If signs are the same … answer is positive (+) - 4 X 5 = -20 4 (2) = 8 7 X –2 = -14 -3 X –6 = 18 ii) Multiply the coefficients 2c(3d) = 6cd 3z4y = 12zy iii) Multiply the variables 12a X 2 = 24a If the letters are different … sit the letters beside each other, in alphabetical order If the letters are the same … add the indices a X b = ab f2 X af3 = af5 Practise: 1. –2 X 4y 2. 3b X 7b 3. 3(7de).2 4. 5.2f 5. zy2 X y 6. –2d(6abc) 7. 6s X s3 X 7s2 q X rs = qrs s X s 2 = s3 8. m(n . n X q) 9. 5 X zy X 4 10. a X a X B X B Updated 22/06/2017 Multiply and Divide with Algebra Nelson Marlborough Institute of Technology TE WHARE WANANGA O TE TAU IHU How to recognise division Usually shown by the sign. “15 3” means 15 divided by 3. Also shown in fraction form. “ ½ “ means 1 divided by 2. How to divide i) Divide the numbers This can be done as simple division If it is fraction form, you have the option of dividing by simplifying = find a number that will go in both numerator and denominator evenly. 24a 2 = 12a -16 8 = -2 4/6 = 42/62 = 2/3 6/12 = 0.5 ii) Divide the variables Any letter divided by itself is 1, so both become an unwritten 1 (they disappear; are ‘cancelled out’) If the letters are the same and have indices … subtract the indices ab a = b 72qrs rq = 72s Practise: 1. 5ac / 10abc 2. 2abc / 4b 3. 8mn 2m 4. 4b (k/4) 5. –3r / r 6. –6d 2abc -cd /d = -c ab3 / a2 b2 = b/a 7. q3 q2 8. f4 g3 9. 15k / 15k 10. a a X B Answers for multiplication 1) –8y 2) 21b2 3) 42de 4) 10f 5) y3z 6) –12abcd 7) 42s6 8) mn2q 9) 20yz 10) a2B2 Answers for division 1) 1/2b = 0.5/b 2) ac/2 = 0.5ac 3) 4n 4) bK 5) –3 6) (–3d)/(abc) 7) q 8) f4g3 9) 1 10) B Updated 22/06/2017 Library Learning Centre STUDY SUPPORT