EXERCISE B INDIVIDUAL PATHWAYS Activity -B- Integer multipliction doc-69 Activity -B- More integer multipliction doc-698 Activity -B- Advnced integer multipliction doc-699 Multiplying integers FLUENCY Copy nd complete the following tles. 4 ì 4 = - ì 4 = 4 ì = - ì = 4 ì = - ì = 4 ì = - ì = 4 ì 0 = - ì 0 = 4 ì - = - ì - = 4 ì - = - ì - = 4 ì - = - ì - = 4 ì -4 = - ì -4 = -6 ì -4 = -6 ì - = -6 ì - = -6 ì - = -6 ì 0 = -6 ì = -6 ì = -6 ì = -6 ì 4 = WE Evlute ech of the following. - ì ì -8 c -6 ì - d ì - e -8 ì -6 f - ì 6 g -0 ì h - ì -0 i - ì 9 j +9 ì -8 k - ì - l 0 ì - Use n pproprite method to evlute the following. - ì ì -8 ì -0 8 ì - ì ì - ì c 8 ì -4 ì - ì - ì 6 d - ì - ì - ì - ì - ì - e - ì -8 ì - ì - 4 Complete the following equtions. ì = -6 - ì = c 6 ì = - d ì - = 6 e ì = -4 f ì -9 = - g ì -4 = 80 h -0 ì = 60 i - ì = WE 4 Evlute ech of the following. (-) (-) c (-) 4 d (-) 4 e (-) f (-4) g (-) h (-4) 4 i (-) 4 j (-6) 6 Use your nswers to question to help complete the following sttements. If negtive numer is rised to n even power the nswer is (positive/negtive). If negtive numer is rised to n odd power the nswer is (positive/negtive). WE 4 Evlute the squre root of the following numers. 8 c 49 d e 00 8 If = -, = -6, c = 4 nd d = -, clculte the vlues of the following expressions. ì ì c ì - ì -d c ì -c ì -d d c ì - ì - e d ì -(-c) f ì d ì ì c UNDERSTANDING 9 For ech of the following, write three possile sets of integers tht cn e plced in the oxes to mke the eqution true sttement. ì ì = - ì ì = 6 c ì ì ì = -6 0 For ech of the following, determine whether the result is positive or negtive vlue. You do not hve to work out the vlue. - ì 4 ì -4-6 ì -0 ì -4 c - ì - ì -c ì -d ì -e Wht hppens when numer is multiplied y -? Use some exmples to illustrte your nswer. Chpter Integers 9
Digitl doc WorkSHEET. doc-6400 C The nottion -(-) is short wy of writing - ì -. Write the expression represented y ech of the following nd then use n pproprite method to determine the nswer. -(-) -(+) c -(-) d -(-(+)) e -(-(-)) f -(-(+4)) Dividing integers Division is the inverse opertion of multipliction. We cn use the multipliction fcts for directed numers to discover the division fcts for directed numers. Multipliction fct Division fct Pttern ì = 6 6 ó = or 6 = nd 6 ó = or 6 = - ì - = 6 6 ó - = - or 6 = - nd 6 ó - = - or 6 = - - ì = -6-6 ó = - or 6 = - nd -6 ó - = or = 6 positive positive = positive positive negtive = negtive negtive positive = negtive nd negtive negtive = positive When dividing two directed numers: if their signs re the sme, the nswer is positive if their signs re different, the nswer is negtive. Rememer tht division sttements cn e written s frctions nd then simplified. For exmple, = + 4 4 + =+ + = = 4 = =+ + = REFLECTION Cn we find squre roots, cue roots, fourth roots nd so on for negtive numers? WORKED EXAMPLE Evlute ech of the following. -6 ó 8 THINK 6 9 WRITE The two numers hve different signs, so the nswer is negtive (6 ó 8 = ). Cncel the common fctors (-). The two numers hve the sme signs, so the nswer is positive. -6 ó 8 = - 6 = 6 9 9 = 6 9 = 4 40 Mths Quest 8 for the Austrlin Curriculum
WORKED EXAMPLE 6 Evlute the following. 4 ó -6-8 ó -4 THINK Complete the division s if oth numers were positive numers. Determine the sign of the nswer. A positive numer divided y negtive numer is negtive numer. Complete the division s if oth numers were positive numers. Determine the sign of the nswer. A negtive numer divided y negtive numer is positive numer. WRITE 9 6 4 ) 4 ó -6 = -9 4) 8 4 4 4 0-8 ó -4 = REMEMBER When dividing two directed numers: if their signs re the sme, the nswer is positive if their signs re different, the nswer is negtive. EXERCISE C INDIVIDUAL PATHWAYS Activity -C- Integer division doc-640 Activity -C- More integer division doc-640 Activity -C- Advnced integer division doc-640 Dividing integers FLUENCY WE Evlute ech of the following. -6 ó 9 8 ó - c -8 ó d -6 ó - e 88 ó - f 0 ó - g 48 ó - h -9 ó i -6 ó - j +84 ó -4 k - ó - l 04 ó -8 WE Evlute ech of the following. 6 c d e 00 0 f - ì WE 6 Evlute the following. 960 ó -8-4 ó 9 c -66 ó - d - ó -4 e -8 ó 6 f 440 ó -9 g 4 ó - h -060 ó i -6000 ó -4 j -94 ó - k 4860 ó l -86 ó -6 Chpter Integers 4
UNDERSTANDING 4 Write three different division sttements, ech of which hs n nswer of -8. Copy nd complete the following y plcing the correct integer in the ox. - ó = -9-68 ó = 4 c ó = -8 d -8 ó = -6 e ó = - f ó -4 = -6 g - ó = h -0 ó = 6 Clculte the vlue of ech of the following y working from left to right. -0 ó 6 ó - -0 ó 4 ó - c -800 ó -4 ó - ó If = -, =, c = -4 nd d = -6, clculte the vlue of ech of the following expressions. ó c ó c ó d d ó c e ó d f ó ó d 8 If = -4, =, c = -4 nd d = -, clculte the vlue of ech of the following expressions. ó ì c d ì c ó ó c c ó c ó d ì d c ì ó d ó e ì ó d ó d f ó d ì c ó 9 Copy nd complete the following tles: ì -6 +8 ì -9-0 -40 8 0 0 - -6 +6 0-4 6-99 -6-8 0 Copy nd complete the following tles. Divide the numer on the top y the numer on the side. ó 4-0 -8 ó -4 - - -0 - -8-4 6-6 REFLECTION Cn you list 4 res in rel life where directed numers re used? D Comined opertions on integers The mthemticl rules out order of opertions pply when we work with directed numers. BIDMAS helps us to rememer the correct order in which we should perform the vrious opertions. This mens tht we do rckets first; then powers or indices; then ì nd ó (working from left to right); nd finlly + nd - (working from left to right). 4 Mths Quest 8 for the Austrlin Curriculum
Answers CHAPTER Numercy A Set A D D B 4 A B 6. cm A 8 0è 9 A 0 C B C 8 cm 4 D B 6. m 4 8 C 9 B 0 C D A B 4 B C 6 A D 8 C 9 B 0 C B Set B B C D 4 A C 6 B B 8 4.6 s 9 C 0 C B D B 4 D C 6 B C 8 C 9 C 0 D D 0 B 4 C 0è 6 40% pegs in ech yellow ucket; 8 pegs in ech lue ucket. 8 B 9 D 0 B C Set C D A pm 4 B C 6 B D 8 C 9 C 0 4 0 dys B A 4 B B 6 A D 8 A 9 B 0 8 cm 4 B B 4 C D 6 A C 8 B 9 B 0 D D Set D B C D 4 D C 6 A D 8 A 9 B 0 D C B A 4 B 6 A D 8 A 9 D 0 D C C 4 4 C C 6 B B 8 A 9 C 0 B E Set E A B B 4 D C 6 60 km C 8 D 9 C 0 B B C C 4 D C 6 A C 8 4 km 9 C 0 C C A 4 C D 6 A C 8 D 9 B 0 C F Set F C D C 4 C D 6 B B 8 A 9 A 0 B B B 6 800 4 C 6 6 C C 8 9 9, 90 0 D True C A 4 A % 6 C 0 8 B 9 B 0 C CHAPTER Integers Are you redy? 0 4 6 8 9 0, 8 0, 4 c, 0 4869 6 c 944 4,,, 9, 0, 9, 4, 6 6, 4, 9, 0, 9,,, 4 84 6 4 6 c 8 8 c d e f 80 A Adding nd sutrcting integers, -4, 0, -6 0, -, -4-0, -, -0 c,, d -8, -6, -4 - -0 c - d - e 9 f g - h 0 4-4 c - d e 6 f -6 g h -8 c -4 d - e f - g -9 h 8 6 - -9 c d e -0 f g -40 h 8 i j -4 k - l 0 m - n o - p q 9 r - + -8-8 -6-4 9-4 6 - - - 9-6 -4 9-4 6-9 - 6 - Answers A A A E Answers 449
c d - - - 8-4 -4 0-6 - - 6-9 4-8 -8 66-9 -9 4 + - 9 - - -6 4 8-6 6 0 0 - - 8-8 -8-9 -9 - - - 9-4 6 - - -4 6-4 - 6 - - 44-4 - -8 9 8 Check with your techer. 9 èc 6 èc c 98 èc 0 èc -0-96 c 0 d -4 c d -0 e f Correct Incorrect; 6 c Incorrect; - d Correct e Correct f Incorrect; - 4 - - c - The nswers re the sme. 6 - - c - The nswers re the sme. B Multiplying integers 4 ì 4 = 6 - ì 4 = -0-6 ì -4 = 4 4 ì = - ì = - -6 ì - = 8 4 ì = 8 - ì = -0-6 ì - = 4 ì = 4 - ì = - -6 ì - = 6 4 ì 0 = 0 - ì 0 = 0-6 ì 0 = 0 4 ì - = -4 - ì - = -6 ì = -6 4 ì - = -8 - ì - = 0-6 ì = - 4 ì - = - - ì - = -6 ì = -8 4 ì -4 = -6 - ì -4 = 0-6 ì 4 = -4-0 -4 c 4 d -6 e 48 f -4 g -0 h 0 i -6 j - k l -00-800 c -9 d 4 e 60 4-9 - c - d - e -6 f 8 g -0 h -6 i - -8 9 c 6 d 8 e - f 6 g - h 6 i 6 j -6 6 Positive Negtive ê ê9 c ê d ê e ê0 8 48-6 c d 6 e - f -6 9 Check with your techer. 0 Positive Negtive c Negtive If positive numer is multiplied y -, the numer ecomes negtive. If negtive numer is multiplied y -, the numer ecomes positive. - c d e - f 4 C Dividing integers - -4 c -4 d 6 e -8 f 0 g -6 h -4 i 8 j -46 k l -8-4 c d - e f -0 - c 8 d e -4 f -60 g - h -80 i 0 j 6 k 4 l 6 4 Check with your techer. - c -9 d e - f 4 g - h -0 6 6 c -0-4 c 4 d e f 8 48-6 c - 9 d -4 e ì - 4-6 8-6 - 8-4 -0 0-40 60-80 - 0-0 0-40 - 4-8 4-6 ì - -9-6 0-8 -4-4 - -60 6 08 84 - - 99 0-6 -8-4 0 4-0 -8 - - -6 4 - -0 4 4 0 0-4 6 8 8 4-4 -6-4 8-8 -4 6 6 - - 9-4 -6-4 -8 6 9 f -4 40 Answers