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1 Types f numers Nturl numers re ll the psitive unting numers ",,,...,. Integers re ll the psitive (+) n negtive (-) whle numers (inluing zer). irle ll the numers elw tht elng t the fmily knwn s integers. (psst!: sme f them nee t e simplifie y lulting their vlue first) Ple eh f these numers int their rret grup elw t lssify them. Irrtinl numers n t e written s frtin Rtinl numers n e written s frtin Integers: the psitive n negtive whle rtinl numers inluing 0. Put the speil - types f rtinl numers int their rret grup Nturl numers: the unting rtinl numers (nt inluing 0). H SERIES TOPI P Lerning

2 Mesuring instruments n integers There re mny pplitins fr irete numers. Thermmeters re gret exmple euse the temperture n g elw zer. The temperture t miy ws 0 egrees elsius. During the fternn, the temperture rse egrees efre flling 9 egrees in the lte fternn. (i) She in the thermmeter shwing the lte fternn temperture. Strting t 0, temperture hnge + then -9 rse =+ n flling =- Temperture t miy 0 Temperture y lte fternn entigre (ii) Wht irete numer gives the verll hnge in temperture etween the tw reings? Overll hnge =+ - 9 =-5 Digitl sles nee t use irete numers t lulte hnges in mss. Use this infrmtin t lulte the mss f lives purhse y Mri t her ll Deli: Mri ske fr 500 g f lives. After first weighing 575 g f lives, the Deli wner tk ut 98 g n then put k 6 g. The irete numer sentene fr this is: + 575g- 98g+ 6g Inrese = + n erese = - ` Mri purhse + 575g- 98g+ 6g = 5g f lives If the first term is psitive, we usully n't write in the plus sign. P Lerning H SERIES TOPI

3 Mesuring instruments n integers She in eh thermmeter elw t urtely isply these tempertures: (i) (ii) - 5 (iii) 6 (iv) 0 (v) 8 ve zer (vi) elw zer entigre entigre entigre entigre entigre entigre This thermmeter shws reing f t the strt. Write the new reings tht wul e isplye fter eh f these hnges in temperture: entigre (i) Inreses y (ii) Bemes 8 ler (iii) Dereses y (iv) Wrms up y (v) Rse y (vi) Drppe 8 9 (vii) Derese y 7 then inrese y (viii) Wrms y n then further 9 (ix) ls 5 efre wrming y 9 (x) hnges t 0 efre rpping H SERIES TOPI P Lerning

4 MEASURING INSTRUMENTS AND INTEGERS * Hw es it wrk? Mesuring instruments n integers The mss f glss ntiner with sme wter in it is shwn elw:.../.../ grms Write wn the new reing n the sles fter ny ne f the fllwing hnges urre. (i) 0 g f wter pure int the glss grms (ii) g f wter ws spille ut f the glss grms (iii) 88 g f flvur syrup ws stirre in n then 50 g ws runk grms (iv) A similr glss with the sme munt f wter ws ple n the sles next t this ne. grms (v) A up fille with 6 g f wter ws emptie int the glss n uring the y, 7 g evprte wy euse the rm ws ht. grms Try this triky ne! A glss ntiner hling l wter elw ws ple n the igitl sles fter eing mve frm rm int rm. The glss h llete grms f wter (thrugh press lle nenstin) n the utsie fr every egree rise in rm temperture. Wht ws the riginl mss f the wter fille glss if grms f wter ws spilt uring the mve? 6 55 entigre 058 grms P Lerning H SERIES TOPI 5

5 Mgnitue n iretin f integers Integers re psitive (+) n negtive (-) whle numers, inluing zers. They tell us the size (mgnitue) n iretin f vlues ssite with hnge. - + It is imprtnt t first eie wht will e the psitive iretin. If up ( ) is psitive, then the ppsite iretin wn ( ) is negtive If right ( ) is psitive, then the ppsite iretin left ( ) is negtive If htter is psitive (+), then the ppsite ler is negtive (-) GROW, FORWARD, ABOVE, FURTHER, MORE, FASTER, EXTRA, ASEND, HIGHER, OVER, INREASE, WARMER, NORTH, EAST, REVERSE, BELOW, LOSER, LESS, SLOWER, REDUE, DESEND, LOWER, UNDER, DEREASE, OOLER, SOUTH, WEST, SHRINK, POSITIVE NEGATIVE These re sme ther wrs usully ssite with psitive n negtive irete numers Only negtive numers must hve the sign written in frnt. Write wn the irete numer fr eh f these sttements: (i) 5 egrees elw the zer: =-5 The mgnitue f the temperture is 5 egrees (ii) 0 egrees ve the zer: =+ 0 The mgnitue f the temperture is 0 egrees = 0 (iii) $ extr mney: The psitive sign (+) n e hien =+ $ = $ The mgnitue f the mney is $ The irete numer f n munt left fter sme hnges represents the verll hnge. One y Mtt strte with n mney n ws given $0. He spent $ f it wnling musi. Wht is his verll hnge f mney n this y? The hnge in mney fr Mtt uring this y ws: $ 0 + $0 - $ = $6 left ` the verll hnge in mney fr Mtt n this y is +$6 The finl irete vlue = verll hnge 6 H SERIES TOPI P Lerning

6 MAGNITUDE AND DIRETION OF INTEGERS * Hw es it wrk? Mgnitue n iretin f integers Fr eh f these sttements, write wn: (i) the irete numer tht mthes it n, (ii) the mgnitue f the irete numer..../.../0... The tree in Jmie s yr grew metres in ne yer. (i) Direte numer: (ii) Mgnitue f the tree s grwth: The sme tree ws then trimme whih reue the height f the tree y metres. (iii) Direte numer: (iv) Mgnitue f the reutin in height: Aki wlke 50 m West frm her strting pint. (i) Direte numer: (ii) Mgnitue f the istne Aki wlke: Aki then turne run n wlke nther 600 m Est (iii) Direte numer: (iv) Mgnitue f this istne wlke y Aki: Sen s nk unt lne erne interest n inrese y $. (i) Direte numer: (ii) Mgnitue f Sen's nk lne inrese: Sen s nk unt lne then hnge ue t eing hrge $ in nk fees. (iii) Direte numer: (iv) Mgnitue f the hnge in Sen's nk lne: Think refully fr eh f these sttements n write wn the irete numer tht mthes the verll hnge. Pip ws given $ n then spent $5 n ress the sme y. Direte numer fr the verll hnge in mney tht y: The temperture initilly inrese y 6 egrees n then inrese y further egrees. +$9 Direte numer fr the verll hnge in temperture: Nigel went wn 6 rungs n ler n then up rungs. Direte numer fr the verll hnge in ler rungs: mern's lness rse y pints when he plye guitr, n further 0 pints when he i mths. Direte numer fr the verll hnge in mern's lness fter ing th tivities: e Shirmee hike km Nrth, km Est n then 9 km Suth. Nrth is the psitive iretin. Direte numer fr the verll hnge in Shirmee's Nrth-Suth mvement: f Aele's hir grew frm 0 m t 0 m lng t the k. After hir ut it ws nly 7 m lng. Direte numer fr the verll hnge in Aele's hir length frm the initil 0 m: P Lerning H SERIES TOPI 7

7 Asening n esening rer When mpring irete numers, it ften helps t rrnge them int numeril rer. Asening Desening Asening rer = lwest t highest Desening rer = highest t lwest Dn t e trike y the mgnitue f numer. Whih f these tw vlues is higher? -0-0 represents very l temperture (elw/less thn 0 ) is l temperture, hwever it is (ve/greter thn 0 ) ` is higher vlue thn is igger numer in mgnitue thn, hwever the negtive sign mkes it lwer in vlue entigre Let s lk t n sening n esening rer exmple. Fr the numers -,0,.5, -6,5.,, - 0,5. : (i) Arrnge them int sening rer -0, -6, -,0,,5.,5.,.5 Lwest negtive Highest psitive (ii) Arrnge them int esening rer.5,5.,5.,,0, -, -6, -0 Highest psitive Lwest negtive Orer is ppsite t sening 8 H SERIES TOPI P Lerning

8 ASENDING AND DESENDING ORDER * Hw es it wrk? Asening n esening rer irle the wr tht represents the rer f the vlues in these sttements:.../.../0... e f Shrtest t Tllest Asening Desening Lngest t shrtest Asening Desening lsest t frthest Asening Desening Wrmest t lest Asening Desening Heviest t lightest Asening Desening Thinnest t wiest Asening Desening Arrnge the fllwing grups f numers int sening rer (lwest t highest).,0,7,,,,,5,0,9, 0, 8,,, ,.,.6,0, - - e -,,, -.5,, 5, Arrnge the fllwing grups f numers int esening rer (highest t lwest).,6,5,8,,, 0,,,8,9 9,, 6, 8, e.6,.9,.,.0, , -, -, -.,., -0, P Lerning H SERIES TOPI 9

9 OMBO TIME * OMBO TIME * OMBO TIME * Hw es it wrk? m Time! Elevtr Riing Asening n esening rer A eprtment stre elevtr pertr strte wrk n the r flr f the 5 strey uiling. Fr the first 5 minutes f wrk, the pertr trvelle t the fllwing flrs in the rer written: th flr G > < > < 8 th flr Grun flr n flr Grun flr 5 th flr th flr 0 th flr 5 th flr If up is psitive n wn is negtive, write numers tht represent the mvement f the elevtr pertr uring the first 5 minutes f wrk. Arrnge the irete mvements int esening rer. During the first 5 minutes, i the pertr mstly sen r esen in the elevtr? Explin yu nswer..../.../ H SERIES TOPI P Lerning

10 The numer line Direte numers n e pltte n numer line t instntly see their rer f vlue. Vlues erese (esening) Vlues inrese (sening) Lwer numers re further left n higher numers re further right. Disply the numers -, -, 7 n numer line Use the pltte pints t mpre the vlues f: (i) -, -: - is further left thn -, `- - (ii) -, 7: - is further left thn 7, `- 7 Rememer: mens 'less thn' n mens 'greter thn' This exmple requests numers t e pltte using given rule. Disply ll the even psitive integers etween -5 n n numer line. Even n psitive Write these numers in esening rer. Re the numers frm right t left ( ) ` The numers in esening rer re:,0,8,6,, Hlf vlues re pltte y pling the t hlf-wy etween the integers n either sie. Disply the numers, -,, - 55., 9, n numer line is hlf wy etween -5 n -6 is hlf wy etween n 5 Write these numers in sening rer. Re the numers frm left t right ( ) ` The numers in sening rer re: -5.5,-,0,,, 9 P Lerning H SERIES TOPI

11 THE NUMBER LINE * THE NUMBER LINE * Hw es it wrk? The numer line Insert the rret syml (less thn) r (greter thn) fr eh f these..../.../ e 8-8 f g - 0 h i j k l List the numers isplye elw in sening rer List the numers isplye elw in esening rer H SERIES TOPI P Lerning

12 The numer line Disply the fllwing sets f numers n numer line. 5, 8,,, = ,.5,, 7.5, ,, 6, -, , 7.5,, 0,, Disply the fllwing sets f numers n numer line. The first six integers ve All the negtive even integers less thn 7 ut greter thn negtive All the multiples f higher thn 7 ut lwer thn All the integers tht re r 7 whle numers wy frm P Lerning H SERIES TOPI

13 Aitin n sutrtin using numer line Strting frm zer eh time, lultins invlving irete numers n e me using numer line. Negtive iretin Psitive iretin Use numer line t lulte these: Rememer Alwys strt frm 0 n mve using eh irete numer ne t time. (i) (ii) Strting t +8, t the right finishes t right (+) 8 ` + = Strt Finish Finish Strt Strting t -6, then 7 t the left finishes t left (-) ` -6-7 =- (iii) + (-) (iv) (-) + Negtive numers re ften written insie prentheses - Sme s (iii) ut in ifferent rer Finish Strt Strt Finish Strting t + then t the left finishes t right (+) Strting t -, t the right finishes t right (+) ` + (- ) = ` (- ) + = (v) Finish Strt Strting t +0, then 6 t the left fllwe y t the right finishes t left (-) ` =- H SERIES TOPI P Lerning

14 Aitin n sutrtin using numer line Shw the lultin fr eh f these n numer line n write wn the nswer. 5 + = (- ) + 8 = (-)- = = e = Write wn the lultin t get the given nswer shwn n eh f these numer lines: = = = P Lerning H SERIES TOPI 5

15 Aitin n sutrtin using numer line Shw the lultin fr eh f these n numer line n stte the nswer..5 + = (-5. )- 5. = Strt Finish = = Try these trikier nes! Write wn the lultin shwn n eh f these numer lines: = ADDITION AND SUBTRATION USING A NUMBER LINE *.../.../ = = = H SERIES TOPI P Lerning