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978--07-670- - CmbridgeMths: NSW Syllbus for the Austrlin Curriculum: Yer 0: Stte./. Chpter Finncil mthemtics Chpter Finncil Mthemtics Wht you will lern A Review of percentges REVISION B Applying percentges REVISION C Income D The PAYG income tx system E Using budget to mnge income nd expenditure F Simple interest G Compound interest nd deprecition H Investments nd lons I Compring interest using technology FRINGE
978--07-670- - CmbridgeMths: NSW Syllbus for the Austrlin Curriculum: Yer 0: Stte./. NSW Syllbus for the Austrlin Curriculum Strnd: Number nd Algebr Number nd Algebr Substrnd: FiNANCiAl MAtHEMAtiCS Outcomes A student solves fi nncil problems involving erning, spending nd investing money. (MA. NA) A student solves fi nncil problems involving compound interest. (MA. NA) Sving nd borrowing money for expensive items For mny people, cr is the fi rst expensive item tht involves long-term sving nd borrowing. There is lso need to budget for the ongoing costs of petrol, insurnce nd repirs, s well s the hidden costs, such s interest on the lon nd deprecition.
978--07-670- - CmbridgeMths: NSW Syllbus for the Austrlin Curriculum: Yer 0: Stte./. Chpter Finncil mthemtics pre-test Find the following totls. $.9 + $7.0 + $6.0 b $ + $7 + $0 c $7 6 d $6. e $87 60 (to the nerest cent) Write ech of the following frctions s decimls. 7 b c d e Express the following frctions with denomintors of 00. b c Round the following decimls to deciml plces. 6.789 b 7.7 c. d 6.889 e 0.8999 d 7 e 9 0 Copy nd complete the following tble. Gross income ($) Deductions ($) Net income ($) 976 6.7 7 6 66.80 b 9 c 6 89 6 79 d 0 96 e 8 7.0 79.6 Net income gross income - deductions 6 Clculte the following nnul incomes for ech of these people. Tom: $6 per week b Vivin: $ 600 per month c Anthony: $9 per fortnight d Crystl: $7.90 per hour, for 0 hours per week, for 0 weeks per yer 7 Without clcultor, find: 0% of $00 b % of $000 c % of $00 d % of $8 e 0% of $.80 f 7% of $000 8 Find the simple interest erned on the following mounts. $00 t % p.. for yer b $000 t 6% p.. for yer c $800 t % p.. for yers Simple interest I PRN 9 Complete the following tble. Cost price Deduction Sle price $ $6 $60 $7 b $00 c $6 d $ $67 e $.6 $.7 0 The following mounts include the 0% GST. By dividing ech one by., find the originl costs before the GST ws dded to ech. $ b $6.60 c $60
978--07-670- - CmbridgeMths: NSW Syllbus for the Austrlin Curriculum: Yer 0: Stte./. Number nd Algebr A Review of percentges It is importnt tht we re ble to work with percentges in our everydy lives. Bnks, retilers nd governments use percentges every dy to work out fees, prices nd interest. let s strt: Which option should Jmie choose? Jmie currently erns $8 60 p.. (per yer) nd is given choice of two different py rises. Which should she choose nd why? Choice A Choice B REVISION Stge.#..... Increse of $0 week Increse of % on p.. slry A percentge mens out of 00. It cn be written using the symbol %, or s frction or deciml. For exmple: 7 per cent 7% 7 00 or 0.7 To convert frction or deciml to percentge, multiply by 00%, or 00%. To convert percentge to frction, write it with 00% denomintor of 00 nd simplify. For exmple: % 00 Frction % 0 00% To convert percentge to deciml, divide by 00%. For exmple: % 00 0. To find percentge of quntity, write the percentge s frction or deciml, then multiply by the quntity. x x% of P 00 P Deciml 00% 00% % Percentge A convenient wy of writing frctions with denomintors of 00 Denomintor The prt of frction tht sits below the dividing line Key ides
978--07-670- - CmbridgeMths: NSW Syllbus for the Austrlin Curriculum: Yer 0: Stte./. 6 Chpter Finncil mthemtics Exercise A R E V I S I O N Write the following with denomintors of 00. b 7 0 7 9 d e 0 c 9 0 Mke sure you hve n equivlent frction: 00. WORKING U M AT H E M ATIC A LLY R C F PS Complete the following. 7 7% b 0.9 % c % Use mentl strtegies to find: 0% of $7.0 b 0% of $00 c 0% of $98 d 7% of $668 e % of $ f % of $60 g % of $70 h % of $00 i 0% of $ 0% 0 00 Of mens times. Exmple Converting to percentge WORKING U M AT H E M ATIC A LLY R C F PS Write ech of the following s percentge. 9 0 SolutioN 9 0 9 0 9 00 9% b 8 8 7 % 7.% 00 % c 0.07 0.07 00% 7% b 8 c 0.07 ExplANAtioN Write using denomintor of 00. Alterntively, multiply the frction by 00%. 9 00 % 9 % 9% 0 Multiply the frction by 00%. Cncel common fctors, then simplify. Multiply the deciml by 00%. Move the deciml point two plces to the right.
978--07-670- - CmbridgeMths: NSW Syllbus for the Austrlin Curriculum: Yer 0: Stte./. Number nd Algebr 7 Convert ech frction to percentge. b d e 0 00 g h 0 9 99 j k 00 c f i l 7 8 7 0 First, write using denomintor of 00 or lterntively multiply by 00%. WORKING U F M AT H E M ATIC A LLY R C PS Write these decimls s percentges. 0.7 b 0.7 c 0.8 d 0.09 e 0.06 f 0. g. h.0 i 0.8 j 0.9 k 0.99 l 0.7 To multiply by 00%, move the deciml point two plces to the right. Exmple Writing percentges s simple frctions Write ech of the following percentges s simple frction. 7% b 8% c 6 % S o l u t i o n 7% 7 00 b 8% 8 00 9 0 E x p l n t i o n Write the percentge with denomintor of 00. Write the percentge with denomintor of 00. Simplify 8 by cncelling, using the HCF of 8 nd 00, which is. 00 8 00 9 0 9 0 c 6 6 % 00 00 Write the percentge with denomintor of 00. Double the numertor 6 nd the denomintor (00) so tht the numertor is whole number. 6 Write ech percentge s simple frction. 7% b 80% c % d % e 0% f 88% g % h 6 % Write with denomintor of 00, then simplify if possible. i 7 % j % k % l %
978--07-670- - CmbridgeMths: NSW Syllbus for the Austrlin Curriculum: Yer 0: Stte./. 8 Chpter Finncil mthemtics A Exmple Writing percentge s deciml Convert these percentges to decimls. 9% b 7% c 0% WORKING U F M AT H E M ATIC A LLY R C PS SolutioN 9% 0.9 ExplANAtioN Divide the percentge by 00. This is the sme s moving the deciml point two plces to the left. 9 00 0.9 b 7% 0.07 Divide the percentge by 00. 7 00 0.07 c 0% 0. Divide the percentge by 00. 0 00 0.0 Write 0.0 s 0.. 7 Convert to decimls. 6% b 8% c 7% d % e 9% f 90% g 0% h 6.% i 7.% j 00% k 0% l 0.% Exmple Finding percentge of quntity Find % of $800. SolutioN % of $800 0. 800 $76 ExplANAtioN Remember tht of mens multiply. Write % s deciml or frction: % 0. 00 Then multiply by the mount. If using clcultor, type 0. 800. Without clcultor: 8 00 8 00 8 Use clcultor to find: 0% of $0 b 0% of $00 c 7% of $80 d % of $70 e 9% of $0 f % of 800 grms g 90% of $6 h 0% of $98 i 7 % of 000 m
978--07-670- - CmbridgeMths: NSW Syllbus for the Austrlin Curriculum: Yer 0: Stte./. Number nd Algebr 9 9 A 00 g pie contins g of sturted ft. Wht frction of the pie is sturted ft? b Wht percentge of the pie is sturted ft? WORKING U M AT H E M ATIC A LLY R C F PS g out of 00 g. 0 About 80% of the mss of humn body is wter. If Hugo is 8 kg, how mny kilogrms of wter re in his body? Rem spends % of the 6.6 hour school dy in Mths. How mny minutes re spent in the Mths clssroom? In cricket mtch, Brett spent minutes bowling. His tem s totl fielding time ws hours. Wht percentge of the fielding time, correct to deciml plces, did Brett spend bowling? First convert hours to minutes, nd then write frction compring times. Mlcolm lost 8 kg, nd now weighs 6 kg. Wht percentge of his originl weight did he lose? 7.9% of locl council s budget is spent on grbge collection. If rte pyer pys $07.0 per qurter in totl rte chrges, how much do they contribute in yer to grbge collection?
978--07-670- - CmbridgeMths: NSW Syllbus for the Austrlin Curriculum: Yer 0: Stte./. 0 Chpter Finncil mthemtics A Enrichment: Austrli s sttistics Below is the preliminry dt on Austrli s popultion growth, s gthered by the Austrlin Bureu of Sttistics for September 0. popultion t end September qurter 0 ( 000) Chnge over previous yer ( 000) New South Wles 7. 86.0 Victori 69. 9.8 Queenslnd 8.6 9. South Austrli 68. 6. Western Austrli. 8.7 Tsmni. 0. Northern Territory 6.. Austrlin Cpitl Territory 76. 7. Austrli 78. 8. Chnge over previous yer (%, deciml plce) Clculte the percentge chnge for ech Stte nd Territory shown using the previous yer s popultion, nd complete the tble. b Wht percentge of Austrli s overll popultion, correct to deciml plce, is living in: i NSW? You will need to clculte the previous yer s popultion; e.g. for NSW, 7. - 86.0. ii Victori? iii WA? c Use spredsheet to drw pie chrt (sector grph) showing the popultions of the eight Sttes nd Territories in the tble. Wht percentge of the totl is represented by ech Stte/Territory? d In your pie chrt in prt c, wht is the ngle size of the sector representing Victori?