Rates and Ratios. Rates and Ratios. Solutions. Curriculum Ready.

Transcription

1 Rtes nd Rtios Rtes nd Rtios Solutions Curriulum Redy

2 Copyright 009 P Lerning. All rights reserved. First edition printed 009 in Austrli. A tlogue reord for this ook is ville from P Lerning Ltd. SBN Ownership of ontent The mterils in this resoure, inluding without limittion ll informtion, text, grphis, dvertisements, nmes, logos nd trde mrks (Content) re proteted y opyright, trde mrk nd other intelletul property lws unless expressly indited otherwise. You must not modify, opy, reprodue, repulish or distriute this Content in ny wy exept s expressly provided for in these Generl Conditions or with our express prior written onsent. Copyright Copyright in this resoure is owned or liensed y us. Other thn for the purposes of, nd sujet to the onditions presried under, the Copyright At 968 (Cth) nd similr legisltion whih pplies in your lotion, nd exept s expressly uthorised y these Generl Conditions, you my not in ny form or y ny mens: dpt, reprodue, store, distriute, print, disply, perform, pulish or rete derivtive works from ny prt of this resoure; or ommerilise ny informtion, produts or servies otined from ny prt of this resoure. Where opyright legisltion in lotion inludes remunerted sheme to permit edutionl institutions to opy or print ny prt of the resoure, we will lim for remunertion under tht sheme where worksheets re printed or photoopied y tehers for use y students, nd where tehers diret students to print or photoopy worksheets for use y students t shool. A worksheet is pge of lerning, designed for student to write on using n ink pen or penil. This my led to n inrese in the fees for edutionl institutions to prtiipte in the relevnt sheme. Pulished P Lerning Ltd For more opies of this ook, ontt us t: Designed P Lerning Ltd Although every preution hs een tken in the preprtion of this ook, the pulisher nd uthors ssume no responsiility for errors or omissions. Neither is ny liility ssumed for dmges resulting from the use of this informtion ontined herein.

3 How does it work? Solutions Rtes & Rtios Pge questions Rtios (i) The rtio of girls to oys is: 7 :. (ii) The rtio of oys to girls is: : 7. (iii) The rtio of ll students in the lssroom to the numer of oys is: 9 :. (iv) The rtio of the numer of girls in the lssroom to the totl numer of students is: 7 : 9. (i) The rtio of sketll plyers to rugy plyers: : 6. (ii) The rtio of soer plyers to swimmers: : 9. (iii) The rtio of rugy plyers to soer plyers: 6 :. (iv) The rtio of tennis plyers to netllers: 7 :. (v) The rtio of sport plyers to non-plyers: : 8. Shded to Non-shded prts = 7 : 9. Shded to Non-shded prts = 9 :. P Lerning

4 How does it work? Solutions Rtes & Rtios Pge questions Rtios (i) : : 7 : : 7 (ii) : 9 : 9 7 : : 9 (i) : (i) : 6 (i) 0 : 7 or : (ii) : 9 (ii) 6 : 9 (ii) 7 : 7 or : P Lerning

5 How does it work? Solutions Rtes & Rtios Pge 6 questions Equivlent rtios (i) = 6 : = : = 8 : = : (ii) = : = : = : = : (i) = 7 : = 6 : 0 = 8 : 6 = : = : = : simplest form simplest form simplest form (ii) = : 0 = 9 : = : 9 or : 6 or : 0 or 6 : or : 8 or : or 0 : or 6 : or 8 : 0 or : 8 P Lerning

6 How does it work? Solutions Rtes & Rtios Pge 7 questions Equivlent rtios : 0 0 : 0 : 8 : 0 0 : 0 : : : : d : e 70 : 6 f 8 : 8 : 70 : 6 8 : : : 8 : 9 : : A : W : 69 8 : A L R 9 : : 6 8 : T 6 : 6 T M 0 9 : 80 : 0 : O T E 9 : 0 : 0 8 : : S 90 : 0 D : 9 : S : 7 : 9 R E 7 : : E 8 : 80 : 0 L 8 : 6 L O W E S T T E R M S P Lerning

7 How does it work? Solutions Rtes & Rtios Pge 9 questions Using frtions to redue rtios in lowest terms : 7 : 0 7 = 0 = 9 ` : 7 = : 9 ` : 0 = : 8 : 8 d 0 : = 0 00 = ` 8 : 8 = : ` 0 : 00 = : e : 70 f 00 : = = 0 6 ` : 70 = : 0 ` 00 : = : 6 Rits to rrots Lettue to slugs Spikey puffer fish ( ) to ll fish 9 7 = 0 = 6 = ` 9 : 7 = : ` 0 : = 6 : ` : = : P Lerning

8 How does it work? Solutions Rtes & Rtios Pge questions Rtios with deimls. :.. :. = : (Gretest ommon ftor = ) = :. : 7.. : 7. = : 7 (Gretest ommon ftor = ) = : 6 9. :. 9. :. = 9 : (Gretest ommon ftor = ) = : : : 0.60 = 8 : 60 (Gretest ommon ftor = ) = :.8 : 0..8 : 0. = 80 : (Gretest ommon ftor = 7) = 0 : :. :. =.00 :. (Gretest ommon ftor = 8) = 00 : = : : : : : 0.00 = 8 : 8 = : 00 = : 9 = :.0 :.8.00 :.80 d 6. : : = 00 : 80 = 60 : 600 = 0 : = 07 : 0 e. :.8.0 :.80 f 0.0 : : 0.00 = 0 : 80 = : 00 = : = : 00 6 P Lerning

9 How does it work? Solutions Rtes & Rtios Pge questions Rtios with frtions : = : 7 : 7 = : = 7 : 7 : = : 7 d 6 : = 6 : = 8 : 7 = : 6 = : = : 6 7 : : 7 : = : 7 : = : = 0 : = 0 : 7 = : = 8 : 6 : d : : = : 8 : = : = : 8 = : 0 = : = 6 : 6 = 9 : 8 P Lerning 7

10 How does it work? Solutions Rtes & Rtios Pge questions Best uys nd the unitry method pples ost $6.60 pple = $0. 0 g of heese osts $.0 g heese = $0.0 7 vodos ost $.7 vodo = $. d 00 m of wire osts $6 m wire = $.78 Hlf pket of pegs ost $.0 pket of pegs = $.0 wtermelon ost $6.60 wtermelon = $ kg of pst osts $. kg pst = $.88 (to d. p.) d 0.7 m of gold osts $ m of gold = $8.7 (to d. p.) kg of fish for $.00 or 8 kg of fish for $0? sks of pottoes for $ or sks of pottoes for $7? ( kg for $.00) = 8 kg for $8.00 ` kg of fish for $.00 is the est uy. ( sks for $.00) = sks for $6.00 ( sks for $7.00) = sks for $.00 ` sks for $7.00 is the est uy. sets of guitr strings for $78.7 or d 8 loves of sourdough red for $.60 or 7 sets of guitr strings for $0.9? loves of sourdough red for $.? ( sets for $78.7) 7 = sets for $. (8 for $.60) = 00 for $00 (7 sets for $0.7) = sets for $.7 ( for $.) 8 = 00 for $00 ` sets for $78.7 is the est uy. ` 8 loves for $.60 is the est uy. 8 P Lerning

11 How does it work? Solutions Rtes & Rtios Pge 6 questions Best uys nd the unitry method mn who n run 0 m in seonds or mn who n run 0 m in seonds. 0 m in seonds = 9. m in seond 0 m in seonds = 0 m in seond ` mn wh n run 0 m in seonds is the fster runner. 8 video gmes for $6.80 or video gmes for $00. 8 video gmes for $ = video gme for $7.8 video gmes for $00. = video gme for $7.7 ` 8 video gmes for $6.80 is more expensive. Find the mode of trnsport tht trvels t the fstest speed etween two towns if: y us you trvel 6 km in.7 hours or y trin you trvel km in. hours. 6 km in.7 hours (6.7)km in hour = 60 km in hour (or 60 km/h) km in. hours (.)km in hour = 6.79 km in hour (or ~ 6.8 km/h) ` trin hs the fstest speed etween two hours. g of flour osts $0.0 g = $0.008 `00 g = $ ml of lvender oil osts $7.6 ml = $0.0 `00 ml = $ ml of milk osts $.8 ml = $0.00 `00 ml = $0. d minutes of mhine hire osts $7.00 min = $0.06 `00 ml = $.6 P Lerning 9

12 How does it work? Solutions Rtes & Rtios Pge 7 questions Best uys nd the unitry method 6 g of fish for $.60 or 70 g of rie for $.60 or 7 g of fish for $ g of rie for $.68 g for $ g for $.60 ` g for $0.08 ` 00 g for $.8 (to d. p.) ` g for $ ` 00 g for $0.76 ~ $0.7 (to d. p.) 7 g for $.70 ` g for $0.09 ` 00 g for $.9 (to d. p.) 600 g for $.68 ` g for $ ` 00 g for $0.78 ` g for $.60 is the est uy. ` 70 g for $.60 is the est uy g Corinder (A) = $.0 00 g Corinder (B)? to e the etter uy 60 g Corinder (A) = $.0 ` g = $0.07 ` 00 g = $7.00 ` 00 g Corinder (B) must e $7.00 to e the etter uy kg Soil (X) = $ kg Soil (Y)? to e the more expensive uy kg Soil (X) = $77.0 ` kg = $.60 ` 0 kg = $60 ` 0 kg Soil (Y) $60 to e the more expensive uy 0 P Lerning

13 How does it work? Solutions Rtes & Rtios Pge 9 questions Dividing quntity in given rtio $00 into the rtio :. Totl numer of prts is + =. ` prts is $00. ` prt is $ 00 = $ 00. prts ` prts is $ 800. ` $00 is divided into the mounts $ 00 nd $ kg into the rtio :. Totl numer of prts = + =. ` prts = 700 kg prt = 700 = 0 kg ` prts = 0 kg prts = 0 kg ` 700 kg in rtio : = 0 kg : 0 kg 60⁰ into the rtio :. Totl prts = + = 9 prts. ` 9 prts = 60o ` prt = 60o 9 = 0o ` prts = 00o ` prt = 60o ` 60o in rtio : = 00o: 60o Hrry = prts Slly = prt ` prts = 6 ookies ` prt = 6 = 9 ookies ` prts = 7 ookies ` Hrry gets 7 ookies. Slly gets 9 ookies. P Lerning

14 How does it work? Solutions Rtes & Rtios Pge 0 questions Dividing quntity in given rtio (i) Totl mount shred = $0 + $60 = $00 (ii) 0 : 60 = 0 60 = 9 ` money ws divided in the rtio 9 :. 80 : ` 9 : = x : 9 : ` x = 9 = Fion = x - 0 Jon = x x + (x - 0) = $00 x - 0 = $00 x = $0 x = $0 ` x - 0 = $9 ` Fion gets $9 Jon gets $0 Pge questions Dividing quntity in given Rtio 6 : : Gretest ommon ftor = ` : : = : : = : : : 6 : Gretest ommon ftor = ` : 6 : = : 6 : = : : : : d : : : 8 Gretest ommon ftor = ` : : = : : = : : Gretest ommon ftor = ` : : : 8 = : : : 8 = : : : e 0 : : : 0 f 6 : : 9 : 7 : 8 Gretest ommon ftor = ` 0 : : : 0 = 0 : : : 0 = : : 7 : Gretest ommon ftor = ` 6 : : 9 : 7 : 8 = 6 : : 9 : 7 : 8 = : : : 9 : 7 P Lerning

15 How does it work? Solutions Rtes & Rtios Pge questions Dividing quntity in given rtio rtio = : : : : : : : = 0 prts ` $ = $ ` Lim wins $ = $ Everyody else wins $ Pge questions Dividing quntity in given Rtio 8 : : 6 = : : 6 = 6 : 6 : 6 ` Totl numer of prts = + + = prt of whet seed = 000 kg = 66.6 kg d ` Eh frmer gets = 66.6 : 66.6 : 66.6 = 00 kg : kg : 8. kg = 00 kg : 667 kg : 8 kg rounded to the nerest kg. e 0 seeds =.6 g ` 000 kg.6 g = g.6 g = ` squre metres of lnd re required to sow ll the seeds. P Lerning

16 Where does it work? Solutions Rtes & Rtios Pge questions Equivlent rtios with missing terms x : 6 = : x = 6 method : x 6 = x 6 = 6 ` x = (to get ommon denomintors) method : x 6 = x = 6 x = ` x = 6 : = x : 0 x = 0 method : = x = x 0 6 = x (to get ommon denomintors) method : 6 = x = x 80 = x ` x = 6 6 = x ` x = 6 x : = 0 : method : x = 0 x = 0 (to get ommon denomintors) method : x = 0 x = 0 x = 0 x = 0 ` x = 0 ` x = 0 : x = : x = (use ross multiplition) = x 9 = x ` x =. or P Lerning

17 Where does it work? Solutions Rtes & Rtios Pge questions Dividing quntity in given rtio y : 0 = : method : y 0 = y = (to get ommon denomintors) method : y 0 = y = y = y = y = y = ` y = 6y = 6 6 y = 6 ` y = 6 : = : 8 method : = = 8 (to get ommon denomintors) method : = 8 8 = 0 = 0 0 = 0 0 = = 0 0 ` = = ` = = 7 x : = 6 : 6 method : x 6 6 = 6 6 8x 0 = 0 0 8x = x = 0 8 (to get ommon denomintors) method : x = 6 6 8x = x = 0 8 ` x = = ` x = = 8 y : 6 = 6 : y ` y 6 = 6 y (use ross multiplition) ` y = 6 ` y = 6 ` y =!6 (sine (-6) nd 6 oth equl 6) P Lerning

18 Where does it work? Solutions Rtes & Rtios Pge 7 questions Sle drwings m : m = m : 00m (m = 00m) = : 00 m : m = m : 00m (m = 00m) = : 0 0m : km = 0m : 00000m (km = 00000m) = m : 000m = : 000 d m : m = 00m : m = : e 0mm : 0km = 0mm : mm (km = mm) = mm : 00000mm = : : =. : x ` =. x x =. x = 0.7 ` n rel life, the nt is 0.7 m long.. m 6 P Lerning

19 Where does it work? Solutions Rtes & Rtios Pge 8 questions Sle drwings : : : 6 : = 6. : x : = 6. : x : 6 = 6. : x = 6. x x = 7. = 6. x x = 6. 6 = 6. x x = 0 ` Rel life length = 7. m x = 0. ` Rel life length = 0. m x = 0.8 ` Rel life length = 0.8 m : : 9 : 0 : = x : : 9 = x : : 0 = x : = x 76 = x 9 = x = 9x 0 = x = 0x ` Sle drwing = 76 m ` x = 0. ` x = 0. ` Sle drwing = 0. m ` Sle drwing = 0. m m m Kithen m Comined lounge/edroom m Bthroom 7 m Sle: : 00 length = m + 7 m : 00 = 0 : x = 0 m 00 = 0 x x = 000 m ` Studio in rel life is 0 m long. Are = 7 m m = m P Lerning 7

20 Where does it work? Solutions Rtes & Rtios Pge 0 questions Mps : 9000 = : x 9000 = x x = 0000 ` Rel life distne = 0000 m =. km P R Q m m (i) ` 6 m = 8 km (ii) PR = grids prt ` 6 m : 8 km = 6 m : m ` m :. m ` m = m =. km ` Sle of mp = : 8 P Lerning

21 Where does it work? Solutions Rtes & Rtios Pge questions Rtes Bins piked =. = 0 Weekly inome = h $7.0/h = $ rs/dy ins/0 dys = 90 rs/ hours = 80 rs/hour = 0 ins/dy = 7.6 ins/dy, 7 ins/dy (to nerest in) yer = weeks ` workdys = weeks = 60 dys ` Totl workdys = 60 ` $8 0/60 dys = $8 0 60/dy = $7/dy P Lerning 9

22 Where does it work? Solutions Rtes & Rtios Pge questions Rtes involving flow of liquids 0 L/min ` After min = 0 L = 0 L in min L 0 L/min = Totl minutes to empty = 600 min ` 600 min 60 min = 0 hours 9000 L t rte of 000 L/hour = 000 L/60 min = 000 L/600 se =. L/s =. L/s (to d.p.) km/ L ` km/l =. 87 km/l ` 00 km. 87 km = L ` 00 km/8. L (to d.p.) 0 P Lerning

23 Where does it work? Solutions Rtes & Rtios Pge questions Rtes involving flow of liquids L/00 km = 68 L/x km 00 = 68 x x = 6800 ` x = 700 km L/s ` Time to empty = =.76 s L/s ` Time to empty = = 79. s ` The first tnk empties in the shortest time. Pge 6 questions Rtes involving urreny onversions USD / AUD = $ x USD / $000 AUD ` 0.96 = x 000 $800 = x ` $000 AUD = $800 USD 0.96 = $980 USD x 0.96x = $980 USD x = $ USD x = $00.8 (to d.p.) AUD Pge 7 questions Rtes involving urreny onversions 7 Y GBP = 8. ZAR ` Y 000 GBP = 000 # 8. ZAR = R6 00 Y GBP = 8. ZAR ` ZAR = 8. GBP ZAR, 0.0 GBP ` ZAR, # 0.0 GBP = Y GBP P Lerning

24 Where does it work? Solutions Rtes & Rtios Pge 7 questions Rtes involving urreny onversions 8 Rupee = 0.07 USD ` (NR), # 0.07 USD = $68 USD Pge 8 questions Rtes involving urreny onversions 8 $ New Zelnd dollr = 0.76 USD $ USD =.60 JPY `$60 NZD, 60 # 0.76 USD ` $00 USD, 00 #.60 JPY = $86.6 USD = 76 JPY d $ USD = $.7 SGD `$600 USD, 600 #.7 SGD = $89.0 SGD e $9 000 (NZD) $ 000 (AUD) $ NZD = $0.76 USD $ AUD = $0.767 USD `$9 000 NZD = # 0.76 USD `$ 000 AUD = 000 # USD = $9 88 USD = $9 7 USD Y6 00 (GBP) $6 800 (SGD) Y GBP = $. USD $ SGD = $0.7 USD `Y6 00 GBP = 6 00 #. USD `$6 800 SGD = # 0.7 USD = $0 6.0 USD = $ USD )9 000 (EUR) ) EUR = $.096 USD `)9 000 EUR = #.096 USD = $0 98 USD `)9 000 (EUR) will exhnge for the lrgest mount in USD t the rtes urrently given. P Lerning

25 Wht else n you do? Solutions Rtes & Rtios Pge 0 questions Speed Averge speed = 0 km/ h Averge speed = 00 km/0. h = km/h = 800 km/h Averge speed = 876 km/9 h = 97 km/h Distne = 00 km/h. hours = 0 km Distne in first hours = 80 km/h hours = 0 km Distne in lst hours = 0 km/h hours = 0 km Totl distne = 0 km + 0 km = 760 km d Totl time period = 8 hours e ` 760 km/8 h = Averge speed for 8 hours = 9 km/h = Averge speed P Lerning

26 Wht else n you do? Solutions Rtes & Rtios Pge questions Speed T = D S = 7000 km 900 km/h = 7.7 hours = 7 hours 6 min 0 se = 7 hours 7 min (to nerest minute) Totl distne rn = (6 m ) for k & forth = 80 m Time rn = minutes, seonds = 9 se ` 80 m/9 se = 0.9 m/s (to d.p.) 6 6 m/s for min 0 se = 6 m/s for 70 se D = ST = 6 m/s 70 se = 60 m P Lerning

27 Wht else n you do? Solutions Rtes & Rtios Pge question Speed nd different units 80 km/h in 0 min = 80 km/h in 6 hour ` D = 80 km/h 6 h = 0 km 8 km/h = 8000 m/h = 8000 m/60 min = 8000 m/600 se =. m/s km/h = 000 m/h = 000 m/600 se =. m/s ` Cylist trvelling t m/s is fster km/7. dys = m/7. dys = m/6. h = m/9 min = m/ 870 se = m/s = 0.7 m/s, 0 m/s P Lerning

28 Wht else n you do? Solutions Rtes & Rtios Pge questions Popultion growth rte Chnge in Popultion = Popultion in 0 - Popultion in 990 = = 09 0 Popultion Growth Rte, 090 PGR = 00% % ( dp) Popultion t eginning of time period = Find 7% of this nd dd in to find the new popultion: 7% of = = ` Popultion in 00: ` = P Lerning

29 Wht else n you do? Solutions Rtes & Rtios Pge 6 questions Popultion growth rte Country Popultion in 000 Popultion in 0 Chnge in Popultion Popultion Growth Rte PGR (%) Austrli % ndonesi % Jpn % Chin % Vietnm % United Sttes % ndi d Ppu New Guine % Afghnistn % North Kore % South Kore % Pkistn % Ppu New Guine Popultion in 000: Popultion (000) = = Chin Popultion in 0: Popultion (0) = = 798 ndonesi Chnge in Popultion: Chnge = = 899 d ndi Popultion Growth Rte: % = 7. % (to d.p.) P Lerning 7

30 Notes Solutions Rtes & Rtios 8 P Lerning

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32 Rtes nd Rtios