Introduction to ratios

Transcription

1 A Introdution to ratios Ratios are used to ompare quantities of the same kind. Ratios do not have a name or unit of measurement. The order of the numbers in a ratio is important. If the ratio of flour to water is 1 :, the 1 orresponds to the quantity of flour and the orresponds to the quantity of water. Ratios an also be written in frational form: 1:. Ratios an also be written as perentages; for example if 0% of a lass of Year 8 students walked to shool then 80% did not walk to shool a ratio of 1 :. Before ratios are written, the numbers must be expressed in the same units of measurement. One the units are the same, they an be omitted. Ratios ontain only whole numbers. 1 WORKED EXAMPLE 1 Look at the ompleted game of noughts and rosses at right and write the ratios of: a rosses to noughts b noughts to unmarked spaes. a Count the number of rosses and the number of noughts. Write the numbers as a ratio (the number of rosses must be written first). b Count the number of noughts and the number of unmarked spaes. Write the numbers as a ratio, putting them in the order required (the number of noughts must be written first). a : b : WORKED EXAMPLE Rewrite the following statement as a ratio: 7 mm to 1 m. 1 Express both quantities in the same units. To obtain whole numbers, onvert 1 m to mm (rather than 7 mm to m). Omit the units and write the numbers as a ratio. 7 : 10 7 mm to 1 m 7 mm to 10 mm REMEMBER Weblink Introduing ratios 1. Ratios ompare quantities of the same kind.. The ratios themselves do not have a name or unit of measurement.. The order of the numbers in a ratio is important.. Before ratios are written, the numbers must be expressed in the same units of measurement.. Ratios ontain only whole numbers. Chapter Ratios and rates 11

2 EXERCISE A INDIVIDUAL PATHWAYS Ativity -A-1 Ripper ratios do-19 Ativity -A- Radial ratios do-196 Ativity -A- Real ratios do-197 Interativity Fruit salad ratio int-0076 Introdution to ratios FLUENCY 1 WE 1 Look at the ompleted game of noughts and rosses and write the ratios of: a noughts to rosses b rosses to noughts rosses to total number of spaes d total number of spaes to noughts e noughts in the top row to rosses in the bottom row. Look at the oloured irles on the right and then write the following ratios. a Blak : red b Red : blak Aqua : blak d Blak : aqua e Aqua : red f Blak : (red and aqua) g Aqua : (blak and red) h Blak : total irles i Aqua : total irles j Red : total irles For the diagram shown, write the following ratios. a Shaded parts : unshaded parts b Unshaded parts : shaded parts Shaded parts : total parts In the bag of numbers shown to the right, write the ratios of: a even numbers to odd numbers b prime numbers to omposite numbers numbers greater than to numbers less than d multiples of to multiples of e numbers divisible by to numbers not divisible by. WE Rewrite eah of the following statements as a ratio. a mm to mm b 6 s to 19 s $ to $11 d 7 teams to 9 teams e 1 goal to goals f 9 boys to boys g weeks to 1 month h mm to 1 m i 17 seonds to 1 minute j ents to $1 k 11 m to 1 m l 1 g to 1 kg m 1 L to kl n 7 hours to 1 day o months to 1 year p 1 km to 7 m q 7 apples to 1 dozen apples r 1 pears to dozen pears s females to males t 1 teaher to students 6 Out of 100 people seleted for a shool survey, 9 were junior students, were teahers and the rest were senior students. Write these ratios: a teahers : juniors b juniors : seniors seniors : teahers d teahers : students e juniors : other members of the survey Maths Quest 8 for the Australian Curriulum

3 7 Write eah of the following, using a mathematial ratio. a In their hess battles, Lynda has won games and Karen has won 17. b There are 1 first-division teams and 17 seond-division teams. Nathan ould long jump twie as far as Rahel. d On the amp there were teahers and 9 students. e In the mixture there were ups of flour and 1 up of milk. f Elena and Alex ran the 00 m in the same time. g The radius and diameter of a irle were measured. h The length of a retangle is three times its width. i On Friday night 9 out of every 10 people enjoyed the movie. j The length of one side of an equilateral tri angle ompared to its perimeter. k The length of a regular hexagon ompared to its perimeter. l The number of orret options ompared to inorret options in a multiple-hoie question ontaining five options. UNDERSTANDING 8 A pair of jeans originally pried at $1 was purhased for $179. What is the ratio of: a the original prie ompared to selling prie? b the original prie ompared to the disount? 9 Matthew reeived a sore of 97% for his Maths test. What is the ratio of: a the marks reeived ompared to marks lost? b the marks lost ompared to total marks possible? 10 For eah omparison that follows, state whether a ratio ould be written and give a reason for your answer. (Remember: Before ratios are written, numbers must be expressed in the same unit of measurement.) a Anna s mass is kg. Her at has a mass of 7 kg. b Brian an throw a riket ball 0 metres, and John an throw the same ball metres. The ost of painting the wall was $; its area is 10 m. d For a trip, the ar s average speed was 8 km/h; the trip took h. e Brett s height is.1 m. Matt s height is 10 m. f Jonathon apples ost $.0 per dozen; Deliious apples ost $.0 per dozen. g Mary is paid $108; she works days a week. h David kiked goals and behinds; his team sored 189 points. 11 a If 17% of students in a lass have sports training one a week, write as a ratio the number of students who have sports training one a week ompared to the students who do not. b A survey found that only % of workers take their lunh to work on a regular basis. Write as a ratio the number of workers who do not take their lunh to work ompared to those who do. REFLECTION Why doesn t a simplified ratio have units? Chapter Ratios and rates 11

4 B Simplifying ratios When the numbers in a ratio are multiplied or divided by the same number to obtain another ratio, these two ratios are said to be equivalent. (This is a similar proess to obtaining equivalent frations). Like frations, ratios are usually written in simplest form; that is, redued to lowest terms. WORKED EXAMPLE Express the ratio 16 : in simplest form. 1 Write the ratio. 16 : Determine the largest number by whih both 16 and an be divided (that is, what is the highest ommon fator)? It is 8. Divide both 16 and by 8 to obtain an equivalent ratio in simplest form. ó 8 ó 8 : WORKED EXAMPLE Write the ratio of m to 1. m in simplest form. 1 Write the question. m to 1. m Express both quantities in the same units by hanging 1. m into m. (1 m = 100 m) m to 10 m Omit the units and write the numbers as a ratio. : 10 Simplify the ratio by dividing both and 10 by 1 the HCF. ó 1 ó 1 : 10 WORKED EXAMPLE Simplify the following ratios. a : 7 10 b 6 : 8 a 1 Write the frations in ratio form. a Write equivalent frations using the lowest ommon denominator (in this ase, 10). Multiply both frations by 10. Chek if the remaining whole numbers that form the ratio an be simplified. In this ase they annot. : 7 10 : ì 10 ì 10 : Maths Quest 8 for the Australian Curriulum

5 b 1 Write the frations in ratio form. b Write equivalent frations using the lowest ommon denominator (in this ase, ). Multiply both frations by. Chek if the remaining whole numbers that form the ratio an be simplified. In this ase divide eah by the HCF of. 6 : 8 0 : 1 ì ì 0 : 1 ó ó : If the ratio uses deimals, we multiply by the smallest power of 10 that will produe a whole number for both parts of the ratio. WORKED EXAMPLE 6 Write the following ratios in simplest form. a.1 to. b 1. : 0.7 a 1 Write the deimals in ratio form. a.1 :. Both deimals have one deimal plae, so multiplying eah by 10 will produe whole numbers. Simplify by dividing both numbers by the HCF of 7. ì 10 ì 10 1 : ó 7 ó 7 : b 1 Write the deimals in ratio form. b 1. : 0.7 Beause 0.7 has two deimal plaes, we multiply eah deimal by 100 to produe whole numbers. Simplify by dividing both numbers by the HCF of. ì 100 ì : 7 ó ó 8 : 1 If the ratio ontains algebrai terms, divide both parts of the ratio by the highest ommon fator (HCF) inluding ommon algebrai terms. WORKED EXAMPLE 7 Simplify the ratios: a 10a b : 1ab b mn : 6mn. a 1 Write the ratios. a 10a b : 1ab Simplify the ratio by dividing both sides by ab (the HCF). Canel ommon fators to obtain the ratio in simplest form. 10ab 1ab : ab ab a : b b 1 Write the ratios. b mn : 6mn Simplify the ratio by dividing both sides by mn (the HCF). Canel ommon fators to obtain the ratio in simplest form. mn 6mn : mn mn 1 : Chapter Ratios and rates 117

6 REMEMBER 1. If eah number in a ratio is multiplied or divided by the same number, the equivalent (or equal) ratio is formed.. It is ustomary to write ratios in the simplest form. This is ahieved by dividing eah number in the ratio by the highest ommon fator (HCF).. To form a ratio using frations, onvert the frations so that they have a ommon denominator and then write the ratio of the numerators.. Deimals an be easily hanged into whole numbers if they are multiplied by powers of 10 (that is, 10, 100, 1000 and so on).. If the ratio ontains algebrai terms, divide both parts of the ratio by the highest ommon fator (HCF) inluding ommon algebrai terms. EXERCISE B INDIVIDUAL PATHWAYS Ativity -B-1 Simplifying ratios do-198 Ativity -B- More simplifying of ratios do-199 Ativity -B- Advaned simplifying of ratios do-00 Interativity Converting perentages, deimals, frations, ratios int-70 Simplifying ratios FLUENCY 1 WE Express eah ratio in simplest form. a : b : 9 : 10 d 6 : 18 e 1 : 16 f 1 : 18 g : 16 h 1 : 1 i : 1 j 1 : 6 k 1 : l 7 : 6 m 6 : n : 8 o : p 0 : 1 q 6 : 6 r 7 : 100 s 8 : 1 t 88 : 1 Complete the patterns of equivalent ratios. a 1 : : 6 _ : 9 _ : 1 : b : 1 : _ : _ : 8 0 : _ : : 6 6 : : 1 _ : d 6 : : 16 : 8 8 : : 1 e 8 : 6 : 1 : : 8 : WE Write the following ratios in simplest form. a 8 m to 1 m b $6 to $18 0 s to 0 s d 80 m to m e 7 ents to $ f h to min g 00 ml to L h 00 g to. kg i mm to m j $ to $6.0 k 00 L to kl l 00 m to km m 0 ents to $1.0 n h min to 0 min o 00 m to 0. km p 0.8 km to 0 m q 1 1 min to 00 s r 1.8 m to 1 mm s 00 mg to 1. g t $1.7 to $10.0 Compare the following, using a mathematial ratio (in simplest form). a The Hawks won 8 games and the Lions won 10 games. b This jar of offee osts $ but that one osts $6. While Joanne made 1 hits, Holly made 8 hits. d In the first innings, Ian sored 8 runs and Adam sored 1 runs. e During the rae, Rebea s average speed was 00 km/h while Donna s average speed was 10 km/h. f In the basketball math, the Tigers beat the Magi by 10 points to 8 points. g The apaity of the plasti bottle is 0 ml and the apaity of the glass ontainer is L. h Joseph ran the 600 m in minutes but Maya ran the same dis tane in 6 seonds. i In the movie audiene, there were 80 hildren and adults. j On a page in the novel Moby Dik there are 60 words. Of these, 80 begin with a vowel. 118 Maths Quest 8 for the Australian Curriulum

7 A serving of Weet Bisuit Cereal ontains:.6 g of protein 0. g of fat 0 g of arbohydrate 1 g of sugar. g of dietary fibre 8 mg of sodium. Find the following ratios in simplest form: a sugar to arbohydrate b fat to protein protein to fibre d sodium to protein. 6 WE Write the following ratios in simplest form. a d g 1 to : 6 b e 7 to 6 7 to : 1 h 1 to 1 f 1 : 1 : i 1 1 : 11 Digital do Spreadsheet Simplifying ratios do-1 j 1 to 1 k 1 : 1 l 1 to 7 WE 6 Write the following ratios in simplest form. a 0.7 to 0.9 b 0. : to 0.1 d 0.8 : 1 e 0. : 1. f 0.7 to 0.8 g 0.9 : 0.09 h 1 to 1. i 0.01 : 0.1 j 1. : 0.87 k 0.00 to 0.08 l 0. : WE 7 Simplify these ratios. a a : 10b b 6p : p x : x d 7xy : 1xy e 6m n : 8m n f ab : ab g 10 x : 10x h 0(d) : UNDERSTANDING 9 In a primary shool that has 910 students, 0 students are in the senior shool and the remainder are in the junior shool. Of the senior shool students, 10 are females. There are the same number of junior males and junior females. Write the following ratios in simplest form: a senior students to junior students b senior females to senior males senior males to total senior students d junior males to senior males e junior females to whole shool population. 10 Compare the following, using a mathematial ratio (in simplest form): a Of the people who attended the test math, 11 were females. Compare the number of males to females. b A Conorde jet ruises at 170 km/h but a Cessna ruises at 0 km/h. Compare their speeds. A house and land pakage is sold for $ If the land was valued at $90 000, ompare the land and house values. d In a kilogram of ferti liser, there are 0 g of phosphorus. Compare the amount of phosphorus to other omponents of the fertiliser. e Sasha saves $10 out of his take-home pay of $700 eah fortnight. Compare his savings with his expenses. 11 The table at right represents the selling prie of a house over a period of time. a Compare the prie of the house purhased in Deember 00 with the purhase prie in April 007 as a ratio in simplest form. b Compare the prie of the house purhased in Deember 00 with the purhase prie in Deember 007 as a ratio in simplest form. Date of sale Marh 010 Deember 007 April 007 Selling prie $1.7 mil lion $1.07 mil lion $1.0 million Deember 00 $ Chapter Ratios and rates 119

8 Compare the prie of the house purhased in Deember 00 with the purhase prie in Marh 010 as a ratio in simplest form. d i How muh has the value of the house inreased from Deember 00 to Marh 010? ii Compare the inrease obtained in part d i to the prie of the house purhased in Deember 00 as a ratio in simplest form. e Comment on the results obtained in part d. 1 a MC Toowoomba s population is and Brisbane s population is 1.8 million. The ratio of Toowoomba s population to that of Brisbane is: A : B : 9 C 1 : 1.8 D 9 : E none of these b When he was born, Samuel was 0 m long. Now, on his 0th birthday, he is.1 m tall. The ratio of his birth height to his present height is: A : 7 B 1 : 1 C 7 : 10 D 1 : 7 E none of these The ost of tikets to two different onerts is in the ratio :. If the more expensive tiket is $110, the heaper tiket is: A $180 B $80 C $0 D $ E $66 d A oin was tossed 100 times and Tails appeared 60 times. The ratio of Heads to Tails was: A : B : C : D : E : e Out of a 1. L bottle of soft drink, I have drunk 00 ml. The ratio of soft drink remaining to the original amount is: A : B : C : D : E : REFLECTION In what ways is simplifying ratios similar to simplifying frations? C Proportion A proportion is a statement of equality of two ratios. In general, if a =, then, using ross-multipliation, a ì d = ì b. b d WORKED EXAMPLE 8 Use the ross-multipliation method to determine whether the following pair of ratios is in proportion: 6 : 9; : 6. 1 Write the ratios in fration form. 6 9 Perform a ross-multipliation. 6 ì 6 = 16 ì 9 = 16 Chek whether the produts are equal. 16 = 16 Therefore, the ratios are in propor tion Maths Quest 8 for the Australian Curriulum

9 WORKED EXAMPLE 9 Find the value of a in the following proportion: a 6 =. 9 1 Write the proportion statement. a 6 = 9 Cross-multiply and equate the produts. a ì 9 = 6 ì Solve for a by dividing both sides of the equation by 9. 9a = 18 9a 18 = 9 9 a = WORKED EXAMPLE 10 The ratio of girls to boys on the shool bus was :. If there were 8 girls, how many boys were there? 1 Let the number of boys be b and write a proportion statement. (Sine the first number in the ratio represents girls, plae 8 (the number of girls) as the numerator.) 8 = b Cross-multiply and equate the produts. ì b = 8 ì Solve for b by dividing both sides by. b = 8 b 8 = b = 1 Write the answer. There are 1 boys. REMEMBER 1. Proportion is a statement of equality of two ratios.. In any proportion, the produts of the numbers, diagonally aross from eah other, are equal.. In general, if a =, then, using ross-multipliation, a ì d = ì b. b d Chapter Ratios and rates 11

10 EXERCISE C INDIVIDUAL PATHWAYS Ativity -C-1 Proportion do-01 Ativity -C- More proportion do-0 Ativity -C- Advaned proportion do-0 Digital do Spreadsheet Proportion do-1 Proportion FLUENCY 1 WE 8 Use the ross-multipliation method to determine whether the fol lowing pairs of ratio are in proportion. a : ; 8 : 1 b : 7; 8 : 1 : 7; 10 : 1 d : 8; 10 : 16 e ; f ; 9 8 g ; h ; i ; j 8 ; k ; l ; 18 WE 9 Find the value of a in eah of the following proportions. a a 8 a a = b = = d a = 1 e 7 1 a = 8 f 10 a = 1 g = a 1 h = a 8 i = a j = k = l = 7 a 16 a a WE 10 Solve eah of the following, using a proportion statement and the ross-multipliation method. a The ratio of boys to girls in a lass is :. If there are 1 girls, how many boys are in the lass? b In a room the ratio of length to width is :. If the width is 8 m, what is the length? The team s win loss ratio is 7 :. How many wins has it had if it has had 1 losses? d A anteen made ham and hiken sandwihes in the ratio : 6. If 0 ham sandwihes were made, how many hiken sandwihes were made? e The ratio of onentrated ordial to water in a mixture is 1 :. How muh onentrated ordial is needed for litres of water? f The ratio of hairs to tables is 6 : 1. If there are hairs, how many tables are there? g The ratio of flour to milk in a mixture is 7 :. If 1 ups of flour are used, how muh milk is required? h The ratio of protein to fibre in a ereal is 1 : 11. If there are 6 grams of protein, what is the mass of fibre? i In a supermarket, the ratio of 600 ml artons of milk to litre ar tons is :. If there are sixty 600 ml artons, how many litre artons are there? j In a rowd of mobile-phone users, the ratio of men to women is 7 : 8. How many women are there if there are 870 men? While we know that only whole numbers are used in ratios, some times in a proportion statement the answer an be a fration or a mixed number. Consider the following proportion: a 6 7 = a ì = 7 ì 6 a = a = 10. (or 10 1 ) 1 Maths Quest 8 for the Australian Curriulum

11 Calulate the value of a in eah of the following proportion state ments. Write your answer orret to 1 deimal plae. a 8 a a 7 a 9 7 a = b = = d = e a = f a = 7 g 9 = a 1 h = a i = j = a 8 a UNDERSTANDING Write a proportion statement for eah situation and then solve the problem. If neessary, write your answer orret to 1 deimal plae. a A rie reipe uses the ratio of 1 up of rie to ups of water. How many ups of rie an be ooked in ups of water? b Another reipe states that ups of rie are required to serve 6 people. If you have invited 11 people, how many ups of rie will you need? In a hemial ompound there should be 1 g of hemial A to every g of hemial B. If my ompound ontains 0 g of hemial A, how many grams of hemial B should it ontain? d A saline solution ontains parts of salt to 17 parts of water. How muh water should be added to parts of salt? e To mix onrete, bukets of sand are needed for every bukets of blue metal. For a big job, how muh blue metal will be needed for 1 bukets of sand? 6 Deide whether a proportion statement ould be made, using eah of the following ratios: a height : age b mass : age intelligene : age d distane : time e ost : number f age : shoe size g sausages ooked : number of people h eggs : milk (in a reipe) i number of words : pages typed j length : area (of a square). 7 a MC If p q l =, then: m A p ì q = l ì m B p ì l = q ì m C p ì m = l ì q p l D = E none of these is true. m q b If x = y, then: 6 A x = and y = B x = 1 and y = C x = and y = 6 D x = 6 and y = 1 E all of these are true. If = x then, orret to the nearest whole number, x equals: 19 A 1 B 1 C D 8 E 17 d The diretions on a ordial bottle suggest mixing ml of ordial with 0 ml of water. How muh ordial should be mixed with. L of water? A 0. ml B. ml C ml D 0 ml E 00 ml REASONING 8 In a family, hildren reeive their allowanes in the ratio of their ages, whih are 16 years, 1 years and 10 years. If the total of the allowanes is $80, how muh does eah hild reeive? Chapter Ratios and rates 1

12 Digital do WorkSHEET.1 do-16 D 9 In jewellery, gold is often ombined with other metals. Pink gold is a mixture of pure gold, opper and silver in the ratio of 1 : : 1. White gold is a mixture of pure gold and platinum in the ratio of : 1. a What fration of both pink and white gold jewellery is pure gold? Pure gold is arats and is not mixed with other metals. For most jewellery, however, 18 arat gold is used. b Using your answer to part a, show why jewellery gold is labelled 18 arats. If an 18 arat braelet weighs 8 grams, what is the weight of gold in the braelet? d If the prie of gold is $ per gram, what is the ost of the gold in the braelet? 10 Two lasses eah ontain 8 boys. In one lass, the ratio of boys to girls is 1 : ; in the other it is : 1. If the two lasses ombine, what will the new ratio be? Comparing ratios REFLECTION Can you think of an example of how a proportion statement might be used? In some ases it is neessary to know whih of two given ratios is the larger. In some ases it is neessary to know if two given ratios are equal. To ompare ratios, write them as frations with a ommon denominator. WORKED EXAMPLE 11 Whih is the larger ratio in the following pair? : : 1 Write eah ratio in fration form. Change eah fration to the lowest ommon denominator (whih is 1). Compare the frations: sine both frations have a denominator of 1, the larger the numerator, the larger the fration. The seond fration is larger and it orresponds to the seond ratio in the pair. State your onlusion < 10 1 Therefore, : is the larger ratio. When measuring the steepness of various slopes or hills, we need to ompare the gradient. Gradient is alulated by finding the ratio vertial distane horizontal distane between any points on a hill. This is also known as alulating rise run. The larger the gradient, the steeper the hill. 1 Maths Quest 8 for the Australian Curriulum

13 WORKED EXAMPLE 1 Find the gradient of the hill (AB) if AC = m and BC = 10 m. B Horizontal distane A Vertial distane C 1 Write the rule for finding the gradient. Gradient = Vertial distane is m and horizontal distane is 10 m. Substitute these values into the formula. vertial distane horizontal distane = 10 Simplify by dividing both numerator and denominator by. = 1 REMEMBER 1. To ompare ratios, write them in fration form first and then ompare the frations by writing them with a ommon denominator.. Gradient is a measure of the steepness of the slope and is alulated by finding the ratio vertial distane. (The distanes are measured between any points on the slope.) horizontal distane EXERCISE D INDIVIDUAL PATHWAYS Ativity -D-1 Comparing ratios do-0 Ativity -D- More omparisons of ratios do-0 Ativity -D- Advaned omparisons of ratios do-06 Comparing ratios FLUENCY 1 WE 11 Whih is the greater ratio in eah of the following pairs? a 1 :, : b : 9, 7 : 9 6 :, : d :, 7 : 10 e 7 : 9, : f :, 1 : g :, : h : 6, 7 : 8 i : 9, 7 : 1 j 9 : 8, 6 : In eah of the following ases, deide whih netball team has the better reord. a St Marys won mathes out of. Cola won out of 10. b Bright 0 won 1 out of 18. Corio won 7 out of 1. Seymour won 1 out of 0. Geelong won 1 out of. d Bell Post Hill won 8 out of 1. Bairnsdale won 1 out of 0. In a riket math, Jenny bowled wides in her 7 overs and Lisa bowled wides in her 6 overs. Whih bowler had the higher wides per over ratio? Chapter Ratios and rates 1

14 a WE 1 Find the gradient of eah of the hills represented by the following triangles. i A ii C m m B m D m iii E iv G F m m H 7 m 1. m Digital do Spreadsheet Comparing ratios do-1 b Whih slope has the largest gradient? Whih slope has the smallest gradient? d List the hills in order of inreasing steepness. Draw triangles that demonstrate a gradient of: a 1 b 1 d e UNDERSTANDING 6 a MC If the gradient of LN in the triangle at right is 1, then: A a > b B a < b C a = b D a = 1 E b = 1 b If > a, then a ould be: 6 A B C 6 D 7 E all of these numbers. N b L a If a b <, then: A a < B b < C a < b D b < a E a = REASONING E 7 Draw a right-angled triangle on a piee of graph paper so that the two sides at right-angles to eah other are 6 m and 8 m. Measure the third side length of the triangle. a What is the ratio of the three sides of this triangle? b If you hange the size of your triangle but keep the shape the same, what happens to the ratio of the three sides of the triangle? If you had metres of string to mark out a triangle with its sides in the same ratio as the one you have drawn, what would be the length of eah side marked out with string? Test your answer with a piee of string. Dividing in a given ratio REFLECTION What does it mean if the gradient is 0? When something is shared, we often use ratios to ensure that the sharing is fair. Consider this situation. Two people buy a lottery tiket for $. They win a prize of $60. How is the prize divided fairly? 16 Maths Quest 8 for the Australian Curriulum

15 elesson Dividing in ratios eles-001 Eah person ontributes $1.0 One person ontributes $1 and the other $ The ontribution for the tiket is in the ratio 1 : 1. The prize is divided in the ratio 1 : 1. Eah person reeives $0. The ontribution for the tiket is in the ratio 1 :. The prize is divided in the ratio 1 :. The person who ontributed $1 reeives $0 and the other reeives $0. In the situation above: the 1 : 1 ratio has = total parts. Eah person reeives 1 of the prize money ($0). the 1 : ratio has 1 + = total parts. Person 1 paid for 1 part of the tiket so reeives 1 of the prize money ($0); person paid for parts of the tiket so reeives of the prize money ($0). WORKED EXAMPLE 1 Share the amount of $ in the ratio : 7. 1 Determine how many shares (parts) are in the ratio. The first share represents parts out of a total of 10, so find of the total amount. 10 The seond share is the remainder, so subtrat the first share amount from the total amount. Total number of parts = + 7 = 10 First share = ì $ = $ Seond share = $ $ = $0 000 In Worked example 1, the seond share represents 7 parts out of the total of 10. Another way to alulate the size of the seond share would be to find 7 of the total amount. 10 Seond share = 7 ì $ = $0 000 WORKED EXAMPLE 1 Conrete mixture for a footpath was made up of 1 part of ement, parts of sand and parts of blue metal. How muh sand was used to make. m of onrete? 1 Find the total number of parts. Total number of parts = = 7 There are parts of sand to be used in the mixture, so find of the total amount of onrete made. 7 Amount of sand = ì. m 7 = 1. m Chapter Ratios and rates 17

16 REMEMBER To share a ertain amount in a given ratio, find the total number of shares (parts) first. The size of eah share is given by the fration this share represents out of the total number of shares. EXERCISE E INDIVIDUAL PATHWAYS Ativity -E-1 Dividing in a given ratio do-07 Ativity -E- More dividing in a given ratio do-08 Ativity -E- Advaned dividing in a given ratio do-09 Dividing in a given ratio FLUENCY 1 Write the total number of parts for eah of the following ratios. a 1 : b : : 1 d : e : 9 f : 8 g 6 : 7 h 9 : 10 i 1 : : j : : WE 1 Share the amount of $1000 in the following ratios. a : b : 1 1 : d 1 : 1 e : f : g : 7 h 9 : 1 i 7 : 1 j 9 : 11 If Nat and Sam deided to share their lottery winnings of $ in the following ratios, how muh would eah reeive? a 1 : 1 b : : d : 7 e 7 : f 1 : g 9 : 1 h : i 1 : 1 j : 7 Rosa and Mila bought a lottery tiket osting $10. How should they share the first prize of $0 000 if their respetive ontributions were: a $ and $8? b $ and $7? $ and $6? d $ and $? e $.0 and $7.0? WE 1 Conrete mixture is made up of 1 part ement, parts sand and parts blue metal. a How muh sand is needed for 7 m of onrete? b How muh ement is needed for. m of onrete? How muh blue metal is required for.8 m of onrete? d How muh sand is used for.6 m of onrete? e How muh ement is needed to make 8. m of onrete? 6 Three of your teahers buy a Lotto tiket osting $0. How should they share the first prize of $ if they eah ontribute: a $, $7 and $10? b $6, $6 and $8? $1, $8 and $11? d $, $6 and $9? e $, $7.0 and $7.0? Digital do Spreadsheet Dividing in a given ratio do-89 7 In a family, hildren reeive their allowanes in the ratio of their ages, whih are 1 years, 1 years and 9 years. If the total of the allowanes is $60, how muh does eah hild reeive? 18 Maths Quest 8 for the Australian Curriulum

17 UNDERSTANDING 8 In a shool, the ratio of girls in Years 8, 9 and 10 is 6 : 7 : 11. If there are 60 girls in the shool: a how many Year 8 girls are there? b how many more Year 10 girls are there than Year 8 girls? 9 In a moneybox, there are ent, 10 ent and 0 ent oins in the ratio 8 : :. If there are oins altogether: a how many ent oins are there? b how many more 10 ent oins than 0 ent oins are there? what is the total value of the ent oins? d what is the total value of the oins in the moneybox? 10 a MC A square of side length m has its area divided into two setions in the ratio :. The area of the larger setion is: A m B m C 8 m D 10 m E 16 m b A blok of heese is ut in the ratio :. If the smaller piee is 10 g, the mass of the original blok was: A 7 g B 00 g C 00 g D 7 g E 0 g Contributions to the ost of a lottery tiket were $1.7 and $1.. What fration of the prize should the larger share be? 7 7 A B C D E d A television hannel that teleasts only news, movies and sport does so in the ratio : : respetively. How many movies, averaging a length of 1 1 hours, would be shown during a -hour period? A B C D E 6 REASONING F 11 Three angles of a triangle are in the ratio 1 : :. What is the magnitude of eah angle? 1 The angles of a quadrilateral are in the ratio : : : 6. What is the differene in magnitude between the smallest and largest angles? Rates A rate is used to ompare how quantities hange. Unlike ratios, rates have units. An example of a rate is speed (measured in km/h or m/s) A rate is in its simplest form if it is per one unit. REFLECTION Think of some examples of instanes where you need to divide in a ratio other than 1 : 1. WORKED EXAMPLE 1 Express the following statement using a rate in simplest form: The 0 litre ontainer was filled in minutes. 1 A suitable rate would be litres per minute (L/min). Put the apaity of the ontainer in the numerator and the time in whih it was filled in the denominator of the fration. Rate = 0 L min = 10 L 1min Simplify the fration. = 10 L/min Chapter Ratios and rates 19

18 WORKED EXAMPLE 16 Joseph is paid $8.0 per hour as a asual worker. At this rate, how muh does he reeive for 6 hours of work? 1 The rate is given in $ per hour. So it atually tells us the amount of money earned in eah hour; that is, the hourly payment. Payment per 1 hour = $8.0 State the number of hours worked. Hours worked = 6 To find the total payment, multiply the hourly payment by the total number of hours worked. Total payment = $8.0 ì 6 = $1 REMEMBER 1. Rates are used to measure and ompare the hanges in different quantities.. Rates are usually written using per or a slash (/ ).. Rates are onsidered to be in simplest form if they are expressed per one unit (for example, per minute, per hour, per kg and so on). EXERCISE F INDIVIDUAL PATHWAYS Ativity -F-1 Rates do-10 Ativity -F- More rates do-11 Ativity -F- Advaned rates do-1 Rates FLUENCY 1 WE 1 Express eah of the following statements using a rate in simplest form. a A lawn of 600 m was mown in 60 min. b A tank of apaity 0 kl is filled in 70 min. A balloon of volume 00 m was inflated in 1 s. d The ost of 10 L of fuel was $1.80. e A ar used 16 litres of petrol in travelling 00 km. f A 1 m length of material ost $0. g There were 0 ows grazing in a paddok that was 000 m in area. h The gate reeipts for a rowd of people were $ i The ost of painting a 0 m area was $160. j The ost of a 1 minute phone all was $.00. k The team sored 8 points in games. l Last year 7 kg of fertiliser ost $0. m The winner ran the 100 m in 1 s. n To win, Australia needs to make 60 runs in 0 overs. o For 6 hours work, Bill reeived $19. p The. kg parel ost $19. to post. q Surprisingly, 780 words were typed in 1 minutes. r From 6 am to noon, the temperature hanged from 10 èc to èc. 10 Maths Quest 8 for the Australian Curriulum

19 s t When Naoum was 10 years old he was 10 m tall. When he was 18 years old he was 17 m tall. A ylist left home at 8.0 am and at am had travelled 0 km. WE 16 Sima is paid $1.0 per hour. At this rate, how muh does she earn in a day on whih she works 7 hours? A basketball player sores, on average, points per math. How many points will he sore in a season in whih he plays 18 mathes? A ar s fuel onsumption is 11 L/100 km. How muh fuel would it use in travelling 0 km? To make a solution of fertiliser, the diretions reommend mixing apfuls of fertiliser with L of water. How many apfuls of fertiliser should be used to make L of solution? 6 Anne an type 60 words per minute. How long will she take to type 00 words? 7 Marie is paid $ per day. For how long will she have to work to earn $0? 8 The rate of 1 teaher per 16 students is used to staff a shool. How many teahers will be required for a shool with 78 students? 9 Land is valued at $ per m. How muh land ould be bought for $6 000? 10 On average, a test bowler took 1 wiket every. overs. How many wikets did he take in a season in whih he bowled 189 overs? UNDERSTANDING 11 What quantities (suh as distane, time, volume) are hanging if the units of rate are: a km/h? b m /se? L/km? d $ per h? e $ per m? f kl/min? g ents/litre? h $ per dozen? i kg/year? j attle/hetare? 1 What units would you use to measure the hanges taking plae in eah of the following situations. a A rainwater tank being filled. b A girl running a sprint rae. A boy getting taller. d A snail moving aross a path. e An ink blot getting larger. f A ar onsuming fuel. g A batsman soring runs. h A typist typing a letter. 1 Water flows from a hose at a rate of L/min. How muh water will flow in h? 1 Tea bags in a supermarket an be bought for $1. per pak (pak of 10) or for $.8 per pak (pak of ). Whih is the heaper way of buying the tea bags? 1 Car A uses 1 L of petrol in travelling 00 km. Car B uses L of petrol in travelling 00 km. Whih ar is the more eonomial? Chapter Ratios and rates 11

20 16 Coffee an be bought in 0 g jars for $9.0 or in 100 g jars for $.10. Whih is the heaper way of buying the offee and how large is the saving? 17 MC a A ase ontaining 70 apples was bought for $180. The ost ould be written as: A 0 ents eah B 0 ents eah C $.00 per dozen D $.00 per dozen E $.80 for 10 b Mark, a test riketer, has a batting strike rate of 68, whih means he has made 68 runs for every 100 balls faed. What is Steve s strike rate if he has faed 6 overs and has made 80 runs? (Note: Eah over ontains 6 balls.) A 6 B 68. C 71.8 D 7. E 7.1 A arport measuring 8 m ì m is to be paved. The paving tiles ost $6 per m and the tradesperson harges $1 per m to lay the tiles. How muh will it ost to pave the arport (to the nearest $0)? A $100 B $10 C $100 D $10 E $1600 d A tank of apaity 0 kl is to be filled by a hose whose flow rate is 10 L/min. If the tap is turned on at 8 am, when will the tank be filled? A Between 1.00 pm and 1.0 pm B Between 1.0 pm and.00 pm C Between.00 pm and.0 pm D Between.0 pm and.00 pm E Between.00 pm and.0 pm REASONING Digital do WorkSHEET. do A hiroprator sees 160 patients every week. a What is his rate of seeing patients eah hour if he works a 0-hour week? b How long, on average, does he spend with eah patient? Using these rates, if the hiroprator wants to make at least $ every week, what is the minimum he must harge eah patient? 19 If monkeys eat bananas in minutes, how long does it take 1 monkeys to eat 1 bananas? 0 If Bill takes hours to paint a room, and James takes hours to paint a room, how long will it take to paint a room if they work together? REFLECTION Why do we need units with rates? 1 Maths Quest 8 for the Australian Curriulum

21 Summary Introdution to ratios Ratios ompare quantities of the same kind. The ratios themselves do not have a name or unit of measurement. The order of the numbers in a ratio is important. Before ratios are written, the numbers must be expressed in the same units of measurement. Ratios ontain only whole numbers. Simplifying ratios If eah number in a ratio is multiplied or divided by the same number, the equivalent (or equal) ratio is formed. It is ustomary to write ratios in the simplest form. This is ahieved by dividing eah number in the ratio by the highest ommon fator (HCF). To form a ratio using frations, onvert the frations so that they have a ommon denominator and then write the ratio of the numerators. Deimals an be easily hanged into whole numbers if they are multiplied by powers of 10 (that is, 10, 100, 1000 and so on). If the ratio ontains algebrai terms, divide both parts of the ratio by the highest ommon fator (HCF) inluding ommon algebrai terms. Proportion Proportion is a statement of equality of two ratios. In any proportion, the produts of the numbers, diagonally aross from eah other, are equal. In general, if a =, then, using ross-multipliation, a ì d = ì b. b d Comparing ratios To ompare ratios, write them in fration form first and then ompare the frations by writing them with a ommon denominator. Gradient is a measure of the steepness of the slope and is alulated by finding the ratio vertial distane. (The distanes are measured between any points on the slope.) horizontal distane Dividing in a given ratio To share a ertain amount in a given ratio, find the total number of shares (parts) first. The size of eah share is given by the fration this share represents out of the total number of shares. Rates Rates are used to measure and ompare the hanges in different quantities. Rates are usually written using per or a slash (/ ). Rates are onsidered to be in simplest form if they are expressed per one unit (for example, per minute, per hour, per kg and so on). Homework Book MAPPING YOUR UNDERSTANDING Using terms from the summary, and other terms if you wish, onstrut a onept map that illustrates your understanding of the key onepts overed in this hapter. Compare this onept map with the one that you reated in What do you know? on page 111. Have you ompleted the two Homework sheets, the Rih task and the two Code puzzles in your Maths Quest 8 Homework Book? Chapter Ratios and rates 1

22 Chapter review FLUENCY 1 On a farm there are dogs, ats, 17 ows and 1 horse. Write the following ratios. a ats : dogs b horses : ows ows : ats d dogs : horses e dogs : other animals Express eah of the following ratios in simplest form. a 8 : 16 b : 6 mm : 10 m d $ : 60 ents e 0 s : 1 1 min f 1 1 : 1 g : 10 h 6 : 80 i hours : 0 min j 1. km : 00 m Find the value of n in eah of the following proportions. a e n 0 = 1 b 8 = n d n = = n 6 n = 8 f = n 10 The diretions for making lime ordial require the mixing of 1 part ordial to 6 parts of water. a Express this as a ratio. b How muh ordial would you have to mix with 9 L of water? Whih is the larger ratio? a, b 7 1, 8 6 Plae a number in the box to make a ratio greater than : but less than : 1. : 6 7 The horizontal and the vertial distanes between the top and bottom points of slide A are m and m respetively. For slide B the horizontal distane between the top and bottom points is 10 m, and the vertial distane is m. a Calulate the gradients of slide A and slide B. b Whih slide is steeper? Justify your answer. 8 a Divide $ in the ratio :. b Share $70 in the ratio 7 :. 9 Three people share a Lotto prize of $6600 in the ratio : : 6. What is the differene between the smallest and largest shares? 10 A ar travels 80 km on 7 litres of petrol. Find the fuel onsumption of the ar in L/100 km. 11 David s ar has a fuel onsumption rate of 1 km/l, and Susan s ar has a fuel onsumption rate of 11 km/l. a Whih ar is more eonomial? b How far an David s ar travel on 6 L of fuel? How muh fuel (to the nearest litre) would Susan s ar use in travelling 60 km? 1 A 1 kg paket of flour osts $.80 and a 70 g paket osts $.0. Whih is the heaper way of buying flour? PROBLEM SOLVING 1 The sides of a triangle are in the ratio : :. If the longest side of the triangle measures 0 m, what is the perimeter of the triangle? A 77 airplane has a length of 70.7 m and a wingspan of 6. m. A model of this plane has a wingspan of 0 m. How long is the model? The triangle ABC at right is an isoseles right-angled triangle. The length of AC is 0 m. If the lengths of AD and BD are the same and the lengths of CE and BE are the same, what is the length of DE? To make two -up servings of ooked rie, you add of a up of rie, 1 teaspoon of salt and 1 teaspoon of butter to 1 1 ups of water. How many -up servings of ooked rie an you make from a bag ontaining 1 ups of rie? Lahlan was driven from Rihmond to Kinglake National Park, a distane of 60 km, at an a verage speed of 80 km/h. He yled bak at an average speed of 0 km/h. What was his average speed for the whole journey? (Hint: It is not 0 km/h.) 6 The speed of the Disovery spae shuttle while in orbit was miles per hour. What is this in km/h? (1 kilometre = 0.6 miles) 7 The rate of asent for the Disovery spae shuttle is 71 miles in 8. minutes. a What speed is this in km/min? b What speed is this in km/h? A D C E B 1 Maths Quest 8 for the Australian Curriulum

23 8 A ylist riding at 1 km/h ompletes a rae in h min. a What is the distane of the rae? b At what speed would he have to ride to omplete the rae in h? 9 You have a plasti bag that ontains 80 tennis balls. This bag of balls weighs kg (the weight of the plasti bag is insignifiant). You add 10 more balls to your bag. How muh does your bag of balls weigh now? 10 The steps of a stairase are to have a ratio of rise to run that is to be. If the run is 0 m, what is the rise? 11 Travelling from Noort to Bastion takes me 1 hour and 0 minutes by ar at an average speed of 7 km per hour. I stop for 1 minutes in Bastion before travelling to Smoop, whih is 16 km away. The trip from Bastion to Smoop takes me hours and 1 minutes. What is my average speed for the whole trip? 1 A sum of money is divided in the ratio : : 7. Given that the smallest share is $00, alulate the largest share. 1 It takes me hours to mow my lawn. My son takes. hours to mow the same lawn. If we work together using two lawnmowers, how long will it take us to mow the lawn? Give your answer in hours, minutes and seonds. Interativities Test yourself Chapter int-6 Word searh Chapter int-6 Crossword Chapter int-6 Chapter Ratios and rates 1

24 11 The magi sum is is an answer. There are others. Chek with your teaher. 1 = % 1 Yes, rounded to two deimal plaes, Jak s perentage mark is 7%, whih is higher than the other students marks. 16 8% 17 $68.0 CHAPTER Ratios and rates Are you ready? 1 a 00 b 00 0 d 000 e 00 f 600 g 800 h 0 i 10 j 8 k l 10 a b d a a a, b b b 9, 1 1 8, d d d 18 1, a 1.7 b d a 0 b 8 10 d 60 8 a 1 b A Introdution to ratios 1 a : b : : 9 d 9 : e 1 : a : b : 1 : d : 1 e 1 : f : g 1 : 8 h : 9 i 1 : 9 j 1 : a : 7 b 7 : : 1 a : b : 6 : 1 d : 1 e : a : b 6 : 19 : 11 d 7 : 9 e 1 : f 9 : g : h : 10 i 17 : 60 j : 100 k 11 : 100 l 1 : 1000 m 1 : 000 n 7 : o : 1 p 1000 : 7 q 7 : 1 r 1 : s : t 1 : 6 a : 9 b 9 : 8 8 : d : 97 e 9 : 1 7 a : 17 b 1 : 17 : 1 d : 9 e : 1 f 1 : 1 g 1 : h : 1 i 9 : 1 j 1 : k 1 : 6 l 1 : 8 a 1 : 179 b 1 : 6 9 a 97 : b : 100 d a Yes (same units) b Yes (same units) No (different units) d No (different units) e Yes (same units) f Yes (same units) g No (different units) h Yes (same units) 11 a 17 : 8 b 97 : B Simplifying ratios 1 a 1 : b 1 : 1 : d 1 : e : f : 6 g : h : i : j 1 : k : 7 l : m : n : o : 6 p 10 : q 7 : 8 r : s 7 : 1 t : a 1 : : 6 : 9 : 1 : 1 d 6 : : : 8 8 : : 1 b : 1 : 8 : 16 : 8 0 : 10 e 8 : 6 : 1 : 16 6 : 8 : : : 6 6 : 9 8 : 1 16 : a : b 1 : : d : e 1 : f 8 : g : 0 h 1 : i 9 : j 8 : 1 k : l : m 1 : n 11 : o : p 16 : 9 q : 10 r : s 7 : t 1 : 6 a : b : : d : 1 e : f : g 1 : 8 h 10 : i 8 : 1 j 9 : a 1 : 0 b 1 : 9 1 : 11 d 7 : 00 6 a 1 : b : 6 1 : d : e 16 : 9 f 10 : 9 g : 10 h : 1 i : 6 j : k : 8 l 6 : 6 7 a 7 : 9 b 1 : 7 1 : d : e 1 : 6 f 1 : g 10 : 1 h : i 1 : 10 j 8 : k 1 : 0 l : 6 8 a a : b b : 1 x : d y : e m : f 1 : b g 10 : x h d : 1 9 a : 8 b : : d : e : 1 10 a 99 : 1 b 17 : 9 : 16 d 11 : 9 e 6 : 9 11 a 8 : 10 b 0 : 71 : d i $ 000 ii 1 : e In a period of just over 6 years, the prie of the house has inreased by half its purhase prie (in 00). 1 a A b D E d A e B C Proportion 1 a Yes b Yes Yes d Yes e No f Yes g No h No i No j Yes k No l Yes a a = 1 b a = a = 6 d a = e a = f a = 0 g a = 1 h a = 6 i a = 6 j a = 1 k a = l a = a 9 boys b 10 m 1 wins d hikens 6 Answers

25 e litres f 7 tables g ups h g i 7 artons j 80 women a 11. b.8.1 d 8.1 e 7.1 f 9. g 7.7 h 10.8 i 11.7 j a = n b = n 1 0 = 6 11 n n = 1.7 n =.7 n = 1. 1 d = e = 17 n n n =. n =. 6 a No b No No d Yes e Yes f No g Yes h Yes i Yes j No 7 a C b E A d D 8 The 16-year-old reeives $, the 1-year-old reeives $8, the 10-year-old reeives $0. 9 a White gold, pink gold. b Beause 18 =. 6 g d $10 10 : D Comparing ratios 1 a : b 7 : 9 6 : d 7 : 10 e 7 : 9 f : g : h 7 : 8 i 7 : 1 j 6 : a Cola b Bright 0 Seymour d Bairnsdale Jenny a i 1 ii iii b AB GH d iv, iii, ii, i a b 1 e 6 a C b A C 7 a : : b The ratio of the sides stays the same. 0.7 m, 1 m, 1. m d 1 iv 1 E Dividing in a given ratio 1 a b d 8 e 1 f 1 g 1 h 19 i 6 j 1 a $00, $600 b $70, $0 $00, $800 d $00, $00 e $7, $6 f $6, $7 g $00, $700 h $900, $100 i $0, $60 j $0, $0 a $000, $000 b $000, $6000 $6000, $000 d $000, $7000 e $7000, $000 f $000, $8000 g $9000, $1000 h $70, $60 i $800, $00 j $600, $00 a $10 000, $0 000 b $1 000, $ 000 $0 000, $0 000 d $ 000, $ 000 e $1 00, $7 00 a m b 0. m 1.6 m d 1.6 m e 1. m 6 a $90 000, $10 000, $ b $ , $ , $0 000 $0 000, $0 000, $0 000 d $10 000, $ , $ e $10 000, $ 000, $ $, $0, $1 8 a 90 b 7 9 a 10 b $6 d $ a D b D A d D 11 0è, 60è, 90è 1 96è F Rates 1 a 10 m /min b kl/min 00 m /s d $1.8/L e 8 L/100 km or 1. km/l f $.0/m g 0 ows/hetare or (0 m /ow) h $1.0/person i $.0/m j /min k 16 points/game l $.0/kg m 8 1 m/s n. runs/over o $6.0/h p $.0/kg q words/min r èc/h s 6. m/year t 16 km/h $ points 60. L min 7 1 days m a distane volume apaity b time time distane d money money apaity e f time length time g money money mass h i apaity number time j number area 1 a ml/min b m/s m/year d m/h e mm /se f L/km g Runs/over h Words/min 1 60 L 1 Paks of 10 1 Car A 16 0 g jar; 7 17 a C b C D d B 18 a patients per hour b 1 min $6.0 per patient 19 min hours or 1 hour minutes 0 seonds 8 Answers A F Answers 7

26 Chapter review Flueny 1 a : b 1 : : d : 1 e : 1 a 1 : b : 7 : 0 d 10 : e : 9 f 1 : g : h 7 : 10 i : 1 j 1 : a n = b n = 0 n = 1 d n = 1 e n = 9.6 f n = 1. a 1 : 6 b 1. L a 6 10 or 11 7 a Slide A:, slide B: b Slide A 8 a $10, $1 b $0, $00 9 $ L/100 km 11 a David s b km L 1 1 kg paket Problem solving 1 96 m.9 m 10 m 16 km/h km/h 7 a 1. km/min b 808. km/h 8 a km b 1 km/h 9. kg 10 0 m km/h 1 $ h 6 min 0 s CHAPTER 6 Appliation of perentages Are you ready? 1 a $.0 b $07.90 a 0. b d 0.67 e 0.08 f 0.17 a 8% b 87.% 10% d 9.% a $ b $6 $160 d $71. a 1% b 6% 0% 6 a 1% b 10% 00% d 11.% 6A Common perentages and shortuts 1 a $1.00 b $1.80 $.0 d $8.10 e $1.00 f $11.0 g $9.0 h $7.90 i $.70 j $.0 k $1.6 l $1.70 m $1. n $0.1 o $.0 p $.80 q $8.1 r $19. s $0.70 t $6.00 u $19.60 v $0.1 w $71.9 x $00.00 a $1.0 b $.10 $1.70 d $0.90 e $1.70 f $17.0 g $0. h $0.6 i $0.80 j $.90 k $7.0 l $1.0 m $10.0 n $6.80 o $.0 p $1.80 q $0.0 r $6.8 s $10.0 t $0.70 a $0.0 b $0.0 $0.10 d $0.10 e $7.00 f $.0 b 8 g $.10 h $0. i $1.1 j $1. k $0 l $.1 m $.1 n $1.60 o $0.0 a $.0 b $8. $1.6 d $0.6 e $1.80 f $0.0 g $0.1 h $.0 i $7.1 j $. k $7.0 l $ a $1.80 b $1.0 $.00 d $9.00 e $7.0 f $11. g $.0 h $.00 i $.0 j $7.0 k $1. l $0.6 6 a $.70 b $7.1 $.7 d $6.0 e $0.0 f $0.10 g $0.1 h $0.1 i $0.0 j $0.80 k $0.0 l $.0 m $0.0 n $0.0 o $0.10 p $0.00 q $0.00 r $1.6 7 a $1.0 b $10.0 $.0 d $0.6 e $.0 f $.0 g $1.80 h $7.0 i $18.00 j $1. k $1.0 l $.0 m $.0 n $.80 o $1.60 p $0. q $1.0 r $9 8 a D b B A d C 9 $ residents 11 $ students seonds 1 a people b 8 people 1 a people b people 16 10% + % + 1 % = $ $.80 + $1.90 = $ $ $ $ years old 1 $ kg 0 years old 9 years old, 90 years old 6B Disount 1 a $ b $6. $9.0 d $76 a 10% b 0% d % 1 % a $80 b $00 $8.60 d $10 e $6.70 a $ b $ $6 a 0% b 8% 8% d % 6 Estimate 0% 7 a Mobile phone $9 b Surfboard and bike $8. d No 8 a $70 b $80 9 $ a $1.6 b Yes 11 $ % 1 % 1 17.% 1 0% 16 60% 17 $ a $11.60 $10.80 b Gain 8 Answers