meer Workbook EUR. RIM)MY’ Workbook PAL Sy ARE HERE!| ___gpntene . aN. Maths 6APreface My Pals Are Here! Maths (3rd Edition) is a comprehensive, task-based and learner-centred programme designed to provide pupils with a solid foundation in mathematics and opportunities to become efficient problem solvers. In this edition of the Workbook, pupils are given opportunities to master concepts learnt. Questions marked with an asterisk (*) are higher-order thinking questions meant to stimulate pupils’ thinking. calculator may be used when jj appears 4 C...., °t Practice provides a quick reinforcement through questions concepts. wen! L Chapter Review reinforces learning through questions that facilitate mastery of concepts. [— Maths Journal allows pupils to share their thoughts with their teachers, create their own mathematics questions and become aware of their IX \ ‘own mathematical thinking. Put On Your Thinking Cap!— develops pupils’ creative and critical thinking skills with higher-order and non-routine questions. ae [— Review after every few chapters provides a ‘comprehensive consolidation of concepts. -—— Revision provides a summative assessment of pupils’ understanding. Questions are pupils’ leaming progress. that require pupils to recall facts and purposefully crafted to determine Enjoy learning mathematics with My Pals Are Here! Maths (3rd Edition)!CONTENTS @O Algebra Practice 1 Using Letters to Represent Numbers Practice 2_ Evaluating Algebraic Expressions Practice 3. Simplifying Algebraic Expressions Practice 4 Solving Word Problems Chapter 1 Review Maths Journal Put On Your Thinking Cap! @ Fractions Practice 1 Dividing a Fraction by a Whole Number Practice 2 Dividing by a Proper Fraction Practice 3 Solving Word Problems Chapter 2 Review ‘Maths Journal Put On Your Thinking Cap! Review 1 © Ratio Practice 1 Ratio and Fraction Practice 2. Comparing Ratios Practice 3. Solving Word Problems Chapter 3 Review Maths Journal Put On Your Thinking Cap! @ Percentage Practice 1 Finding Percentages Practice 2 Percentage Change Practice 3 Solving Word Problems Chapter 4 Review Maths Journal Put On Your Thinking Cap! 1 7 19 20 2 23 27 39 44 45 47 55 67 77 84 85 87 7 101 109 5s WwWReview 2 © Circles Practice 1A Radius and Diameter Practice 1B Circumference Practice 2 Area of a Circle Practice 3 Composite Figures Chapter 5 Review Maths Journal Put On Your Thinking Cap! © Angles in Geometric Figures Practice 1 Finding Unknown Angles in Geometric Figures Chapter 6 Review Maths Journal Put On Your Thinking Cap! Review 3 Revision 1 ng 129 133, 139 143 153 158 159 161 167 169 170 m 79Name: Class: Date: Algebra Practice 1 Using Letters to Represent Numbers (1) Write an algebraic expression for each of the following. (a) _ Siti bought x kg of green apples and 3 kg of red apples. What was the total mass of all the apples she bought? (b) Padma cycled p km on Monday. She cycled 8 km less on Tuesday. What was the distance she cycled on Tuesday? (._Erynn glued k seashells on a photo frame. She made 5 such photo frames a How many seashells did she use? (4) Jioyi typed wwords in 40 minutes. How many words did she type in 1 minute? tasson Using tors to Represent numbers EB(2) Write an algebraic expression for each of the following (a) (b) {c) (d) le) Add m to 12 Subtract 9 from y 6 groups of y Divide s by 6 Subtract 1 from the product of h and 9 @ Chapter! AlgebraName: Class: Date: Practice 2. Evaluating Algebraic Expressions a) (2) (3) (4) (5) (6) Find the value of 5 + m when m Find the value of 12 — p when p = 7. Find the value of 5z when z = 2. Find the value of # when n = 12 Find the value of 2/ - 9 when j = 6 Find the value of € + 5 when d = 40 Lesson 2 Evaluating Algebraic Expressions 7(7) Complete the following table. Expression Value of Expression When x = 5 x+9 7x 20 -— 3x x $-1 (8) There were m children in a class. Write an expression in terms of m for each of the following and find the value when m = 35. (a) There were 16 girls. How many boys were there? Expression Value (b) Each child received 3 candies and there were 7 candies left over. How many candies were there altogether? Expression Value ~ (c) 3 children were absent and the remaining children formed groups of 4 How many groups of 4 children were there? Expression: Value 5 4 4 j i z @w Chapter 1 AlgebraName: Class: Date: Practice 3 Simplifying Algebraic Expressions 0) simplify (] ctctcte= (b) Sxd= () 60+5a= () b+2b+3b= () 10w—4w= () %p-S5p—p= (g) 82-3z-5z= th) War—3rtr= (i) 8n+2n-3n= ) 20h+5h—h= Lesson 3. Simplifying Algebraic Expressions =>(2) Simply la) 3b+ 8b+2= (dQ 2x+14+3x= le) 10p-7p— (g) 3+3m-14+6m l) %e-2e-7+5e yy Chapter? Algebra (b) (d) th) a ay-9+y= d-24+4d= 5+9k-k= Ja+3-4a+4 l0n+10+n-8Name: Class: Date: Practice 4 Solving Word Problems () Ann has 3 kg of flour. She buys 2 more packets of flour, each of mass m kg (a) Find the amount of flour Ann has altogether in terms of m. (b] If m = 2, how much flour does Ann have altogether? Ans: (a) {b) (2) ‘Mrs Tham bought z bottles of oil at $7 each. She gave the cashier $50. (a) Find the change Mrs Tham received in terms of z. (b} If z= 3, how much change did Mrs Tham receive? Ans: (a) (b) teson Shing Word Potions EDD(3) Alvin and Bala had 26 stickers. Alvin had 8 more stickers than Bala. How many stickers did Bala have? Ans: (4) Cindy and David made 32 paper cranes altogether. Cindy made 6 fewer paper cranes than David. How many paper cranes did David make? Ans: ey Chapter 1 Algebra ‘oars concen ete(5) ‘Ata market, a pear cost be and an apple cost 5¢ less than a pear. Mrs Ravi bought 5 pears and an apple (a) Find the total amount in cents Mrs Ravi paid in terms of b. (b) Tfeach pear cost 60¢, how much did Mrs Ravi pay? Leave your answer in cents. Ans: (a) (b) Lesson 4 Solving Word Problems 2»(6) Huda had y m of cloth. She used 2 m to sew a skirt. She used the remaining cloth to make 3 dresses. (a) Find the amount of cloth used to make each dress in terms of y. (b) Tf Huda had 11 m of cloth, how much cloth was used for each dress? Ans: (a) {b) < Chapter 1 Algebrai) Sandy sold 4 times as many oranges as apples. She sold a total of 70 apples and oranges. How many apples did Sandy sell? Ans: Lesson 4 Shing Word Pabons ED(8) Sally uses a piece of wire 60 cm long to form a rectangle. The length of the rectangle is 5 cm longer than its breadth. What is the length of the rectangle? Ans: a < Chapter 1 AlgebraName: Class: Date: Chapter 1 Review (1) Write an algebraic expression for the following, Subtract 20 from p 2] Find the value of 22 — e+ 1 when e = 3. (3) Simplify 12x + 7+ x- 3 chapter Aledo E>(4) Angela had $6w. After buying some books at $17 each, she had $w left. (al Find the number of books Angela bought in terms of w. b) If w= 34, how many books did Angela buy? “a Ans: (a) ) (5) Kelly, Marvin and Indhu saved $100 altogether. Kelly saved $16 more than Indhu Marvin saved twice the amount Indhu saved. How much did Kelly save? é a 3 3 i 3 i Ans: a I creer:e 120Name: Class: Date: a (2) Write down as many algebraic expressions as you can using the two cards. Write a problem sum involving the four operations using the terms 3 and n.‘Name: Class: Date: Tunit o unit FE Figure) Figure2_—— igure 3 Figure 4 Figure 5 2) A rectangle measures 16 cm by 15 cm. Itis divided into 5 smaller rectangles of equal 7 ‘area as shown. Find the lengths labelled a, b and c. a 4am fo > a ’ 16cm |e z o i ism = i i i < Chapter? AlgebraName: Class: Date: _ Fractions Practice 1 Dividing a Fraction by a Whole Number a Find the value of each of the following. a“ (a) ie 408 OQ O @ Leo= } leas(2) Find the value of each of the following. Express your answer in its simplest form. eV Chopter 2. FractionsName: Class: Date: Practice 2. Dividing by a Proper Fraction a Find the value of each of the following. Express your answer in its simplest form. (a) tb) 3}= t (d) } fel Ne5=(2) Find the value of each of the following. Express your answer in its simplest form O 8 #*50 _Oxe O (a (d) i i I i i i & Chapter 2 Fractions(3) Find the value of each of the following, Express your answer in its simplest form. i) Sele 560 6° 6 yo _5xO Oxi igs 8,1. ib) ges a {+5 4.4 Se. 5 (d) a ig = fel tae Lesson 2 Dividing by a Proper Fraction, S&(4) Find the value of each of the following. Express your answer in its simplest form. 342. 3,80 ‘a 75" Cw*2 -O«O OxO (b) ‘@ I cvo202 cosers () + 10Name: Class: Date: Practice 3 Solving Word Problems 0 Gopal pours : € of milk from a jug equally into 2 cups. Find the amount of milk, in tres, in each cup. Ans:(2) Mei Lin had 5 of a pie. She divided the pie equally among her 3 siblings. What fraction of the pie did each of her siblings receive? g EI renree2 Ftens(3) a” A group of children shared 12 pizzas equally among themselves at a party. Each child received z of a pizza. How many children were there at the party? Ans: A cook divided 12 kg of mashed potatoes equally into some bowls. There was z kg of mashed potatoes in each bowl. How many bowls were there? Ans: Lesson 3. Solving Word Problems 2(5) Hazif bought kg of chicken. He repacked the chicken into some bags, each containing qo of chicken. How many bags of chicken were there? Ans: (6) Rahim hos 4 ¢ of lime juice left after a party. How many days will he take to finish the remaining juice if he drinks € of it each day? EI crepe? rcters(7) Mrs Lim had a piece of rope 3 m long. She cut it into 1 (a) How many Sai pieces of rope were there at most? (b) What was the length of the piece of rope left over? Ans: (a) {b) Lesson Sling Word Pobens \EDDgo (9) Miss Shiva pours 8 € of fruit punch equally into 4 glasses. {a} Find the amount of fruit punch in each glass. Give your answer as a fraction in its simplest form. (b) She buys another 2 € of fruit punch. How many more glasses containing the same amount of fruit punch as before can she fill at most? Ps Ans: (a b) Rehna used 1 of a packet of flour to make some muffins an of it to make a cake. She used the remainder to make some cupcakes. She used fof the packet of flour for each cupcake. How many cupcakes did she make? n~ 4 i & i : Ans: §(10) (Carina had some stickers. 2 of them were dinosaur stickers and the rest were flower stickers. She divided the dinosaur stickers equally among some boys such that each boy recelved 51 of the stickers. She divided the flower stickers equally among some girls such that each girl received 7 of the stickers. (a) How many boys were there? (b) How many girls were there? Ans: (al bp} — Lesson 3 Soling Word Problems ‘=(1) Mrs Hamid used m cups of flour to bake a cake, a pie and some loaves of bread. She used 3 cup of flour to bake the pie and twice as much flour to bake the cake. (a) How many cups of flour did she use to bake the loaves of bread? Express your answer as a mixed number in its simplest form. (b) She made 2 identical loaves of bread. How many cups of flour did she use to bake a loaf of bread? Give each answer as a mixed number in its simplest form. Ans: (a) (b) g (13) Jiagj, Gwen and Patricia painted the walls of a room together. Jiaqi painted 4 of the walls. Gwen and Patricia painted an equal amount of the remaining area of the walls. Jiagj painted 2 m? more than the area that Gwen and Patricia each painted. Find the total area of the walls that they painted, Give your answer as a mixed number in its simplest form. Ans: ‘2 20m aha Goer tcten ts1m) Nidehod 2 iene contre. One contsner wes completely filled with water. The other container was filed with syrup. He used some water and some syrup to make a dink, He hed the some amount of water and syrup let. He used 2 ¢ more water than sjrop. How rich syrup dil he have ot frst? Ge your answer as a fraction ints simplest form. ‘© 20 ara Cnneh enn id Ans: Lesion Soking Word oben ERJG_15) During the school holidays, Chris read 312 pages of a book at first. He read the remaining pages in 20 days, with the same number of pages each day. During these 20 days, he read ++ of the book in 6 days. How many pages did he read in the 6 days? << Chapter 2 FractionsName: Class: Date: Chapter 2 Review a Find the value of + 4, Give your answer as a fraction in its simplest form. (2) Find the value of 5 + &, Give your answer as a mixed number in its simplest form. (3) Find the value of 2 3 Give your answer as a fraction in its simplest form. : i 4 & Chapter 2. Fractions >394) 2 of anumberis 69. what is the number? - Ans: (5) Titus has a rectangular piece of fabric 3 m long and 2 m wide. He cuts it into 3 equal pieces. What is the area of each small piece of fabric? Express your answer as a fraction in its simplest form. A i i 4 i i(6) A gardener planted some seedlings at equal distances apart along a straight road, The 3rd seedling and the Sth seediing were = m apart. The 2nd seedling and the last seedling were 6h m apart. How many seedlings did he plant? Ans: Chapter 2. Fractions >(7) Celine had 35 kg of pistachios. She sold 3 of the pistachios on Saturday and 4 of the remaining pistachios on Sunday. She then packed the remaining pistachios into some bags, each containing Q kg of pistachios. (a) How many bags of pistachios did Celine pack at most? {b) What was the mass of pistachios left? Give your answer os a fraction in its simplest form. Ans: (a) (b) AD croe112 rts(8) Mr Abdul made tuna and curry potato filling for some puts, 2 of the filing he made Was tuna and the rest was curry potato. After he used 7 kg GF the tuna filing and made another $ kg of curry potato filing, he then had qual emounts of tuna filing and curry potato filing eft. How much tuna filing did he make at first? Give your answer as a mixed number in its simplest form. Ans:Name: Class: Date: When a whole number is divided by a proper fraction, is the answer greater than or smaller than the whole number? Support your reasoning with examples. 222m asta Come on idName: Class: Date: a) Nadia and Li Gin had a total of 360 buttons. Nadia gave 1 of her buttons to Li Gin. Ui Gin then gave } of her buttons to Nadia. In the end, each of them had the same. number of buttons. How many buttons did Nadia have at first?{2} Thora were:235 mor re llons than green balosns a pert After 4 of the red balloons and 3 of the green balloons burst, there were 92 balloons left Foy many balloons were i altogether at first? <9 Chapter 2 FractionsName: Class: Date: Section A Each question has four options. Choose the correct option (@. @. © or @). Write in the brackets provided. a In 61 803, the valve of the digit 6 is O 6 @ 6000 @ 60000 @ 600000 (0 (2) Express 0.07 as a percentage. oO ™ @ 07% @ 007% © 0.007% to) (3) How many ninths are there in 4 wholes? O° e 27 98 O x (J (4) Which of the following has the same value as 3 + x x x els ols Ble Ble ©6000 ale ale wie ole x(5) Whats the value of 3 eo 2) 8 e (6) Find the value of 8=2 when p = 32. e 8 8 ° 32 45 & 10 4 fea 5 2 ‘ 10 2 9. oe ok 20 { 1 7) The total mass of a block of butter and a box of cherries is 384 g. The mass of the block of butter is twice the mass of the box of cherries. Find the mass of the block of butter. ° Qe 8 ° 969 128g Ww2g 256 g (1 (8) Megan places 2 identical mugs into a basket. The mass of each mug is tg. The basket is 80 g lighter than each mug. Find the total mass of the basket and the 2 mugs in terms of t. oOo 2tg 3tg (2t- 80) g (3t — 80) g I veiw i i ; | i :‘20m mai Cen cen Pei (9) Aaron is twice as old as Ryan. In 3 years, the sum of their ages will be 30 years. Find Aaron's present age. Os @o 8 6 6 6 a) (10) Tammy spent 2 of her savings on a watch. She then spent q of the remainder on a bag. What fraction of her money did she have left? 9 x e ° © ole ale ni Section B Solve the problems. Show your working clearly and write your answers in the spaces provided. (1) Find the value of 200 + 9 + 0.3 + 0.001 Ans; reve WED(12) Find the value of 97 — 2 x (16 — 4). Ans (13) Simplify 8x + 9 — 4x — 2. Ans: (14) Find the value of : +12, Ans:‘© zat Coenen tac Pi (15) 6) 7) Eileen is 3y years old now. Her mother is 4 times as old as her. Find their total age in 7 years’ time. Give your answer in terms of y. Ans: Jessie baked p cupcakes on Saturday. She baked (p + 3] more cupcakes on Sunday than on Saturday. She baked 30 cupcakes altogether. How mony cupcakes did Jessie bake on Saturday? Ans: — The figure is made up of 10 identical squares. The perimeter is y crn. What is the side of each square in terms of y?Section C [| Solve the problems. Show your working clearly and write the answers in the spaces | provided. (18) Usman prepared 8 € of orange juice for some guests. He poured the juice into glasses each with a capacity of } f (a]_ How many glasses of orange juice were there at most? (b} How much orange juice was left? Give your answer as a fraction in its simplest form. Ans: {a} (b)a9) The mass of a pot completely filed with soup is 6 kg. When itis filled with soup, its mass is 2.8 kg. What is the mass of the empty pot? Ans: Review 1 ~»(20) During a sale, a jar of jam costs $2.60 and a bundle of 3 jars of jam costs $5. Sam wants to buy exactly 83 jars of jam. What is the least amount of money he needs?Class: Date: Ratio =—/ Practice 1 Ratio and Fraction () Stick A is 5 cm. Stick B is 4 cm. ~ stick A [ stick B (a) __ The ratio of the length of Stick A to the length of Stick B is —. tb) Lenath of stick _ a) Length of Sick ~ (—) The length of Stick A is of the length of Stick B. {c) The ratio of the length of Stick B to the length of Stick A is fit (a) Lenathot stick B QO Length of Suck ~ The length of Stick B is {e] Total length of Stick A and Stick B = O + O =()m ‘The ratio of the length of Stick A to the total length of Stick A and Stick B is of the length of Stick A. uesson1 ato ona acon EBD(2} Maureen has 3 pencils and 8 pens. {a} Total number of pencils and pens = (_) + (_) =O Number of pencils _O Total number of pencis ondppens ~ (—) ‘The number of pencils is of the total number of pencils and pens. (b) The ratio of the number of pens to the total number of pencils and pens is Number of pens _O (2. Glatnmber of pendis ond pens = O The number of pens is of the total number of pencils and pens. (3) Calvin keeps 2 dogs, 7 hamsters and 3 birds as pets coc: Hamsters. Birds la} The ratio of the number of dogs to the number of hamsters is The number of dogs is of the number of hamsters. (b) The ratio of the number of birds to the number of dogs is The number of birds is of the number of dogs. (c) Total number of pets = O + O + O “0 The ratio of the number of dogs to the total number of pets in its simplest form is The number of dogs is & Chapter 3 Ratio of the total number of pets(4) Pete played 18 tennis matches in a week. Sam played 6 tennis matches in the same week. {co} _ Find the ratio of the number of matches Pete played to the number of matches Sam played. (b) Express the number of matches Sam played as a fraction of the number of matches Pete played. Give your answer in its simplest form. (Express the number of matches Pete played as a fraction of the number of matches Sam played {d) Express the number of matches Pete played as a fraction of the total number of matches the two boys played. Give your answer in its simplest form, Lesson 1 Ratio and Fraction S(5) Zalina’s mass is £ of Magdalene’s mass. (a) (b) {d (d) (e) Draw a model to compare the mass of Zalina and Magdalene. Express Magdalene’s mass as a fraction of Zalina's moss, What is the ratio of Zalina’s mass to Magdalene’s mass? What is the ratio of Magdalene’s mass to the total mass of the two girls? Express Zalina’s mass as a fraction of the total mass of the two girls &y Chapter 3. Ratio(6) Wei iat is 4 times as old as Hafiz. (a) Find the ratio of Wei Kiat’s age to Hafiz’s age. (b) What fraction of Wei Kiat's age is Hafiz’s age? (c)_ What fraction of their total age is Hafiz's age? (a) Find the ratio of Wei Kiat’s age to their total age. : : 4 : i 5 3 Lesson 1 Ratio and Fraction ‘S(7) Liza ears 5 times as much money as Mindy. Jai earns ¢ of what Liza earns. (a) Find the ratio of Mindy's salary to Lizo’s salary. (b) What fraction of Liza's salary is Mindy’s salary? {c)_ How many times of Mindy’s salary does Jai earn? (d) Express Jai’s salary as a fraction of their total salary in its simplest form.(8) 2 of the mass of a lobster is equal to : of the mass of a king crab. The difference in their masses is 4s kg, What is the mass of the king crab? Express your answer as a mixed number in its simplest form Ans:a (9) Zor the length of a side table is equal to w of the length of a dining table. The length Of the side table is 165 cm shorter than the length of the dining table. What is the length of the dining table? Zw Chapter3 RatioName: Class: Date: Practice 2 Comparing Ratios a la) (bo) {ch Pupils in ai school are divided into different groups. The table shows the number of boys and girls in each group. Complete the following table. (Number of Boys| 2 | 4 | 6 | 8 12 (Number of Gis | 5 | 10 | 15 25 The ratio of the number of boys to the number of girls is _ The number of boys is of the number of girls. The table shows the number of cats and dogs in different parts of a pet adoption centre. Complete the following table. (Number of Cats 4] 2] 2 [35] ) | Number of Dogs | 4 | 8 16 | 20 | 24 The ratio of the number of cats to the number of dogs is The number of cats is of the number of dogs. Siti uses different numbers of tablespoons of water and jelly crystals to make some jelly. Complete the following table. {Number of Tablespoons of Water 8 | 16 32 48 (Number of Tablespoons of Jelly Crystals 6] 9 15 | 18 The ratio of the number of tablespoons of water used to the number of tablespoons of jelly crystals used is of the number of The number of tablespoons of water used is tablespoons of jelly crystals used Lesson 2 Comparing Rates! WED(2) Mariam uses 5 g of baking powder and 240 g of flour to bake a cake. (a) Find the ratio of the amount of baking powder used to the amount of flour used. Give your answer in its simplest form: (b) Mariam uses 25 g of baking powder. How much flour does she need to use? a (Mariam uses 720 g of flour. How much baking powder does she need to use? (a) Mariam wants to bake 4 cakes. How much baking powder and flour does she need to use? 3 é 4 4 : 1 § z i 5 I rceers sore(3) A chef uses salt and sugar in the ratio 2 : 7 to make a sauce. The chef uses 133 g of sugar. How much sait does he use? (4) A painter mixed red and blue paint in the ratio 4 ; 9 to obtain purple paint. He used 12 € of red paint. How much blue paint did he use? Lesson 2 Comparing Ratios >(5) Mrs Rama uses three types of fruit juice for a party. The ratio of the amount of watermelon juice to the amount of apple juice is 4 : 9. The ratio of the amount of apple juice to the amount of orange juice is 27 : 14. Find the ratio of the amount of watermelon juice to the amount of apple juice to the amount of orange juice in its simplest form. (6) A bookstore sells cookbooks, novels and reference books. The ratio of the number of cookbooks to the number of novels is 2 : 11. The ratio of the number of cookbooks to the number of reference books is 3 : 4. What is the ratio of the number of cookbooks to the number of novels to the number of reference books at the bookstore? <9 Chapter 3 Ratio eco tmast Ciarehston PedName: Class: Date: Practice 3. Solving Word Problems a) The amount of money Suri spends is Zot the amount of money Linda spends. Linda spends $116. How much money does Suri spend? A Ans: (2) Maria and Rizal entered a competition as a team. Rizal's score was + of Maria's score. Maria scored 46 more points than Rizal. How many points did Maria score? Ans: Lesion Shing Word Plens| ED i i 7 5 i iJB ©) The length of a rectangle is 6 times os long as its breadth, “ (a) What fraction of the perimeter of the rectangle is the length of the rectangle? Give your answer in its simplest form. (b] Find the ratio of the length of the rectangle to its breadth to its perimeter. (0. The perimeter of the rectangle is 336 cm. Find the length of the rectangle. a Ans: (a) i (o) i ; 2 0 i Road ‘Chapter 3 Ratio(4) Li Zhen, Kara and Rose were typing. Li Zhen typed 2 times as fast as Kara, The ratio of the number of words Kara typed to the number of words Rose typed was 4 : 1 (a) What was the ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed? (b) Kara typed 48 words. How many words did Li Zhen, Kara and Rose type altogether? Ans: (a) (by — Lesson 3. Solving Word Problems A 694(5) The ratio of the number of marbles Zali had to the number of marbles Muthu had was 3 : 4. Muthu gave half of his marbles to Zali. What was the new ratio of the number of marbles Zali had to the number of marbles Muthu had? a Ans: (6) Mrs'Neo has two packets of flour. The ratio of the mass of flour in Packet A to the mass of flour in Packet Bis 1: 2. Mrs Neo uses 2 of the flour in Packet A and has 800 g of flour left altogether. How much flour is there in Packet B? ~ i { 3 Ans: 8 I creme too” ‘Mr Lim put some red pens and blue pens into a box. The ratio of the number of red pens to the number of blue pens was 3: 4. He put another 20 red pens into the box and the ratio of the number of red pens to the number of blue pens became 2 : 1 (o]_ How many red pens were there in the end? (b] How many blue pens were there? Ans: (a) (b) Lesson 3 Solving Word Problems >(8) The ratio of the number of cakes Ann had to the number of cakes Beth had was 5 : 2. After Ann sold 28 cakes, the ratio of the number of cakes Ann had to the number of cakes Beth had became 3 : 4. How many cakes did Ann have at first? Ans: CP) cores wx9) The ratio of the number of goats in Farm X to the number of goats in Farm Y was 9:4, After 35 goats were transferred from Farm X to Farm Y, there was an equal number of goats in each farm. How many goats were there in Farm Y at first? Ans: Lesson 3. Solving Word Problems >(10) Mr Rahim had the same amount of money in his three bank accounts at first. He deposited $44 into Account 8 and $80 into Account C. In the end, the ratio of the amount of money in Account A to the amount of money in Account C was 2 : 7. How much money was there in Account B in the end?m, Ethan had some solid-coloured socks and patterned socks. He had i as many solid-coloured socks as pattemed socks. He threw away 16 pairs of solid-coloured socks and 16 pairs of patterned socks. 7 of his socks were now solid-coloured socks. How many pairs of pattemed socks did Ethan have at first?(12) Galvin bought 2 as many non-fiction books as fiction books from a book fair. He read 6 non-fiction books and 13 fiction books. He then had 3 ‘as many non-fiction books left to read as fiction books. How many books did Galvin buy altogether? “ Chapter 3 RatioName: Class: Date: Chapter 3 Review m The diagram shows the mass of two bags of rice, X and Y. ry 0 A FS - 5 \ \ 10 (a) The ratio of the mass of Bag X to the total mass of Bag X and Bag Y in its simplest form is __ (b) The mass of Bag Y is of the mass of Bag X. {The mass of Bag X is of the mass of Bag Y. {d) The mass of Bag X is of the total mass of Bag X and Bag Y. le} The mass of Bag Y is of the total mass of Bag X and Bag Y. (2) Abox contained some pens and pencils. The total number of pens and pencils is 8 of the number of pencils. (a) The ratio of the total number of pens and pencils to the number of pencils is __ : (b} Draw a model to compare the number of pens and pencils. 2 | i 2 (The ratio of the number of pens to the number of pencils is __: __.(3) (4) Miss Heng uses 110 g of sugar and 30 g of milk to make some cupcakes. (a) (b) (a The ratio of the amount of milk used to the amount of sugar used is To make the same type of cupcakes, Miss Heng needs uses 675 g of milk of sugar if she To make the same type of cupcakes, Miss Heng needs of mik if she uses 1650 g of sugar. Khairul's savings is 3 of Siew Lee's savings. (a) (b) What is the ratio of Khairut's savings to Siew Lee's savings to their total savings? Siew Lee saves $28 less than Khairul. How much do they save altogether? Ans: (a) (bp) —(9) Anotel ballroom is decorated with tulips, roses and peonies. The ratio of the number of tulips to the number of roses in the ballroom is 2 : 3. There are 4 times as many roses as peonies in the ballroom. There are 575 stalks of flowers in the ballroom altogether. How many tulips are there? Ans: (6) The ratio of the volume of orange juice in Glass A to the volume of orange juice in Glass B is 5 : 3. Half of the orange juice in Glass A is poured into Glass B. What is the new ratio of the volume of orange juice in Glass A to the volume of orange juice in Glass B? Ans: Chapter 3 Ratio >{71 There are some dogs, cats and rabbits in a pet farm. The number of dogs is 3 of the total number of cats and rabbits. The ratio of the number of cats to the number of rabbits is 8 : 7. There are 30 more dogs than rabbits. How many animals are there in ‘the farm? Ans: & Chapter 3 Ratio(8) The ratio of the number of cookies baked by Linus to Omar is 8 : 7. After Linus gave away 36 cookies, Omar had twice as many cookies as Linus. How many cookies did they bake altogether? Ans: Chapter 3 Ratio ‘>(91 The ratio of the number of pupils queuing at a standing broad jump station to the number of pupils queuing at a shuttle run station was 7 : 4. After 18 pupils at the standing broad jump station went to the shuttle run station, there was an equal number of pupils at both stations. How many pupils were queuing at both stations? ew Chopter 3. Ratioma 0) There were some fiction and non-fiction books in a second-hand bookstore, The number of fiction books was 2 of the number of non-fiction books. After an equal number of fiction and non-fiction books were sold, the ratio of the number of fiction books to the number of non-fiction books left was 5 ; 9. There were 240 books altogether at first. How many books were sold altogether? Ans:Name: Class: Date: a Read these statements. (a) The amount of money May had was 4 of the amount of money John had. (b) The amount of money Dave had was 8 of the total amount of money Dave and Wayne had altogether. What does the fraction in each statement mean? Discuss their differences. (2) For each scenario, write down what changed and what remained the same, if any. Use the words ‘decreased, ‘increased! or ‘remained the same’ to help you. (a) The ratio of the number of men to the number of women at a charity function was 4 : 7.7 women left halfway through the charity function. The ratio of the number of men to the number of women who remained became 2 : 3 Number of women; ~ Number of men: Total number of men and women: {b) Velma had some local and foreign coins. The ratio of the number of local coins to the number of foreign coins was 9 : 5. She exchanged 10 local coins for the same number of foreign coins. She then had an equal number of local and foreign coins. Number of local coins: Number of foreign coins: Total number of local and foreign coins: I creee13 200Name: Class: Date: (1) Rectangle PGRS is folded along the line PR. The ratio of the area of Rectangle PGRS to the area of the new figure is 11 : 7. The area of the shaded part is 68 cm*. Find the area of Rectangle PORS, Chopter 3 Ratio ‘=>(2) Ariffin had a total of 40 goats and cows in his farm. After selling 29 of them, the ratio of the number of goats sold to the number of goats left was 4 : 1. The ratio of the number of cows sold to the number of cows left was 3 : 2. What was the ratio of the number of goats left to the number of cows left? : 5 i 5 ' 3 3 : (02 Marl mended(3) Mr Poh has 9 pairs of sneakers. Sneakers make up 60% of his footwear. How many pairs of footwear does he own? a Ans: 4 Aplate of chil crab at a seafood restaurant cost $72.76 including 7% GST. Find the cost of the plate of chilli crab before GST. i : i i 2 Ans: g& go Shirley is thinking of a number. 25% of the number is equal to 110. What number is Shirley thinking of? Ans: Alex has 3 pens in his pencil case. This is 25% of the number of pens that he has. How many pens does Alex have altogether? Ans: Lesson 1 Finding Percentages >a a On a particular day, 55% of the visitors to the zoo were children and the rest were adults. There were 165 children. How many visitors were there at the zoo that day? a Ans: 1 (8) 36% of the members in a gym are females. There are 252 female gym members. How many members are there altogether in the gym? a 3 7 i 4 i 3 Ans: g DI cro 4 bscea96Name: Class: Date: _ Practice 2 Percentage Change 31) A ibrary had 570 books when i first opened. A year later, the number of books increased by 30%. How many books were there in the library a year later? Ans: |B —_ The price of a watch was SIS when it was launched last year. When a new version of = the watch was released this year, the price of the earlier version of the watch decreased by 15%. Find the price of the earlier version of the watch this year. Ans: vesson2 Pacentage charge EDDa (3) Najib bought a handheld game console for $289 after a 15% discount. (a) How much was the discount? (b) What was the usual price of the handheld game console? ry Ans: (a) (b) 3B (4) Onc particular day, the height of the tide at East Coast Park was 0.8 m at dawn At dusk, the height of the tide increased by 40%, Find the height of the tide at dusk, ~ a i ‘ QB Chapter 4 Percentage11 The number of people who visited the Bird Park in February decreased by 30% to 3360 when compared to January. (a) How many people visited the Bird Park in January? (b) How many fewer people visited the Bird Pork in February? i : j j Z Ans: (a) 7 : tb) Lesion? Peranagechonge | EBD| (6) Hannah deposited a sum of money into a savings account. The interest was 3% per year, She did not withdraw any of her savings. After 1 year, Hannah had a total of $2832.50 in the savings account. {a} How much did she deposit into the savings account? (b} How much interest did she receive at the end of the year? SS (b} wy Chapter 4 Percentage1760 upper primary pupils took part in a sports meet in 2014. This was a decrease of 20% when compared to 2015. The number of upper primary pupils who took part in 2016 increased by 5% when compared to 2015. How many upper primary pupils took part in the sports meet in 2016? Ans: tesson 2 Peentge charge ERD(6) The temperature of a piece of metal was 32°C. It was then lowered into a glass of hot water and the temperature of the piece of metal rose to 36°C. Find the percentage increase in the temperature of the piece of metal. a Ans: Pa) The usual price of a bag of oranges was $4. During a promotion, two bags of oranges “ were sold for $5.99. Find the percentage decrease in the price of the two bags of oranges. Give your answer correct to 1 decimal place. a Ans: i i i 2 i(10) Ramesh collected 24 stamps in January. He collected 30 stamps in February and 36 stamps in March. (a) Find the percentage increase in the number of stamps collected between January and February (b) Find the percentage increase in the number of stamps collected between February and March. Ans: (a) (b) Lesson 2. Percentage Change =& ) —_Nazri ran 16 km last week. He ran 1.4 km more this week. Find the percentage increase in the distance he ran this week. Ams; — "121 _Ruzita brought 3000 mi of fruit punch to a picnic. he accidentally spiled 870 ml of fruit punch. What was the percentage decrease in the amount of fruit punch? a q ? i 3 2 Ans; 2a (13) a4) The usual price of a tennis racket was $200. Benny was given a discount of $36 during a sale. Find the percentage discount he enjoyed. Ans: ‘Mrs Koh placed a few boxes of chicken essence in her luggage. As a result, the mass of her luggage increased by 4 kg. This was a 25% increase in the mass of her luggage. Find the mass of her luggage before the boxes of chicken essence were added.a (15) Kamisah cut a 2-m piece of cloth from a roll of fabric. It was 8% of the length of the entire roll of fabric. Find the length of cloth left in the roll of fabric. Ans: (16) Linus received 12 marks more in Test 2 than his score in Test 1. This was a 15% improvement. He then made another 4-mark improvement in Test 3. {a] What was his score for Test 17 (b) What was the percentage increase in his test score from Test 2 to Test 3? Give your answer correct to 1 decimal place. - i & g g a & RP << — Saat i tb) 5 EI) creer recsriogsName: Class: Date: Practice 3 Solving Word Problems {) The table shows the average number of rainy days per month in Singapore in a year. (Month | Jan | Feb | mar] Apr | May| Jun | Jui | Aug | Sep | Oct | Nov | Dec | Number of Doys With | 15 | 11 | 14 | 15 | 15 | 12 | 13 | 14 | 14 | 16 | 20 | 20 Rain {a] What was the percentage decrease in the average number of rainy days per month from May to June? (b) What was the percentage increase in the average number of rainy days per month from October to November? Ans: (a) 3 g i (b) Leeson. sSohing Word Pebions EDThe usual price of a pair of headphones at Store A was $300. Tricia bought it during a sale for $210, {a) How much was the discount? (b] What was the percentage discount Tricia received? Ans: (a) (b) I recta rersniogea go) A piano cost $800 more in 2016 than in 2015. This was a 20% increase from the price in 2015. The price of the piano increased by 25% from 2016 to 2017. Find the cost of the piano (al in 2016. (b) in 2017. Ans: (a) tb) Lesson’3 Solving Word Problems aa (4) An electronics store gave a storewide discount of 15% during a sole, Barry signed up ‘as a member and was entitled to an additional 8% discount on the discounted price. He bought an airfryer for $125.12. What was the usual price of the airfryer? Ans: I crepes recenage (220s tnosot Cede ok Pati(5) There are 1700 seats in a theatre. 40% of the tickets to a concert at the theatre are Category 1 tickets and the rest are of other categories. How many Category | tickets must be added so that the number of tickets of other categories will be decreased to 55%? Ans:a (61 The usual prce of a watch was $87.50. The usual price of a wall clock was 2 of the usual price of the watch. Mandy bought the wall clock at 15% discount during the Great Singapore Sale. Find the discount given on the wall clock. Ans: I) crooter8 recena90a” ‘At a soccer match, 60% of the spectators are men and the rest are women and children. The number of children is 2 of the number of women. There are 252 more men than women at the soccer match. How many spectators are there altogether? Ans: Lesion Song Wor bens! E>@ (8) A bakery sells toro, red bean and green tea pies. 65% of the pies are taro pies. 40% of the remaining pies are red bean pies. (a) What percentage of the pies are red bean pies? (b] There ore 378 green tea pies. How many pies are there altogether? Ans: (a) {b)Name: Class: Date: Chapter 4 Review a (a) David had $12 in his wallet. This was 20% of the amount that he received from his mother. Find the total amount of money that David received from his mother. Ans (2) Alina's home is 15 km from Sentosa. She cycles a distance of 8 km. What percentage . of the total distance does she have left to cover? Give your answer correct to 2 decimal places. 3 & 5 i 3 § g Ans: Chapter 4 Percentage wDa (3) Last year, 3300 people took part in an art competition. This year, the number of participants increased by 50%. How many people took part in the art competition this year? Ans: QW Chapter 4 Percentage44 The midday temperature in Dubai on a particular day was 41°C. At midnight, the temperature decreased to 31.5°C. Find the percentage decrease in the temperature. Give your answer correct to 1 decimal place. Ans: Chapter 4 Percentoge ‘D>@0) The usual price of a washing machine is $899. Eddie pays $269.70 less for the - washing machine atter receiving a discount. Find the percentage discount Eddie receives. Ans: | (6) Anne gains 7.2 kg from January to February. This is an 18% increase in her mass. What is Anne's mass in February? Ans:(7) The usual price of a pair of sunglasses in Store A was $114, This was 95% of the usual price of an identical pair of sunglasses in Store B, Both stores gave the same discount con the pair of sunglasses during c sale. The pair of sunglasses cost $96 after discount in Store B. (a) What was the usual price of the pair of sunglasses in Store B? (b) What was the discount for the pair of sunglasses? i ; ; ! : Ans: (a 1 b) Chapter 4 Percentage >a (8) Jamie's monthly rental for her apartment was $1600. Patrick's monthly rental was 9 10 Find the increase in Patrick's monthly rental. of Jamie's monthly rental. Patrick's landlord increased his monthly rental by 25%. Ans: QI rert:es rerceniogeName: Class: Date: a Aden answered the following questions incorrectly. Explain to Aden his mistakes and show him the correct solutions. (c} 40 pupils took part in a competition. 15 pupils qualified for the finals. What percentage of the pupils qualified for the finals? ‘Aden keyed the following into his calculator: 2 ]banoorrs 40. Aden’s working: 15 = Jo % 100% = 0.375% 0.375% of the pupils qualified for the finals. Explanation Correct solution Chapter 4 Percentage(b) In the morning, the temperature in a garden was 28°C. In the afternoon, the temperature increased to 34°C. What was the percentage increase in the temperature? Give your answer correct to 1 decimal place. Aden’s working Increase in temperature = 34 — 28 =6°C 4 X 100% = 17.6% (correct to 1 decimal place} The percentage increase in the temperature was 17.6%. Explanation Correct solution - (2) You learnt about percentage change in this chapter. What is the most difficult port in learning how to find percentage change? Why? How can you help yourself overcome the difficulty? i 2 2 : ; 3‘Name: Class: Date: () Mr Omar bought a laptop at a discount. If he sold the laptop at its usual price, he would receive $550 more than the amount he paid. If he sold it at 80% of its usual price, he would receive $350 less than the amount he paid, How much did Mr Omar pay for the laptop? Chapter 4 Percentage DpSs FE 2 _twrs Wong sold some cakes to Shops A, B and C. Shop A bought 20% ofthe cakes. Shop B bought 4 times as many cakes as Shop C. Shop B bought 88 more cakes than Shop A. How many cakes did Mrs Wong sell altogether? qe Chapter 4 PercentageName: Class: Date: Section A Each question has four options. Choose the correct option (@), @, © or ©. Write in the brackets provided. (1) MrNg bought 8 oranges, 12 apples and 14 papayas. What was the ratio of the total number of fruits to the number of apples? @ 6:0 @ 6:17 © n:6 @ 7:6 (oy (2) Ina class, 12 pupils walk to school. This is 40% of the total number of pupils in the class, How many pupils are there in the class? O 3 @ 8 2 @«6 to (3) Aboard game cost $20 before GST. There was a 7% GST on the board game. How much was the GST? @ 070 @ si4o © 518.60 © 5321.40 (Co) (4) Kelly spent 40% of her savings and had $21 left. How much did she spend? @ s840 $14.00 $35.00 $49.00 ( 600(5) The price of a camera was $2800. During a sale, there was a 15% discount for the camera. What was the discounted price of the camera? @ $3220 @ $2380 © $2100 © $420 () (6) Tom has some local and foreign stamps. The total number of stamps is 2 of the number of foreign stamps. What is the ratio of the number of foreign stamps to the number of local stamps? 5:4 @ 4:5 oO O 9:5 © 5:9 won (7) The ratio of the number of boys to the number of girls at a birthday party was 4 : 9. 17 girls left. The ratio of the number of boys to the number of girls became 6 : 5. Find the total number of boys and girls at first. @ 2 Oo ua 6 37 © 39 (oo) {8} A box contains some red, yellow and blue beads. The ratio of the number of red beads = to the number of yellow beads is 2 : 5. The ratio of the number of blue beads to the number of red beads is 4 : 7. What fraction of the beads are yellow? 35 57 oa 57 4 57 8 7 (oo) oe) I wis(9) Ameal at a restaurant cost $5. Its price increased to $6 the following week. What was the percentage increase in the cost of the meal? @ 2% @ 2% © 20% © 125% (0 (10) 60% of John’s stamps are local stamps. What is the ratio of the number of local stomps to the number of foreign stamps that John has? @ 3:5 Qe 8 6 Now 3 22 3 Section B Solve the problems. Show your working clearly and write your answers in the spaces provided. (Express 3 as a percentage. 395 4 percentag(12) There are 250 adults and children at a funtair altogether. There ore 90 adults at the funfair. What percentage of the people at the funfair are adults? Ans: {13} The ratio of Sue's age to Tom's age is 5 : 7. Sue is 6 years younger than Tom. How old is Tom? a 3 g 5 5 i ‘ : i Ans: &(14) Jane's monthly allowance decreased from $80 in June to $48 in July. What was the percentage decrease in her allowance from June to July? ~ Ans: 15) Sean, Ryan and Lucas shared $580 in the ratio 2 : 3 : 5. How much less money did Ryan receive than the total amount Lucas and Sean received? é 5 g 3 5 i 5 be(16) 30% of the pupils in a class are boys and the rest are gis, All the boys and 2 of the girls like to play badminton. What percentage of the class like to play badminton?Section C = Solve the problems. Show your working clearly and write your answers in the spaces IB provided (7) Ally has 3 as many stickers as Bella. Bella has 3 ‘as many stickers as Coco. (a]_ What is the ratio of the number of stickers Ally has to the number of stickers Bella has to the number of stickers Coco has? (b) Ally has 24 stickers. How many more stickers does Bella have than Coco? 2 4 i i i Ans: (a) & (b) mae Ne“118) There were 30 pupils in a band. 60% of the pupils were boys. Some boys left the band and the percentage of boys dropped to 20%. How many boys left the band?‘2208 al Cait cabin Pid (19) Mr Tham picked twice as many oranges as mangoes from his farm. While sorting out the fruits, he found that only 60% of the fruits are edible, The ratio of the number of edible oranges to the number of edible mangoes was 5 : 3. There were 90 more edible oranges than edible mangoes. {a} What was the total number of edible oranges and mangoes? {b) How many oranges did Mr Tham pick at first? Ans: (a) (b)*(20) Darren, Muthu and Hafiz shared the cost of a gift equally using their savings. Darren saved $36 more than Muthu. If Darren paid for the gift first, the ratio of Darren’s, remaining savings to Muthu's savings to Hafiz’s savings would be 4: 9 : 1. If Muthu paid for the gift first, the ratio of Darren's savings to Muthu’s remaining savings to Hatiz's savings would be 12 : 1: 1 If Hafiz paid for the gift first, the ratio of Darren's savings to Muthu's savings to Hafiz’s remaining savings would be 4 : 3 : 1. How much did the gift cost? Ans:Name: Class: Date: 3 Circles SS Practice 1A Radius and Diameter a In the following circle, O is the centre. Name a radius and a diameter. ~ . Radius = 5 Diometer = a i 8 g Lesson 1 Radius, Diameter and Circumference >(2) In the circle, O is the centre. (a) Draw a radius. {b) Measure the radius. Ttis _____cm. a (3) In the circle, X is the centre. {a} Draw a diameter. {b) Measure the diameter. Ttis __cm.(4) In the following circle, O is the centre. Draw a radius and a diameter. Measure the radius and the diameter. Radiu: Diameter = ____cm Ce aoi ar Corinto ete Lesson 1 Radius, Diameter and Circumference ‘=(5) In the figure, O is the centre of the circle. A {a} Name all the radii. (b) Name all the diameters. (6) Complete the table. Radius of a Circle @ Chapter 5 Circles Diameter of a Circle 6cm 12cm 4cm 4m Som 64cm 1.3m 020 Macha Crendinedvcton tdName: Class: Date: Practice 1B Circumference (Find the circumference of each circle. (Take x = 22.) ‘a : (_ ~ 2 Find the circumference of each circle. (Take m = i) ; i i ; Lesion Rods, Dameter ond Craumferece WEB