Mathematics 92 Grade 5 Find the product of 1.55 and 24. 1.55 2 4 6 20 31 00 37.20 Therefore, 1.55 × 24 = 37.20. 2.35 × 10 = 235 100 × 10 = 2350 100 = 23 50 100 = 23.5 2.35 × 100 = 235 100 × 100 = 23500 100 = 235 Therefore, 2.35 × 10 = 23.5. Therefore, 2.35 × 100 = 235. MATHS TIPS When multiplying a decimal by 10, 100 and 1000, move the decimal point 1, 2 or 3 places respectively to the right. For example, you can multiply 3.26 by 10, 100 and 1000 as shown below. 1. 3.26 × 10 = 32.6 Move the decimal point 1 place to the right. 2. 3.26 × 100 = 326.0 = 326 3. 3.26 × 100 = 3260 Move the decimal point 2 places to the right. 0 decimal place 2 decimal places 2 decimal places × Move the decimal point 3 places to the right. Find the values of the following. 2 2 1 1
CHAPTER 4 Four operations with decimals 93 Multiplying two 1-decimal place decimals Find the product of 0.4 and 0.8. 0.4 × 0.8 = 4 10 × 8 10 = 4 × 8 10 × 10 = 32 100 = 0.32 2 decimal places Therefore, 0.4 × 0.8 = 0.32. We can also multiply two decimals as shown below. Find the product of 15.8 and 4.3. Step 1: Arrange the numbers in two rows. 15.8 4.3 Step 2: Multiply the numbers as if they were whole numbers. 15.8 4.3 4 74 63 20 67.94 Step 3: Insert the decimal point at the right place in the product to obtain the final answer. The answer should have the same number of decimal places as are in the two numbers being multiplied. 15.8 × 4.3 = 67.94 1 decimal place 1 decimal place 2 decimal places Therefore, 15.8 × 4.3 = 67.94. 1 decimal place 1 decimal place × × 1 2 2 3
Mathematics 94 Grade 5 Find the product of 42.9 and 1.9. 4 2.9 1.9 38 6 1 42 9 0 81.5 1 Therefore, 42.9 × 1.9 = 81.51. Practice Multiply. 1. 0 . 6 × 4 2. 1 2 . 5 3 × 3 3. 3 7 . 8 5 × 8 4. 2 . 2 5 × 4 2 5. 8 . 6 5 × 1 2 6. 6 2 . 8 1 × 2 5 7. 1 0 . 6 × 0 . 6 8. 7 5 . 8 × 2 . 3 9. 1 0 2 . 6 × 6 . 7 10. 23.7 × 10 = 11. 784.3 × 100 = 1 decimal place 2 decimal places 1 decimal place × 2 8
CHAPTER 4 Four operations with decimals 95 F Division of decimals by whole numbers Find the quotient of 1.3 and 3. 1.5 ÷ 3 = 15 10 ÷ 3 1 = 15 10 × 1 3 5 1 = 5 × 1 10 × 1 = 5 10 = 0.5 Therefore, 1.5 ÷ 3 = 0.5. Find the value of 3.24 ÷ 4. 3.24 ÷ 4 = 324 100 ÷ 4 1 = 324 100 × 1 4 81 1 = 81 100 × 1 × 1 = 81 100 = 0.81 Therefore, 3.24 ÷ 4 = 0.81. watch me
Mathematics 96 Grade 5 Let’s find the quotient of 5.14 ÷ 2. Finding quotients by long division Step 1: Divide the ones by 2. Step 3: Divide the hundredths by 2. 2 2 5.14 4 1 2 × 2 ones = 4 ones 5 ones – 4 ones = 1 one Step 2: Divide the tenths by 2. 2.5 2 5.14 4 1 1 1 0 1 2 × 5 tenths = 10 tenths 11 tenths – 10 tenths = 1 tenth 1 one and 1 tenth equal 11 tenths. 2.57 2 5.14 4 1 1 1 0 14 14 0 2 × 5 tenths 2 × 2 ones 2 × 7 hundredths = 14 hundredths 14 hundredths – 14 hundredths = 0 Align the decimal points. Therefore, 5.14 ÷ 2 = 2.57.
CHAPTER 4 Four operations with decimals 97 Do you still remember that adding a zero to the right end of a decimal number does not change the value of the number? To divide a decimal by a whole number using long division Carry out the division of the decimals as the division of whole numbers. Insert the decimal point in the quotient obtained, placing it directly above the decimal point of the dividend. Find the quotient. (a) 4.28 ÷ 8 = (b) 13 ÷ 4 = Align the decimal points. 0.535 8 4.280 0 4 2 4 0 28 24 40 40 0 Zero is added to continue the division. Align the decimal points. 3.25 4 13.00 12 1 0 8 20 20 0 Zeros are added to continue the division. 4.28 ÷ 8 = 0.535 13 ÷ 4 = 3.25
Mathematics 98 Grade 5 The remainder is 1. Every time we add a 0 after the remainder and divide it by 3, a remainder of 1 appears. The resulting quotient, 4.333... is called a repeating decimal. Let 's find the result of 13 ÷ 3 using long division. If the quotient is not a repeating decimal but further division keeps producing remainders, the quotient is called a non-terminating decimal. 4.333... 3 13.000 12 1 0 9 10 9 10 9 1... When the quotient turns out to be a repeating decimal or a non-terminating decimal, round it off to a decimal with one more decimal place than that which the dividend has. MATHS TIPS Let’s Think! Which of these give repeating decimals? 1 ÷ 3 12 ÷ 4 4 ÷ 9 1 ÷ 7
CHAPTER 4 Four operations with decimals 99 Calculate each of the following and round off the quotient to the number of decimal places stated in brackets. (a) 40 ÷ 6 (1 decimal place) (b) 29.1 ÷ 7 (2 decimal places) Then, round off 4.157 to the nearest hundredth. 4.157 ≈ 4.16 Therefore, 29.1 ÷ 7 has an estimated quotient of 4.16. Then, round off 6.66 to the nearest tenth. 6.66 ≈ 6.7 Therefore, 40 ÷ 9 has an estimated quotient of 6.7. MATHS TIPS When dividing a decimal by 10, 100 or 1000, move the decimal point 1, 2 or 3 places respectively to left. For example, you can divide 42.3 by 10, 100 and 1000 as shown below. 1. 42.3 ÷ 10 = 4.23 Move the decimal point 1 place to the left. 2. 42.3 ÷ 100 = 0.423 3. 42.3 ÷ 1000 = 0.0423 Move the decimal point 2 places to the left. Move the decimal point 3 places to the left. Divide until the quotient has 2 decimal places. 6.66 6 40.00 36 4 0 3 6 40 36 4 4.157 7 29.100 28 1 1 7 40 35 50 4 9 1 Divide until the quotient has 3 decimal places. (a) (b)
Mathematics 100 Grade 5 Practice 1. Find the quotient. (a) 30 ÷ 9 = (b) 53 ÷ 3 = (c) 125 ÷ 6 = (d) 110 ÷ 6 = 2. Calculate each of the following and round off the quotient to the number of decimal places stated in the brackets. (a) 5 ÷ 3 (2 decimal places) (b) 88.1 ÷ 3 (3 decimal places)
CHAPTER 4 Four operations with decimals 101 G Word problems (2) Leila bought 5 packets of spices. Each packet had a mass of 0.35 kg. What was the total mass of the spices? 5 × 0.35 kg = 1.75 kg The total mass of the spices was 1.75 kg. Raju used 6 packets of flour to make 4 cakes of the same size. Each packet of flour was 0.75 kg. How much flour did Raju use for each cake? × kg = kg Raju used kg of flour altogether. kg ÷ 4 = kg Raju used kg of flour for each cake. ? 0.35 kg ? 0.75 kg kg ? watch me
Mathematics 102 Grade 5 Maria had 10.25 m of ribbon. She used some of the ribbon to tie 4 gift boxes. She used 1.45 m of ribbon for each gift box. How much ribbon did Maria have left? 4 × 1.45 m = m Maria used m of ribbons to tie 4 gift boxes. m – m = m Maria had m of ribbon left. Kenny is 36.55 kg. His father is twice as heavy as him. Kenny's brother is 28.35 kg lighter than their father. What is the mass of Kenny's brother? × kg = kg Father mass is kg. kg – kg = kg The mass of Kenny's brother is kg. Gift box Gift box Gift box Gift box Left 1.45 m ? 10.25 m Father’s mass ? Kenny’s mass 36.55 kg 28.35 kg Brother’s mass
CHAPTER 4 Four operations with decimals 103 Practice Solve the following word problems. 1. 1 inch is about 2.54 cm. The length of a story book is 12 inches. What is its length in centimetres? 2. Mdm Aisyah bought 12.85 kg of chocolate chips. She kept 3.5 kg of the chocolate chips in a container and divided the remainders into 5 portions. How many kg of chocolate chips was each portion? 3. Julia bought 10 l of pineapple juice. She filled 6 similar bottles with the pineapple juice and had 2.5 l left. Find the amount of pineapple juice in each bottle.
Chapter 5 Percentage 95% of a jellyfish is made up of water and the rest is salt and protein. What does 95% mean? You should be able to • express a fraction as a percentage • express a decimal as a percentage • express a percentage as a fraction or a decimal • find the percentage of a given quantity • solve word problems involving percentage Learning Outcomes https://qr.pelangibooks.com/?u=MOMG5C5mo1 https://qr.pelangibooks.com/?u=MOMG5C5mo2 https://qr.pelangibooks.com/?u=MOMG5C5mo3 Maths Online Maths Online Maths Online Maths Online 2 3
CHAPTER 5 Percentage 105 A Converting more fractions to percentage Look at the figure below. What percentage of the square grid is shaded? Express each fraction as a percentage. 23 100 = % 7 10 = 100 = % Express each decimal as a percentage. 0.59 = 100 = % 0.9 = 10 = 100 = % 0.06 = 100 = % 0.11 = 100 = % Express each percentage as a fraction in its simplest form. 5% = 100 = 45% = 100 = 50% = = 80% = = The square is divided into 100 equal parts. out of 100 squares are shaded. The shaded parts can be expressed: As a fraction As a decimal As a percentage 100 0.39 % watch me
Mathematics 106 Grade 5 Express each percentage as a decimal. 24 % = 100 = 6 % = 100 = 75 % = = 90 % = 100 = Tim used up 3 4 of the storage of his flash drive. What percentage of the storage did he use up? 3 4 = 75 100 = 75 % He used up 75% of the storage. or From the model, 4 4 = 1 whole = 100 % 4 units 100% 1 unit 100 4 = 25% 3 units 3 × 25% = 75% He used up 75% of the storage. or 3 4 of 100% = 4 4 × 100 = 75% He used up 75% of the storage. 25 1 We can use a bar model to express a fraction as a percentage. Recall : 3 4 = 75 100 × 25 × 25 ? 100%
CHAPTER 5 Percentage 107 Express 1 5 as a percentage. 5 units 100% 1 unit = % Therefore, 1 5 = %. Express 1 2 as a percentage. units 100% unit = % Therefore, 1 2 = %. Express 5 8 as a percentage. 8 units 100% 1 unit = % 5 units 5 × % = % Therefore, 5 8 = %. ? 100% ? 100% ? 100%
Mathematics 108 Grade 5 Express 1 4 as a percentage. 1 4 = 25 100 × 25 × 25 or 1 4 of 100% = 1 4 × 100% = 25% = 25% Therefore, 1 4 = 25%. Express 4 5 as a percentage. 4 5 = 100 or 4 5 of 100% = × % = % = % Therefore, 4 5 = % Leo has 200 paper clips. 120 of his paper clips are red. The remaining paper clips are black. (a) What percentage of the paper clips are red? (b) What percentage of the paper clips are black? (a) Fraction of red paper clips = 120 200 = 3 5 Percentage of red paper clips = 3 5 × 100% = 60% 60% of the paper clips are red. (b) Fraction of black paper clips = 100% – 60% = 40% 40% of the paper clips are black. 3 5 × ×
CHAPTER 5 Percentage 109 Murni was reading a 240 page book. She read 180 pages of the book on weekdays and read the rest of the book on the weekend. (a) What percentage of the book was read on weekdays? (b) What percentage of the book was read on weekend? (a) Fraction of the book read on weekdays = 180 240 = 3 4 Percentage of the book read on weekdays = 3 4 × 100% = % % of the book was read on weekdays. (b) Percentage of book read on weekend = % – % = % % of the book was read on weekend. There are 360 books on the shelf. 144 of them are hardback books. The rest of them are paperback books. (a) What percentage of the books are hardback books? (b) What percentage of the books are paperback books? (a) Fraction of hardback books = = Percentage of hardback books = × % = % % of the books are hardback books. (b) Percentage of paperback books = % – % = % % of the books are paperback books. 3 4
Mathematics 110 Grade 5 Practice Solve the following problems. 1. Agus completed 2 5 of his art project. (a) What percentage of his art project is completed? (b) What percentage of his art project is not completed? 2. 550 respondents participated in a marketing survey. 220 of the respondents are male. (a) What percentage of the respondents are male? (b) What percentage of the respondents are female?
CHAPTER 5 Percentage 111 B Percentage of a quantity There are 600 pupils in the school hall. 65% of the pupils are girls. How many pupils are girls? 100% 600 pupils 1% 600 100 = 6 pupils 65% 65 × 6 = 390 pupils 390 pupils are girls. or 65% of pupils = 65% of 600 = 65 100 × 600 = 390 390 pupils are girls. 100% = Total number of pupils Therefore, 100% = 600 pupils. 65% 600 pupils watch me
Mathematics 112 Grade 5 What is 12% of 400? When we find the percentage of a whole number, we let the original number be 100%. 100% 400 units 1% 400 100 = 4 units 12% 12 × 4 = 48 units or 12% of 400 = 12 100 × 400 = 48 Therefore, 12% of 400 is 48. 5% of the pupils in Grade 5 failed their Mathematics exam. If the total number of Grade 5 pupils is 500, how many pupils failed the Mathematics exam? 100% 500 pupils 1% 500 100 = 5 pupils 5% 5 × 5 = 25 pupils or 5% of 500 = 5 100 × 500 = 25 25 pupils failed the Mathematics exam.
CHAPTER 5 Percentage 113 Write 15 out of 20 as a percentage. 20 units 100% 15 out of 20% = 15 20 × 100% 1 unit 100 ÷ 20 = 5 or = 75% 15 units 15 × 5 = 75% 15 out of 20% is 75%. Write 6 out of 40 as a percentage. 40 units 100% 6 out of 40% = 6 40 × 100% 1 unit 100% ÷ 40 = 2.5 or = 15% 6 units 6 × 2.5% = 15% 6 out of 40% is 15%. Write 24 minutes out of an hour in percentage. 1 h = 60 min 24 min out of 60 min = 24 60 × 100% = 40% 24 minutes out of an hour is 40%. Both quantities must be in the same unit. 5 1 5 2 5 3
Mathematics 114 Grade 5 Nadia had Rp 35.000,00. She spent 45% of her money and saved the rest. (a) What percentage of her money did she save? (b) How much money did she save? (a) 45% ? 100% 100% – 45% = 55% She saved 55% of her money. (b) 45% 55% ? Rp 35.000,00 100% Rp 35.000,00 1% Rp 35.000,00 ÷ 100 = Rp 350.00,00 55% 55 × Rp 35.000,00 = Rp 19.250,00 She saved Rp 19.250,00. Henry prepared 1500 ml of mixed juice. 30% of it was apple juice, 45% of it was celery juice and the remaining was carrot juice. How many ml of carrot juice was there? Percentage of carrot juice = 100% – 30% – 45% = 25% 25% of 1500 ml = 25 100 × 1500 ml = 375 ml There was 375 ml of carrot juice. 30% 45% ? ? ml 100%
CHAPTER 5 Percentage 115 Practice 1. Express each of the following as a percentage. (a) 44 out of 80 (b) 5 2 5 out of 50 (c) 15 minutes out of 1 hour (d) 9 months out of 1 year 2. Linda had 500 limes. She sold off 90 percent of them. How many limes did Linda sell off?
Mathematics 116 Grade 5 3. This week Factory A produced 10% more boxes than it did last week. How many more boxes did Factory A produce this week if it produced 2000 boxes last week? 4. A barrel contains 750 litres of water. If Peter uses 60% of the water in the barrel, how much water is left in the barrel? 5. A can of peach in syrup weighs 350 g and it contains 262.5 g of peach. What is the percentage of the peach in the can?
CHAPTER 5 Percentage 117 C Word problems VAT stands for value added tax. Irene bought a T-shirt for Rp 28.000,00. In addition, she paid 10% VAT. (a) How much was the VAT? (b) How much did Irene paid for the T-shirt? (a) VAT paid = 10% of Rp 28.000,00 = 10 100 × Rp 28.000,00 = Rp 2.800,00 The VAT was Rp 2.800,00. (b) Total cost of T-shirt = Rp 28.000,00 + Rp 2.800,00 = Rp 30.800,00 Irene paid Rp 30.800,00 for the T-shirt. David bought some pastries from the bakery. He spent Rp 65.000,00 on the pastries. He also paid 10% VAT. (a) How much did David pay for VAT? (b) How much did David pay in total? (a) VAT paid = 10% of Rp ,00 = × Rp ,00 = Rp ,00 David paid Rp ,00 of VAT. (b) Total cost of pastries = Rp ,00 + Rp ,00 = Rp ,00 David paid Rp ,00 in total. watch me
Mathematics 118 Grade 5 A pair of sandals had a price tag of Rp 88.000,00. Ken bought the pair of sandals at the sale with a discount of 15%. (a) How much was the discount? (b) How much did Ken pay for the sandals? (a) Discount = 15% of original price = 15 100 × Rp 88.000,00 = Rp 13.200,00 The discount was Rp 13.200,00. (b) Amount of money paid = Rp 88.000,00 – Rp 13.200,00 = Rp 74.800,00 Ken paid Rp 74.800,00 for the sandals. Mrs Sumanto bought a set of storybooks for her children. The usual price of the storybooks was Rp 200.000,00. At a sale, she bought the storybooks at a discount of 20%. (a) How much was the discount? (b) How much did she pay for the storybooks? (a) Discount = % of original price = × Rp ,00 = Rp ,00 The discount was Rp ,00. (b) Amount of money paid = Rp ,00 – Rp ,00 = Rp ,00 She paid Rp ,00 for the storybooks. The usual price is the original price of an item. The selling price is the price we pay for the item.
CHAPTER 5 Percentage 119 Rudi has Rp 180.000,00 in his bank account. The interest rate is 3% per year. How much money will Rudi have in his account after 1 year? Interest = 3% of Rp 180.000,00 = 3 100 × Rp 180.000,00 = Rp 5.400,00 Rudi will receive Rp 5.400,00 of interest. Amount of money in account after 1 year = Original amount + Interest = Rp 180.000,00 + Rp 5.400,00 = Rp 185.400,00 Rudi will have Rp 185.400,00 in his account after 1 year. Eva has Rp 250.000,00 in her bank account. The interest rate is 5% per year. How much money will Eva have in her account after 1 year? Interest = % of Rp ,00 = × Rp ,00 = Rp ,00. Amount of money in account after 1 year = Original amount + Interest = Rp ,00 + Rp ,00 = Rp ,00 Eva will have Rp ,00 in her account after 1 year. If you deposit a sum of money into a bank account for a certain period of time, you will receive an interest.
Mathematics 120 Grade 5 Practice 1. Look at the items and their prices. Rp 150.000,00 Rp 80.000,00 Rp 220.000,00 (a) How much does the bag cost after a 10% discount? (b) How much does the blouse cost after a 20% discount? (c) How much does the pair of shoes cost after a 25% discount?
CHAPTER 5 Percentage 121 2. Rafi and Hani went to a cafe. They spent Rp 80.000,00 on their lunch. In addition, they also paid 10% VAT. (a) How much was the VAT? (b) How much did they pay in total? 3. A bank pays an annual interest of 2%. Andy has Rp 300.000,00 in his bank account. How much money will Andy have in his account at the end of 1 year?
6.2 cm Chapter 6 Ratio The building is drawn to a scale of 1 : 200. What is its actual height in metres? Learning Outcomes You should be able to • use ratio to show two or three given quantities • recognise and find equivalent ratios • express a ratio in its simplest form • find the missing term in a pair of equivalent ratios • solve word problems involving ratio • express the scale of a map as a ratio https://qr.pelangibooks.com/?u=MOMG5C6mo1 https://qr.pelangibooks.com/?u=MOMG5C6mo2 https://qr.pelangibooks.com/?u=MOMG5C6mo3 4 https://qr.pelangibooks.com/?u=MOMG5C6mo4 Maths Online Maths Online Maths Online Maths Online Maths Online 2 3 4
CHAPTER 6 Ratio 123 A Simple ratios We use this symbol “: ” when writing ratios. Let’s look at the figures below. There are 2 squares and 3 triangles. The ratio of the number of squares to the number of triangles is 2 : 3. The ratio of the number of triangles to the number of squares is 3 : 2. There are 3 apples and 5 oranges. The ratio of the number of apples to the number of oranges is : . The ratio of the number of oranges to the number of apples is : . We read the ratio “2 : 3” as “2 to 3”. We read the ratio “3 : 2” as “3 to 2”. watch me
124 Mathematics Grade 5 Mdm Mawar bought 4 bags of pears and 3 bags of lemons. 1 unit 1 unit The ratio of the number of pears to the number of lemons is 4 : 3. The ratio of the number of lemons to the number of pears is 3 : 4. Michael bought 2 boxes of cupcakes and 5 boxes of doughnuts. 1 unit 1 unit The ratio of the number of cupcakes to the number of doughnuts is : . The ratio of the number of doughnuts to the number of cupcake is : . The number of items in each bag is the same. Each bag represents one unit. A ratio may not give the actual number of pears and lemons.
125 CHAPTER 6 Ratio Each group has the same number of items. Each group represents 1 unit. 1 unit = 3 candies. The ratio of the number of blue beads to the number of pink beads is : . The ratio of the number of pink beads to the number of blue beads is : . The ratio of the number of blue beads to the total number of beads is : . Mother bought a packet of flour and a packet of rice. 0 4kg 1kg 2kg 3kg RICE 0 8kg 2kg 4kg 6kg The ratio of the mass of the packet of flour to the mass of the packet of rice is : . The ratio of the mass of the packet of rice to the mass of the packet of flour is : . Some lollipops and sweets are placed in the following arrangement. 1 unit 1 unit The ratio of the number of lollipops to the number of sweets is : . The ratio of the number of sweets to the number of lollipops is : .
126 Mathematics Grade 5 The bar models below show the lengths of Ribbons A and B. Ribbon A Ribbon B 1 unit The ratio of the length of Ribbon A to the length of Ribbon B is : . The ratio of the length of Ribbon B to the length of Ribbon A is : . Jasmine cuts a piece of 25-cm long string into two. The shorter piece of string is 11 cm. What is the ratio of the shorter piece of string to the longer piece of string? 25 cm 11 cm ? Length of shorter piece of string = 11 cm Length of longer piece of string = 25 cm – 11 cm = 14 cm The ratio of the length of the shorter piece of string to the length of the longer piece of string is 11 : 14. Ribbon A is 5 units long. Ribbon B is units long. Notice that both quantities are in the same unit. We do not include units when writing ratios.
127 CHAPTER 6 Ratio Practice 1. Find the correct answers. (a) M N (b) P Q Total = units Total = units M : N = : P : Q = : M : Total = : P : Total = : Total : N = : Total : Q = : 2. Draw models to show the ratios below. (a) 3 : 4 (b) 10 : 7 (c) 6 : 13 (d) 15 : 11
128 Mathematics Grade 5 B Equivalent ratios The ratio of the number of blue beads to the number of green beads is 6 : 12. 1 unit 1 unit The ratio of the number of blue beads to the number of green beads is 3 : 6. 1 unit 1 unit The ratio of the number of blue beads to the number of green beads is 2 : 4. Let’s now arrange the beads in groups of 2. We can also arrange the beads in groups of 3. watch me
129 CHAPTER 6 Ratio 1 unit 1 unit The ratio of the number of blue beads to the number of green beads is 1 : 2. The ratios 6 : 12, 3 : 6, 2 : 4, and 1 : 2 are called equivalent ratios. Therefore, 6 : 12 = 3 : 6 = 2 : 4 = 1 : 2 1 : 2 is the ratio in the simplest form. Let’s look at the figure below. The ratio of the number of orange cubes to the number of purple cubes is : . The ratio of the number of orange cubes to the number of purple cube is : . The equivalent ratios are : and : . Next, let’s arrange the beads in group of 6. All the ratios 6 : 12, 3 : 6, 2 : 4, and 1 : 2 compare the same number of blue beads and green beads.
130 Mathematics Grade 5 Ratios in the simplest form What is the simplest form of the ratio 9 : 15? First, find the common factor of 9 and 15. 9 : 15 ÷3 ÷3 = 3 : 5 Since 2 and 3 cannot be divided further, the ratio 3 : 5 is the simplest form of the ratio 9 : 15. What is the simplest form of the ratio 3 : 12? 3 : 12 ÷ ÷ = : The simplest form of the ratio 3 : 12 is : . What is the simplest form of the ratio 14 : 8? 14 : 8 ÷ ÷ = : The simplest form of the ratio 14 : 8 is : . The common factor of 3 and 12 is . The common factor of 14 and 8 is . 3 is a common factor of 9 and 15. Divide both numbers by their common factor, 3.
131 CHAPTER 6 Ratio Finding an unknown quantity Find the missing number in the pair of equivalent ratios. 3 : 4 = 9 : 3 : 4 × × = 9 : The missing number is . What is the missing number in the equivalent ratios? 15 : 21 = : 7 15 : 21 ÷ ÷ = : 7 The missing number is . Find the missing number in the equivalent ratios. 25 : = 5 : 2 7 : 9 = : 36 25 : ÷ ÷ = : 7 : 9 × × = : 36 Look at the first numbers of the equivalent ratios. 3 : 4 = 9 : 3 × = 9 or 9 ÷ = 3 Look at the second numbers of the equivalent ratios. 15 : 21 = : 7 21 ÷ = 7 or 7 × = 21
132 Mathematics Grade 5 Practice 1. (a) The ratio of the number of pencils to the number of erasers is : . (b) The ratio of the number of erasers to the number of pencils is : . (c) The ratio in its simplest form is : . 2. Rope A Rope B (a) The ratio of the length of Rope A to the length of Rope B is : . (b) The ratio in its simplest form is : . 3. What are the missing numbers? (a) 20 : 25 = : 5 (b) 1 : 8 = 8 : (c) 30 : = 5 : 9 (d) : 8 = 21 : 56
CHAPTER 6 Ratio 133 C Word problems Aria has 10 pink hair clips and 15 black hair clips. What is the ratio of the number of pink hair clips to the number of black hair clips? 10 : 15 ÷5 ÷5 = 2 : 3 The ratio of the number of pink hair clips to the number of black hair clips is 2 : 3. Mother bought 8 lemons and 14 oranges. What is the ratio of (a) the number of lemons to the numbers of oranges? (b) the number of oranges to the number of lemons? 8 : 14 ÷ ÷ = : (a) The ratio of the number of lemons to the number of oranges is : . (b) The ratio of the number of oranges to the number of lemons is : . Always write ratio in its simplest form. Divide both numbers by their common factor. Find the common factor of 8 and 14 first. watch me
134 Mathematics Grade 5 There are 28 male teachers at a school. The total number of teachers at the school is 64. What is the ratio of the number of male teachers to the number of female teachers at the school? Number of female teachers = 64 – 28 = 36 There are 36 female teachers at school. 28 : 36 = 7 : 9 The ratio of the number of male teachers to the number of female teachers is 7 : 9. Mr Hamid harvested 96 cabbages and carrots from his farm last week. The number of cabbages he harvested was 56. Find the ratio of (a) the number of cabbages harvested to the number of carrots harvested. (b) the number of carrots harvested to the total number of vegetables harvested. (a) The number of carrots harvested = – = carrots were harvested from Mr Hamid’s farm. : = : The ratio of the number of cabbages harvested to the number of carrots harvested is : . (b) : 96 = : The ratio of carrots harvested to the total number of vegetables harvested is : . 28 : 36 ÷4 ÷4 = 7 : 9
135 CHAPTER 6 Ratio Maya has 48 crayons and 20 highlighters. She buys 10 more highlighters. What is the ratio of the number of crayons to the number of highlighters that she has? The number of highlighters = 20 + 10 = 30 Maya has 30 highlighters altogether. 48 : 30 = 8 : 5 The ratio of the number of crayons to the number of highlighters that Maya has is 5 : 8. Johnny fold 60 paper cranes and 54 paper stars. He gives 15 of the paper cranes away. Find the ratio of the number of paper cranes to the number of paper stars in the end. The number of paper cranes = – = Johnny has paper cranes in the end. : = : The ratio of the number of paper cranes to the number of paper stars in the end is : . Remember: Always write ratios in the simplest form. 48 : 30 ÷6 ÷6 = 8 : 5
136 Mathematics Grade 5 Suraya bought some vanilla cupcakes and chocolate cupcakes. The ratio of the number of vanilla cupcakes to the number of chocolate cupcakes was 2 : 3. Suraya bought 4 vanilla cupcakes. How many chocolate cupcakes did she buy? Numbers of vanilla cupcakes : Numbers of chocolate cupcakes 2 : 3 × 2 × 2 = 4 : 6 She bought 6 chocolate cupcakes. or Vanilla cupcakes Chocolate cupcakes 4 cupcakes ? 2 units 4 cupcakes 1 unit 4 ÷ 2 = 2 cupcakes 3 units 3 × 2 = 6 cupcakes She bought 6 chocolate cupcakes. 2 × 2 = 4 3 × 2 = 6 We can use bar models to represent the number of cupcakes. 2 : 3 = 2 units : 3 units
137 CHAPTER 6 Ratio Sanyo’s pet dog is 14 kg. The ratio of the mass of Sanyo to the mass of his dog is 5 : 2. What is the mass of Sanyo? Sanyo’s mass : Dog’s mass 5 : 2 × × = : 14 The mass of Sanyo is kg. or Sanyo’s mass Dog’s mass 14 kg ? 2 units kg 1 unit kg ÷ = kg 5 units × kg = kg The mass of Sanyo is kg.
138 Mathematics Grade 5 D Ratio of three quantities Ratio can also be used to compare three quantities. The ratio of the number of squares to the number of triangles to the number of circles is 2 : 3 : 5. Mary baked 2 pies, 4 cupcakes and 6 cookies. The ratio of the number of pies to the number of cupcakes to the number of cookies is 2 : 4 : 6. Numbers of pies : Number of cupcakes : Numbers of cookies 2 : 4 : 6 ÷ 2 ÷ 2 ÷ 2 = 1 : 2 : 3 The ratio in its simplest form is 1 : 2 : 3. First, find the common factor of the numbers 2, 4 and 6. 2 × 1 = 2 2 × 2 = 4 2 × 3 = 6 2 is a common factor of 2, 4 and 6. watch me
139 CHAPTER 6 Ratio Rani bought some flowers for mother’s day. The ratio of the number of daisies to the number of roses to the number of tulips is 12 : 9 :15. What is the ratio in it’s simplest form? Numbers of daisies : Number of roses : Numbers of tulips 12 : 9 : 15 ÷ 3 ÷ 3 ÷ 3 = : : The ratio in its simplest form is : : . Find the missing number in the equivalent ratios. 2 : 5 : 4 = 6 : : 12 2 : 5 : 4 × 3 × 3 × 3 = 6 : : 12 The missing number is . Practice Find the missing numbers. 1. : 3 : 6 = 5 : 15 : 30 2. 5 : 6 : 7 = : 18 : Recall: Look at the first numbers of the equivalent ratios. 2 : 5 : 4 = 6 : : 12 2 × 3 = 6
140 Mathematics Grade 5 The picture below shows a diagram of a watch drawn using a scale of 1 : 2. This means a length of 1 unit in the diagram represents an actual length of 2 units. Scale tells us the relationship between the actual size of an object and the size of its image. The height of the pylon in the diagram is 6 cm. The actual height of the pylon is 6 m. What is the scale of the diagram? First, let’s express 6 m in cm. 1 m = 100 cm 6 m = 6 × 100 cm = 600 cm The length of the watch is 10 centimetres. This means that the actual length of the watch is 20 centimetres. Scale 1 : 2 E Scale The ratio of the height of the pylon on diagram to its actual height is 6 : 600. 6 : 600 ÷6 ÷6 = 1 : 100 The scale of the diagram is 1 : 100. Remember: To compare as a ratio, the quantities must be in the same unit. 6 cm watch me
141 CHAPTER 6 Ratio The length of a row of shops is 156 m. It is represented by a length of 12 cm on a map. What is the scale of the map? 1 m = cm m = × = cm 12 : ÷ ÷ = 1 : The scale of the map is : . A building is drawn to a scale of 1 : 1500. The height of the building in the drawing is 4 cm. Find the actual height of the building. Give your answer in metres. 1 : 1500 = 4 : 4 ÷ 1 = 4 1500 × 4 cm = 6000 The actual height of the building is 6000 cm. 100 cm = 1 m 6000 cm = 6000 ÷ 100 = 60 m The actual height of the building is 60 m. Express 156 m in centimetres first. 4 cm
