42 Mathematics Grade 5 Practice Solve the following word problems. 1. Amy walked 1 2 km to the grocery store. She then walked 3 5 km to the restaurant. How many kilometres did she walk altogether? 2. Aman bought a bottle of water. He drank 3 8 of the water and spilled 1 6 of it. What fraction of the bottle of water was left? 3. Rani bought some fruits to make salad. She bought 3 4 kg of apples, 1 2 kg of oranges and 2 5 kg of mangoes. What was the total mass of the fruits?
CHAPTER 2 Fractions (1) 43 D Fractions and divisions Fraction as division 2 similar pizzas are shared equally among 3 children. What fraction of a pizza will each child get? 2 ÷ 3 = 2 3 Each child will get 2 3 of a pizza. 3 similar ribbons are cut and shared among 5 pupils. What fraction of a ribbon will each pupil get? 3 ÷ 5 = 3 5 Each pupil will get 3 5 of a ribbon. 2 divided by 3 is the same as 2 3 . Each pizza is divided into 3 equal parts. Each part is 1 3 of a pizza watch me
44 Mathematics Grade 5 4 similar pies are cut and shared equally among 5 people. What fraction of a pie does each person get? 4 ÷ 5 = Each person get of a pie. Practice 1. Express each of the following as a fraction. (a) 3 ÷ 7 = (b) 5 ÷ 8 = (c) 6 ÷ 11 = (d) 7 ÷ 12 = 2. Express each of the fractions as a division sentence. (a) 2 5 = ÷ (b) 4 7 = ÷ (c) 6 13 = ÷ (d) 8 15 = ÷
CHAPTER 2 Fractions (1) 45 Let’s look at the figure below. 5 similar paper strips are divided equally among 4 pupils. How many pieces of paper strip does each pupil receive? 5 ÷ 4 = 5 4 = 4 4 + 1 4 = 1 1 4 or 5 ÷ 4 = 1 4 5 4 1 ) Each pupil receives 1 1 4 pieces of paper strip. What is 12 ÷ 5? Express your answer as a mixed number. 12 ÷ 5 = 12 5 = 5 5 + 5 5 + 2 5 2 5 1 2 1 0 2 ) = 1 + 1 + 2 5 or = 2 + 2 5 12 ÷ 5 = 2 2 5 = 2 2 5 5 divided by 4 can be written as 5 4 or 1 1 4 .
46 Mathematics Grade 5 What is 20 ÷ 6? Express your answer as a fraction in its simplest form. Then, convert it to a mixed number. 20 ÷ 6 = 20 6 = 10 3 = 3 1 3 Practice 1. Express each division sentence as a fraction in its simplest form. Then, convert the fraction to a mixed number. (a) 17 ÷ 2 = (b) 32 ÷ 6 = (c) 42 ÷ 8 = (d) 45 ÷ 7 = (e) 52 ÷ 5 = (f) 62 ÷ 8 = 3 10 3 3 1 0 9 1 )
CHAPTER 2 Fractions (1) 47 E Adding mixed numbers Marina ate 1 1 2 bottle of blueberry yogurt and 2 1 4 bottle of strawberry yogurt. How many bottles of yogurt did she eat altogether? + 1 1 2 + 2 1 4 = 1 2 4 + 2 1 4 = 3 3 4 She ate 3 3 4 bottle of yogurt altogether. Find the sum of 1 2 3 + 2 3 4 . 1 2 3 + 2 3 4 = 1 8 12 + 2 9 12 = 3 17 12 = 3 + 12 12 + 5 12 = 3 + 1 + 5 12 = 4 5 12 Recall : 1 2 = 2 4 × 2 × 2 Recall : 2 3 = 8 12 × 4 × 4 3 4 = 9 12 × 3 × 3 + watch me
48 Mathematics Grade 5 In a marathon, Joe ran 1 2 5 km and took a rest. He then continued to ran 2 7 10 km. What is the total distance that he ran? 1 2 5 + 2 7 10 = + = = 3 + + = = He ran km altogether. Add 3 1 4 and 2 3 5 . + 3 1 4 + 2 3 5 = + = +
CHAPTER 2 Fractions (1) 49 F Subtracting mixed numbers Max has 2 5 6 m of rope. He cut 1 1 3 m for a DIY project. How many metres of rope does Max have left? 2 5 6 – 1 1 3 = 2 5 6 – 1 2 6 = 1 3 6 = 1 1 2 m Max has 1 1 2 m of rope left. What is 2 3 4 – 1 1 8 ? 2 3 4 – 1 1 8 = 2 – 1 = Find the difference between 4 1 3 – 2 1 5 . 4 5 6 – 2 1 5 = 4 – 2 = 2 1 5 6 = × × 1 5 = × × – 3 4 = 8 × × watch me
50 Mathematics Grade 5 Budi has 2 5 6 bottle of milk. He uses 1 3 8 bottle of milk to make ice cream. How much milk does he have left? 2 5 6 – 1 3 8 = 2 – 1 = He has bottle of milk left. Practice 1. Add. (a) 1 1 3 + 4 2 5 = (b) 2 1 6 + 2 3 4 = 2. Subtract. (a) 2 1 2 – 1 1 5 = (b) 4 1 4 – 2 7 8 = 5 6 = 24 × × 3 8 = 24 × ×
CHAPTER 2 Fractions (1) 51 G Word problems (2) Diana made 7 jars of jam. She divided the jam equally into 5 parts. How much jam were there in each part? 7 ÷ 5 = 7 5 = 5 5 + 2 5 = 1 2 5 There were 1 2 5 jar of jam in each part. Billy has 28 kg of rice. He keeps 5 kg of rice and packs the remaining rice equally into 4 bags. How much rice does each bag contain? 28 kg – 5 kg = 23 kg Billy has 23 kg of rice left. ÷ = = Each bag contain kg of rice. 1 5 7 5 2 ) watch me
52 Mathematics Grade 5 Andre spent 1 1 2 h cleaning his room. He then spent 2 2 5 h painting the walls. How much time did Andre spend on cleaning and painting? ? 1 2 1 h 2 5 2 h h + h = h + h = h Andre spent hours on cleaning and painting. Rika walks 2 3 4 km every day. She jogs 2 3 km less than she walks. How many kilometres does Rika walk and jog every day? Give your answer in its simplest form. 2 3 4 km – 2 3 km = km – km = km Rika jogs km every day. 2 3 4 km + km = km + km = km = km Rika walks and jogs km every day. Walking 2 3 3 2 4 km ? km ? Jogging
Chapter 3 Fractions (2) You should be able to • find the product of proper fractions • find the product of an improper fraction and a proper or improper fractions • find the product of a mixed number and a whole number • divide a proper fraction by a whole number • solve up to two-step word problems related to fractions Learning Outcomes Madam Nina has 2 pizzas. She eats 1 6 of the pizza. Now, she wants to divide the remaining pizzas between her three children. How many pizzas will each of her children get? http://bit.do/IPMT5-C3-MO-1 http://bit.do/IPMT5-C3-MO-2 http://bit.do/IPMT5-C3-MO-3 4 http://bit.do/IPMT5-C3-MO-4 Maths Online Maths Online Maths Online Maths Online Maths Online 2 3 4
54 Mathematics Grade 5 A Product of proper fractions What does 3 — 4 of 1 — 3 mean? 1 3 3 4 of 1 3 3 4 of 1 3 is 3 12. 3 4 of 1 3 = 3 4 × 1 3 = 3 × 1 4 × 3 = 3 12 = 1 4 Therefore, 3 4 of 1 3 is 3 12. Find the product of 3 8 and 2 9 . 3 8 × 2 9 = 3 × 2 8 × 9 = 6 72 = 1 12 12 1 3 8 × 2 9 = 3 8 × 2 9 = 3 8 × 2 9 = 1 4 × 1 3 = 1 × 1 4 × 3 = 1 12 3 1 3 1 4 1 The product of 3 8 and 2 9 is 1 12. Simplest form Divide the numerator and denominator by their common factor, 3. Divide the numerator and denominator by their common factor, 2. or watch me
CHAPTER 3 Fractions (2) 55 Find the product. Give your answer in its simplest form. What is 3 10 × 5 12 ? 3 10 × 5 12 = × × = = 3 10 × 5 12 = × = 2 1 4 1 or Practice 1. 2 3 × 9 16 2. 3 5 × 4 9 3. 5 8 × 4 20 4. 1 2 × 4 13 5. 6 7 × 5 12 6. 8 15 × 5 18
56 Mathematics Grade 5 B Word problems (1) Harry had 3 5 l of sea water. He poured 1 3 of the sea water into a fishbowl. (a) How many l of sea water did he pour into the fish bowl? (b) How many l of sea water did he have left? From the bar model, 5 units 1 l 1 unit 1 5 l 2 units 2 5 l (a) He poured 1 5 l of sea water into the fish bowl. (b) He had 2 5 l of sea water left. or (a) 1 3 l × 3 5 l = 3 15 l = 1 5 l He poured 1 5 l of sea water into the fish bowl. (b) l of sea water left = 3 5 l – l of sea water poured = 3 5 l – 1 5 l = 2 5 l He had 2 5 l of sea water left. 5 1 3 5 l Left 1 3 (Used) watch me
CHAPTER 3 Fractions (2) 57 Bella has 3 4 m of ribbon. She uses 2 3 of the ribbon to decorate some gift boxes. (a) How much ribbon does she use? (b) How much ribbon does she have left? From the bar model, units m units m unit m (a) She uses m of ribbon. (b) She has m of ribbon left. or (a) × m = m She uses m of ribbon. (b) m – m = m She has m of ribbon left. m
58 Mathematics Grade 5 Citra baked a cake. She cut 1 6 of it and saved it for later. She cut 7 10 of the remainder and gave to her friend. (a) What fraction of the cake was given to her friend? (b) What fraction of the cake was left? Saved Remainder Saved Given to friend Left (a) Fraction of cake given to friend = 7 12 7 12 of the cake was given to her friend. or (a) Remainder = 1 whole – 1 6 = 5 6 7 10 × 5 6 = 7 12 7 12 of the cake was given to her friend. 1 2 4 1 (b) Fraction of the cake left = 2 12 = 1 4 1 4 of the cake was left. × 2 × 2 4 1 (b) 5 6 – 7 12 = 10 12 – 7 12 = 3 12 1 4 of the cake was left. From the bar model, Number of units given away = 7 Number of units left = 3 Total number of units = 12
CHAPTER 3 Fractions (2) 59 Putri was reading a novel. She read 1 3 of the novel on Saturday. She then read 5 6 of the remainder on Sunday. (a) What fraction of the novel did she read on Sunday? (b) What fraction of the novel did she have left? (a) Fraction of novel read on Sunday = She read of the novel on Sunday. (a) Remainder = 1 – = 5 6 × = = She read of the novel on Sunday. (b) Fraction of novel left = She has of the novel left. (b) – = – = She has of the novel left. From the model, Number of units read on Sunday = Number of units left = Total number of units = or
60 Mathematics Grade 5 Solve the following word problems. Practice 1. Grace had 7 8 l of milk. She used 4 5 of it to make dessert. (a) How many l of milk did Grace use? (b) How many l of milk did Grace have left? 2. Joe spent 1 6 of his salary and saved 3 5 of his remaining salary. (a) What fraction of his total salary was spent? (b) What fraction of his salary was left?
CHAPTER 3 Fractions (2) 61 C Product of an improper fraction and proper or improper fraction 1 2 of 3 2 = 1 2 × 3 2 = 3 4 1 4 + 1 4 + 1 4 = 3 4 Find the value of 3 4 × 5 3 . 3 4 × 5 3 = 1 × 5 4 × 1 = 5 4 = 1 1 4 1 1 or 3 4 × 5 3 = 3 × 5 4 × 3 = 15 12 = 5 4 = 1 1 4 4 5 1 2 2 2 1 4 1 4 1 4 This figure shows 3 2 . Shade 1 2 of the whole figure. There are 3 shaded parts, therefore, 3 4 is shaded. watch me
62 Mathematics Grade 5 Find the product of each of the following. Give your answer in its simplest form. Practice 1. 9 5 × 5 4 = 2. 3 2 × 7 6 = 3. 3 8 × 4 5 = 4. 1 3 × 6 5 = 5. 8 7 × 15 6 = 6. 12 7 × 24 9 = 7. 32 6 × 2 13 = 8. 27 5 × 1 9 =
CHAPTER 3 Fractions (2) 63 D Product of a mixed number and a whole number Ms Suria brought some origami paper to her art class. She gave each of her 5 pupils 1 1 2 piece of paper. How many pieces of paper did she give altogether? 1 1 — 2 = 3 — 2 1 1 — 2 × 5 = 3 — 2 × 5 5 × 1 1 2 = 5 × 3 2 = 15 2 = 7 1 2 She gave 7 1 2 pieces of paper altogether. 3 2 5 × 3 2 15 2 = 1 2 7 1 2 5 × 1 1 1 2 watch me
64 Mathematics Grade 5 Find the product of 2 1 5 × 6. 2 1 5 × 6 = × 6 = = 65 5 + = 13 + = What is 2 1 4 × 5? 2 1 4 × 5 = × 5 = = + = + = Find the products. Practice 1. 3 1 2 × 7 = 2. 5 1 3 × 3 = 3. 2 1 5 × 4 =
CHAPTER 3 Fractions (2) 65 E Mdm Mawar prepared some breadsticks for a tea party. Each guest ate 2 1 2 breadsticks. There were 15 guests at tea party. How many breadsticks did the guests eat in total? Word problems (2) 1 guest 2 1 2 breadsticks 15 guests 15 × 2 1 2 = 15 × 5 2 = 75 2 = 74 2 + 1 2 = 37 + 1 2 = 37 1 2 breadsticks The guests ate 37 1 2 breadsticks in total. Anna wants to buy a photo frame measuring 15 1 3 cm by 10 cm. What is the area of the photo frame? Area = Length × Breadth = 15 1 3 cm × 10 cm = × = = 159 3 + = cm2 The area of the photo frame is cm2 . watch me
66 Mathematics Grade 5 Melvin has piano lessons on Monday, Wednesday and Friday. Each lesson takes 1 3 4 h. How many hours does Melvin spend on his piano lessons in a week? 1 day 1 3 4 h 3 days × = × = = + = + = h Melvin spends hours on his piano lessons in a week. Joe harvested 4 bags of carrots. Each bag of carrots weights 2 1 2 kg. He sold each kg of the carrots for Rp 30.000,00. How much did Joe receive for selling all the carrots? Joe received Rp for selling all the carrots.
CHAPTER 3 Fractions (2) 67 Solve the following word problems. Practice 1. The length of a table is 2m. Its breadth is 1 3 5 m. What is the area of the table? 2. A cafe uses 30 4 5 kg of ground coffee each month. The cost of 1 kg of ground coffee is Rp 140.000,00. How much money does the cafe spend on the ground coffee in three months?
68 Mathematics Grade 5 F Dividing a fraction by a whole number 1 2 m of ribbon is cut into 4 equal pieces. How long is each piece of ribbon? 1 2 m ÷ 4 = 1 4 of 1 2 m = 1 4 × 1 2 m = 1 8 m Each piece of ribbon is 1 8 m. or 1 2 m ÷ 4 = 1 2 m ÷ 4 1 = 1 2 × 1 4 = 1 8 m Each piece of ribbon is 1 8 m. 4 — 1 switch 1 — 4 Each piece of ribbon is 1 — 4 of 1 — 2 m. 1 2 m ? watch me
CHAPTER 3 Fractions (2) 69 4 5 of a cake is shared among 8 children. What fraction of the cake did each child receive? 4 5 ÷ 8 = 1 8 of 4 5 = 1 8 × 4 5 = 1 10 2 1 4 5 ÷ 8 = 4 5 ÷ 8 1 = 4 5 × 1 8 = 1 10 2 1 or Each child received 1 10 of the cake. Find the value of 8 15 ÷ 4. 8 15 ÷ 4 = × = 4 5 ? ? 8 15
70 Mathematics Grade 5 Solve the following word problems. Practice 1. Anwar had 4 5 of a pizza. He divided the pizza equally into 4 plates. What fraction of the pizza did each plate contain? 2. Sinar has 4 9 kg rice. He divided the rice equally into 3 small containers. Find the amount of rice, in kilograms, in each container.
CHAPTER 3 Fractions (2) 71 G Word problems (3) Lee has 160 paper clips. He uses 1 2 of them and throws away 1 4 rusted paper clips. (a) How many paper clips are used? (b) How many paper clips are rusted? From the bar model, 4 units 160 paper clips 1 unit 160 ÷ 4 = 40 paper clips 2 units 2 × 40 = 80 paper clips (a) 80 paper clips are used. (b) 40 paper clips are rusted. or (a) 1 2 of 160 = 1 2 × 160 = 80 80 paper clips are used. (b) 1 4 of 160 = 1 4 × 160 = 40 40 paper clips are rusted. 1 80 1 40 160 Used Used Rusted Left 1 2 1 4 Recall : 1 — 2 = 2 — 4 × 2 × 2 Therefore, we draw a bar model with 4 equal parts. watch me
72 Mathematics Grade 5 Sheila has a mini library with 480 books. 2 3 of her books are science fictions. 1 4 of her books are biographies and the rest are reference books. (a) How many science fiction books does Sheila have? (b) How many reference books does Sheila have? units books 1 unit ÷ = books 8 units × = books (a) Sheila has science fiction books. (b) Sheila has reference books. or (a) 2 3 of 480 = 2 3 × = Sheila has science fiction books. (b) Number of reference book = 1 whole – 2 3 – 1 4 = 1 – 8 12 – 3 12 = 1 12 1 12 of 480 = 1 12 × = Sheila has reference books. 12 is the first common multiple of 3 and 4. Let’s draw a bar model with 12 equal units. 2 — 3 × 12 units = units 1 — 4 × 12 units = units
CHAPTER 3 Fractions (2) 73 In a marathon, Bruno sprinted 1 5 of the total distance. Then, he jogged 2 3 of his remaining distance and walked the rest of the distance. If Bruno walked for 600 m, what is the total distance of the marathon? or Remaining distance = 1 – 1 5 = 4 5 (Jogged and walked) 2 3 of remaining distance = 2 3 × 4 5 = 8 15 (Jogged) 1 5 + 8 15 = 3 15 + 8 15 = 11 15 (Sprinted and jogged) The rest of the distance = 1 – 11 15 = 4 15 (Walked) 4 15 = 600 m 4 units 600 m 1 unit 600 ÷ 4 = 150 m 15 units 15 × 150 m = 2250 m 15 15 = 2250 m The total distance of the marathon is 2250 m. 15 is the first common multiple of 3 and 5. Therefore, we draw a bar model with 15 equal units. (Sprinted) 1 5 600 m (Walked) ( Jogged) 2 3 From the bar model, 4 units 600 m 1 unit 600 m ÷ 4 = 150 m 15 units 15 × 150 m = 2250 m The total distance of the marathon is 2250 m. × 3 × 3
74 Mathematics Grade 5 Ratna used 1 3 of her beads to make a necklace. She used 1 4 of the remainder to make an anklet. If she used 80 beads for the anklet, how many beads did she have left? From the bar model, 2 units 80 beads 1 unit ÷ = beads Number of beads left = units units × = She had beads left. or Remainder = 1 – 1 3 = 2 3 Fraction of beads used for anklet = 1 4 × 2 3 = 1 6 Fraction of beads left = 1 – 1 3 – 2 3 = 6 6 – 2 6 – 1 6 = 3 6 = 1 1 2 6 80 beads 1 2 = 3 6 240 beads She had 240 beads left. (Necklace) 1 3 Left 80 Beads ? (Anklet) 1 4 is the first common multiple of 3 and 4 1 2 1 2 × 3 × 3
CHAPTER 3 Fractions (2) 75 Solve the following word problems. Practice 1. Mr Lee has a box of pens. 1 3 of the pens are red pens. 2 5 of the remaining pens are blue pens and the rest are black pens. If there are 75 pens in the box, how many blue pens are there? 2. During the weekend, Joe spent 8 hours cleaning his room, studying and watching movies. He spent 1 5 of the time cleaning his room and 1 2 of the time studying. How many minutes did he spend watching movies?
Chapter 4 You should be able to • add and subtract decimals • multiply and divide decimals • solve up to two-step word problems related to decimals Learning Outcomes The box weighs 23.25 kg. What is the mass of three similar boxes? http://bit.do/IPMT5-C4-MO-1 http://bit.do/IPMT5-C4-MO-2 http://bit.do/IPMT5-C4-MO-3 4 http://bit.do/IPMT5-C4-MO-4 Maths Online Four operations with decimals Maths Online Maths Online Maths Online Maths Online 2 3 4
CHAPTER 4 Four operations with decimals 77 A Addition of decimals Find the sum of 0.3 and 0.2. The total shaded part is 0.5 of the figure. Therefore, 0.3 + 0.2 = 0.5. Find the value of 1.23 + 0.54. 1.23 0.54 The total shaded part is 1.77 of the figure. Therefore, 1.23 + 0.54 = 1.77. What is 0.7 + 0.5? 0.7 0.5 1.2 Based on the figure, we know that 0.7 + 0.5 = 1.2. Addition of decimals means finding the sum of two or more decimals. 0.3 0.2 watch me
Mathematics 78 Grade 5 We can add decimals like regular addition. Arrange the decimals in two rows so that the digits in the same place values are in the same column. Find the sum of 4.4 and 6.8. Step 1: Align the digits vertically according to place values. The decimal points must be vertically aligned too. 4.4 6.8 The decimal points are v e r t i c a l l y aligned. Step 2: Add the tenths. 1 4.4 6.8 2 Add up the digits from right to left. Regroup whenever necessary. Step 3: Add the ones. 1 4.4 6.8 11.2 Therefore, 4.4 + 6.8 = 11.2. Find the sum of 18.23 and 2.87. 1 1 1 1 8 . 2 3 + 2 . 8 7 2 1 . 1 0 Therefore, 18.23 + 2.87 = 21.10. + + + We must always align the decimal points when adding decimals.
CHAPTER 4 Four operations with decimals 79 Find the sum of 16.5 and 3.73. 1 1 1 6 . 5 0 + 3 . 7 3 2 0 . 2 3 16.5 = 16.50 Therefore, 16.5 + 3.73 = 20.23. Practice Add. 1. 0 . 2 + 0 . 4 2. 1 . 6 + 0 . 8 3. 3 . 9 + 1 . 4 4. 5 . 2 2 + 4 . 5 4 5. 1 0 . 6 0 + 3 . 7 1 6. 1 4 . 0 2 + 1 1 . 4 4 7. 3 4 . 2 5 + 3 7 . 3 6 8. 7 8 . 6 9 + 3 4 . 0 8 9. 1 2 7 . 3 6 + 8 9 . 8 8 10. 25.36 + 2.88 = 11. 65.70 + 64.21 = 12. 78.01 + 36.45 = 13. 86.37 + 95.36 = 14. 127.88 + 67.97 = 15. 654.36 + 742.08 = Add in zeros wherever necessary. The digit zero represents 0 hundredth. It does not change the value of 16.5.
Mathematics 80 Grade 5 Find the difference between 0.8 and 0.5. 0.8 0.5 The shaded part is 0.8. Take 0.5 away from the shaded part. The remaining shaded part is 0.3. Therefore, 0.8 – 0.5 = 0.3. Find the value of 1.53 – 1.24. The shaded part is 1.53. Take 1.24 away from the shaded part. The remaining shaded part is 0.29. Therefore, 1.53 – 1.24 = 0.29. What is 1.5 – 0.8? Based on the figure, we know that 1.5 – 0.8 = 0.7. Subtraction of decimals means finding the difference between the decimals. B Subtraction of decimals watch me
CHAPTER 4 Four operations with decimals 81 We use a similar method to subtract decimals as we subtract whole numbers. Find the difference between 8.32 and 4.2. Step 1: Align the digits vertically according to place values. The decimal points must be vertically aligned too. 8 . 3 2 – 4 . 2 0 4.2 = 4.20 Step 2: Subtract the hundredths. 8 . 3 2 – 4 . 2 0 2 Step 3: Subtract the tenths. 8 . 3 2 – 4 . 2 0 1 2 Step 4: Subtract the ones. 8 . 3 2 – 4 . 2 0 4 . 1 2 Find the difference between 18.9 and 5.32. 8 10 1 8 . 9 0 – 5 . 3 2 1 3 . 5 8 Regroup 9 tenths into 8 tenths 10 hundredths. 10 hundredths – 2 hundredths = 8 hundredths 8 tenths – 3 tenths = 5 tenths Therefore, 18.9 – 5.32 = 13.58. Therefore, 8.32 – 4.2 = 4.12.
Mathematics 82 Grade 5 Find the difference between 23.57 and 10.69. 14 2 4 17 2 3 . 5 7 – 1 0 . 6 9 1 2 . 8 8 Therefore, 23.57 – 10.69 = 12.88. Practice Subtract. 1. 0 . 8 – 0 . 4 2. 1 . 1 – 0 . 8 3. 4 . 3 – 1 . 4 4. 6 . 2 0 – 5 . 8 8 5. 1 2 . 8 7 – 3 . 9 9 6. 6 4 . 2 8 – 3 7 . 9 3 7. 7 9 . 3 5 – 6 5 . 3 2 8. 1 0 2 . 9 2 – 6 8 . 5 8 9. 3 6 9 . 4 5 – 2 8 7 . 2 7 10. 6.67 – 3.68 = 11. 32.89 – 30.55 = 12. 56.23 – 41.24 = 13. 98.20 – 74.36 = 14. 257.45 – 158.39 = 15. 824.31 – 489.79 = Remember to regroup whenever necessary.
CHAPTER 4 Four operations with decimals 83 C Word problems (1) Nida's mass is 32.3 kg now. She gained 5.28 kg over the last two years. What was Nida's mass 2 years ago? 32.30 kg – 5.28 kg = 27.02 kg 2 12 2 10 3 2 . 3 0 – 5 . 2 8 2 7 . 0 2 Nida's mass was 27.02 kg two years ago. Rika bought 12.55 m of white lace and 7.85 m of black lace. How much lace did Rika buy altogether? m + m = m 1 2 . 5 5 + 7 . 8 5 Rika bought m of lace altogether. Ben drank 0.75 l of milk. His brother drank 0.4 l more milk than him. How much milk did both of them drink altogether? Ben ? 0.4 l 0.75 l ? Brother 0.75 l + 0.4 l = 1.15 l Ben's brother drank 1.15 l of milk. l + l = l Both of them drank l of milk altogether. watch me
Mathematics 84 Grade 5 Sam and Paul cycled 22.52 km altogether. If Sam cycled 12.85 km, how many more kilometres did he cycle than Paul? Sam ? ? 12.85 km 22.52 km Paul 22.52 km – 12.85 km = km Paul cycled km. km – km = km Sam cycled km more than Paul. Yanni bought 30 kg of rice. She kept 12.75 kg of the rice and used some to make rice cakes. If Yanni had 11.65 kg of rice left, how much rice did she use for the rice cakes? Keep Rice cakes Left ? 30 kg 12.75 kg 11.65 kg kg + kg = kg The total mass of rice kept and left is kg. kg – kg = kg She used kg of rice for the rice cakes.
CHAPTER 4 Four operations with decimals 85 Practice Solve the following word problems. 1. Mrs Wong puts 3.6 kg of fruits, 1.25 kg of chicken and 2.3 kg of fish into a basket. If the total mass of the groceries and the basket is 8 kg, find the mass of the basket. 2. Joanne's height is 1.45 m. Her sister is 1.63 m. Their total height is 1.35 m more than their father's. How tall is their father? 3. The baker bought some sugar. He used 37.75 kg of the sugar for some doughnuts and 20 kg of the sugar for muffins. If he had 24.25 kg of sugar left, how much sugar did he buy at first?
Mathematics 86 Grade 5 D Decimals and fractions We have learnt how to write fractions with denominators of 10, 100 or 1000 as decimals. Let us see how we can write fractions with other denominators as decimals. Steps to convert a fraction with a denominator that is a factor of 10 or 100 into decimals: Step 1: Convert the given fraction into its equivalent fraction with a denominator of 10, 100 or 1000. Step 2: Convert the fraction with a denominator of 10, 100 or 1000 into its equivalent decimal. Convert 1 5 into a decimal. 1 5 = 1 5 × 2 × 2 Convert 1 — 5 into an equivalent fraction with a denominator of 10. = 2 10 = 0.2 Therefore, 1 5 = 0.2. Write 9 4 as a decimal. 9 4 = 9 4 × 25 × 25 Convert 9 — 4 into an equivalent fraction with a denominator of 100. = 225 100 = 2 25 100 = 2.25 Therefore, 9 4 = 2.25. There is no equivalent fraction of 9 — 4 with a denominator of 10. Therefore, we can find an equivalent fraction with a denominator of 100. watch me
CHAPTER 4 Four operations with decimals 87 Express 4 3 20 as a decimal. 4 3 20 = 83 20 = 83 20 × 5 × 5 = 415 100 = 4 15 100 = 4.15 Therefore, 4 3 20 = 4.15. Write 2 72 125 as a decimal. 2 72 125 = 322 125 = 322 125 × 8 × 8 = 2576 1000 = 2 2576 1000 = 2.576 Therefore, 2 72 125 = 2.576. Convert 4 3 20 into an improper fraction. Convert 2 72 125 into an improper fraction. Alternative method: 4 3 20 = 4 + 3 20 × 5 × 5 = 4 + 15 100 = 4 15 100 = 4.15 × 8 × 8 Alternative method: 2 72 125 = 2 + 72 125 = 2 576 1000 = 2 576 1000 = 2.576
Mathematics 88 Grade 5 Converting decimals into fractions We can also write a decimal in the form of a fraction. Express 6.8 as a fraction. 6.8 = 6 + 0.8 = 6 + 8 10 = 6 8 10 = 6 4 5 Simplest form Therefore, 6.8 = 6 4 5 . Convert 29.04 into fraction form. 29.04 = 29 + 0.04 = 29 + 4 100 = 29 4 100 = 29 1 25 Simplest form Therefore, 29.04 = 29 1 25. MATHS TIPS When a 1-decimal place number is written as a fraction, the denominator must be 10 before being simplified. When a 2-decimal place number is written as a fraction, the denominator must be 100 before being simplified. When a 3-decimal place number is written as a fraction, the denominator must be 1000 before being simplified. 4 5 1 25
CHAPTER 4 Four operations with decimals 89 Practice 1. Convert each fraction into the equivalent decimal. (a) 55 1000 (b) 34 100 (c) 43 100 (d) 2 7 8 (e) 4 96 250 (f) 97 40 2. Convert each decimal into the equivalent fraction in its simplest form. (a) 0.002 (b) 0.112 (c) 7.450 (d) 20.384 (e) 5.505 (f) 45.300
Mathematics 90 Grade 5 Multiplying decimals by whole numbers Let's look at the figure below. 3 × 0.1 = 0.1 + 0.1 + 0.1 = 0.3 Find the value of 8 × 0.3. 8 × 0.3 = 8 × 3 10 = 8 × 3 10 = 24 10 = 2.4 Therefore, 8 × 0.3 = 2.4. What is 4 × 0.32? 4 × 0.32 = 4 × 32 100 = 128 100 = 1.28 Therefore, 4 × 0.32 = 1.28. 8 has zero decimal place. 0.3 has 1 decimal place. The product 2.4 has 1 decimal place. 4 has zero decimal place. 0.32 has 2 decimal places. The product 1.28 has 2 decimal places. E Multiplication of decimals 0.3 = 3 —— 10 0.32 = 32 ——— 100 We can also use the relationship between decimals and fractions to find the product of a whole number and a decimal. watch me
CHAPTER 4 Four operations with decimals 91 4 × 0.7 = We can multiply as follows: 4 × 7 10 = 4 × 7 10 = 28 10 = 2.8 0.7 × 4 = We can also multiply as follows: 7 10 × 4 = 7 × 4 10 = 28 10 = 2.8 Therefore, 4 × 0.7 = 0.7 × 4. We can also use a similar method to multiply decimals as we multiply whole numbers. Find the product of 22.1 and 35. 2 2 . 1 3 5 1 1 0 5 6 6 3 0 7 7 3 .5 Therefore, 22.1 × 35 = 773.5. 0 decimal place 1 decimal place 1 decimal place × Find the product of 4 and 0.7. 1