Oasis School Mathematics Book-5 101 choose the correct alternatives 1. Among the operations addition subtraction, multiplication and division which operation is to be applied at last? (i) Addition (ii) Multiplication (iii) Subtraction 2. the value of 30 + 12 ÷ 6 – 3 is equal to (i) 34 (ii) 21 (iii) 4 3. the value of 15 × 3 + 3 – 6 is equal to (i) 42 (ii) 0 (iii) 84 4. the product of 7 and 6, divided by 3 equal to (i) 25 (ii) 14 (iii) 126 5. 30 is subtracted from the product of 6 and 8 is (i) – 18 (ii) 3 (iii) 18 6. the quotient of 60 divided 12 is added to the product of 5 and 2 is (i) 8 (ii) 12 (iii) 15 7. the value of 54 ÷ 9 × 3 – 5 × 80 ÷ 20 is equal to (i) – 2 (ii) 4 (iii) 2 8. Which of the following statement is not true? (i) Product of two negative number is positive (ii) Quotient of negative number divided to positive number is negative (iii) Product of negative and positive number is positive. 9. 27 ÷ 3 + 6 × 3 is equal to (i) 45 (ii) 27 (iii) 9 10. if the result of 45 ÷ 9 4–2 is 7, then represents. (i) + (ii) – (iii) × 11. if the result of 20 5 × 3 + 8 is 20 then represents (i) × (ii) ÷ (iii) +
Oasis School Mathematics Book-5 102 Unit Test Full marks – 22 Attempt all the questions. 1. Add: 4 a. b. 372648 + 12679 2. Subtract: 4 a. b. 642903 – 379824 3. multiply: 4 a. b. 5076 × 42 4. Divide: 4 a. 236 ÷ 16 b. 9786 ÷ 72 5. Simplify: 4 a. 44 ÷ 11 × 5 + 36 ÷ 4 – 10 b. 22 + 52 ÷ 13 – 3 × 4 6. make mathematical expression and simplify: 4 a. The quotient of 90 divided by 18 is added to the product of 5 and 2. b. The product of 6 and 7 is added to 15 divided by 5. 657482 + 64921 573768 – 348942 3764 × 36
Oasis School Mathematics Book-5 103 Equal parts of a whole are fractions: 1 2 , 2 3 , 5 6 , etc. are fractions. 2 3 means two parts out of three equal parts. In a fraction 2 3 2 is numerator and 3 is denominator. Diagram Fraction Meaning Numerator Denominator 1 4 One part out of 4 equal parts 1 4 Two parts out of 3 equal parts 2 3 equivalent fractions: 1 2 , 2 4 , 3 6 , etc. are equivalent fractions. Two or more fractions representing the same part of the whole are equivalent fractions. 1 2 2 4 3 6 is shaded is shaded is shaded Each fraction represents the same part but the notation is different. 2 3 Review Fractions UNIT 5
Oasis School Mathematics Book-5 104 to find the equivalent fraction of the given fraction To find the equivalent fractions of given fraction. (i) Multiply both numerator and denominator by the same number (except 0) 1 2 = 1 × 2 2 × 2 = 2 4 1 2 = 1 × 3 2 × 3 = 3 6 1 2 = 1 × 4 2 × 4 = 4 8 1 2 , 2 4 , 3 6 , 4 8 , etc. are equivalent fractions. (ii) Divide both the numerator and the denominator by the same number. 5 10 = 5 ÷ 5 10 ÷ 5 = 1 2 1 2 and 5 10 are equivalent fractions 1 3 and 1 6 are equivalent fractions like and unlike fractions: 1 8 , 2 8 , 5 8 , 6 8 , etc. are like fractions. Fractions having same denominator are like fractions. 2 5 , 1 3 , 5 6 , 3 8 , etc. are unlike fractions. Fractions having different denominators are unlike fractions. 3 6 = 3 ÷ 3 6 ÷ 2 = 1 3 1. Write the fraction of the shaded part. a. b. c. Review Exercise 5.1
Oasis School Mathematics Book-5 105 2. What fraction of these circles are shaded? 3. Write each of the divisions in fraction. a. 11 ÷ 7 b. 9 ÷ 4 c. 3 ÷ 4 d. 11 ÷ 13 e. 8 ÷ 3f. 3 ÷ 13 4. identify the numerator and denominator of given fractions. a. 5 6 b. 11 30 c. 19 24 d. 3 7 5. a. What fraction of an hour is 45 minutes? b. What fraction of a day is 6 hours? c. What fraction of a year is 25 days? d. What fraction of 1 km is 200 m? 6. Write any three equivalent fractions of the following: a. b. c. 1 2 a. 1 4 b. 4 5 c. 2 7 d. 1 5 e. 8. identify whether the given fractions are like or unlike: a. 2 5 , 3 5 , 7 5 , 1 5 b. 7. Write the correct number in the space: 2 5 15 a. = 3 4 12 b. = 1 4 40 c. = 3 5 18 d. = 7. Write any two equivalent fractions, dividing both numerator and denominator by a common number. 10 20 a. 18 24 b. 20 24 c. 9. Separate the like fractions from the given set: 2 5 , 1 10 , 3 9 , 4 7 , 2 6 , 1 7 , 5 7 , 3 7 , 2 11, 3 13 4 7 , 2 5 , 3 11, 6 9 Answers Consult your teacher.
Oasis School Mathematics Book-5 106 Let's take some fraction like 3 7 , 6 5 , 2 5 , 7 5 , 1 6 , 2 7 , 8 3 , 5 4 , etc. • Compare the numerator and denominator of each fraction. • Separate the fractions into two groups with greater numerator and with greater denominator. First group of fractions are like fractions and second group of fractions are improper fractions. Fractions having greater numerator Fraction having smaller numerator 3 7 , 2 5 , 1 6 , 2 7 6 5 , 7 5 , 8 3 , 5 4 Hence, fractions having smaller numerator are proper fraction and fractions having greater numerator are improper fraction. 3 7 , 2 5 , 1 6 , 2 7 , etc. are proper fractions. 6 4 , 7 5 , 8 5 , 5 4 , etc. are the fractions having greater numerator. Such fraction are improper fractions. Mixed Number Observe the given figure and discuss the answer of following questions. • How many halves are there in 1 figure? • How many halves are there in all figure? • How many full circle and how many half circles are there? There are 5 half circles. There are 2 full and one half circle. 1 (2 halves) 1 (2 halves) 1 2 Proper and Improper Fractions
Oasis School Mathematics Book-5 107 5 halves means 2 full and one half \ 5 2 = 2 1 2 Mixed number is the combination of a whole number and a proper fraction. Conversion of a mixed number into an improper fraction and an improper fraction into mixed number 1 full four 's five 's. So it is 5 × = . one 1 4 1 4 1 4 1 4 5 4 5 7 • • = + + × = = = = 1 2 3 11 11 2 80 11 77+3 11 2×5+1 2 11×7+3 11 Remember! 2 Hence, mixed number Quotient • = = = 3 6 Remainder Divisor 15 6 15 ÷ 6 6 15 2 -12 3 In the given figures, how many 1 4 's are there? There many 1 4 's = 5 4 . How many full and 1 4 are there? There is 1 full and one 1 4 . = 1 1 4 Hence, 5 4 = 1 1 4 Improper fraction Mixed fraction
Oasis School Mathematics Book-5 108 1. identify whether the given fractions are proper or improper: 2. a. How many 1 3 are there in one circle? b. How many 1 3 's are shaded in the given figure? 4 7 a. 9 4 b. 3 8 c. 2 9 f . d. 4 13 e. 16 11 g. 3 11 h. 12 7 Exercise 5.2 Mixed number = Quotient Remainder Denominator Convert into mixed number. 17 4 = 17 ÷ 4 Solution: In the given figure, a. How many 1 3 's are shaded? b. Write this in the form of improper fraction. c. How many full stripe and how many 1 3 's are shaded? d. Write the fraction of the shaded part in mixed number. e. Write the relation of mixed number with improper fraction. Solution: a. Eight 1 3 's are shaded in the above figure. b. So, the improper fraction represented by shaded part 8 3 . (Eight 1 3 's) c. Two full stripe and two 1 3 's are shaded in the figure. d. Fraction represented by the shaded part is 2 2 3 . e. From the result of (b) and (d), we get the relation 8 3 = 2 2 3 . Example 1 Example 2 4) 17 (4 - 16 1 Quotient Remainder 1 4 = 4
Oasis School Mathematics Book-5 109 c. Write the fraction of the shaded part d. How many full circles and how many 1 3 are shaded? e. Write the fraction of the shaded part in mixed form. f. Write the relation of improper fraction with mixed number. 3. a. In the given figure, how many 1 4 's are shaded? b. How many full and 1 4 's are shaded? c. From the result of (a), write the shaded part in improper fraction d. From the result of (b), write the shaded part in mixed number. 4. Write the fraction represented by given figure in both ways. a. b. c. d. 6. convert the following improper fractions into mixed numbers: g. h. i. j. 29 11 53 13 65 15 53 11 a. b. c. f. d. 12 7 13 5 18 5 19 3 22 9 32 9 e. 5. convert the following mixed numbers into improper fractions: 1 4 a. 3 5 b. 1 5 c. 6 7 f. d. 3 8 e. 3 7 2 2 5 g. 10 7 h. 1 11 7 2 3 8 3 10 i. 3 j. 5 1 2 5
Oasis School Mathematics Book-5 110 7. Answer the following questions: a. What are the fractions called if they have same denominator? b. What are the fractions called if they have different denominators? c. What is a fraction called if its numerator is less than its denominator? d. What is a fraction called if its numerator is greater than its denominator? e. Are 2 5 and 4 10 equivalent fractions? f. Are 3 5 and 3 4 like fractions? g. is 2 3 4 = 11 4 ? h. How many 1 7 's are there in the fraction 12 7 ? Answers Consult your teacher. Project Work 1. In a chart paper, draw four different figures and divide and colour them in such a way that coloured part represent the equivalent fraction. 2. In a chart paper, draw the figures which can be represented in improper fraction. Represent the same figure in mixed form. Establish the relation between improper fraction and mixed number. It is easy to compare, add and subtract the like fractions. So we must learn to convert unlike fractions into like fractions. Let's see an example and get an idea how we can convert unlike fractions into like fractions. Convert 3 4 , 1 5 and 5 8 into like fractions. example 1 Conversion of Unlike Fractions into Like Fractions
Oasis School Mathematics Book-5 111 Solution: L.C.M. = 4, 5, 8 is 2 × 2 × 1 × 5 × 2 = 40 Now, 3 4 = 3 4 × 10 10 = 30 40 1 5 = 1 5 × 8 8 = 8 40 5 8 = 5 8 × 5 5 = 25 40 30 40, 8 40 and 25 40 are the like fractions representing unlike fractions 3 4 , 1 5 and 5 8 . convert the following unlike fractions into like fractions: 4 5 and 2 3 1 2 , 2 3 and 1 5 2 3 , 4 5 and 3 4 Steps: • Find the L.C.M of denominators • Convert all the fractions into their equivalent fractions having L.C.M of denominator. class Assignment comparison of fractions Let's take two fractions 1 4 and 3 4 From the figure, it is clear that 3 4 > 1 4 1 4 3 4 If the fractions are like, the fraction having greater numerator is the greater fraction. Again, Take two fractions 1 3 and 4 6 From the figure it is clear that 4 6 > 1 3 . 1 3 4 6
Oasis School Mathematics Book-5 112 It is difficult to make figure in every case to compare the fractions. So we have to convert unlike fractions into like fractions to compare them. 1 3 and 4 6 L.C.M. of 3 and 6 is 3 × 1 × 2 = 6 \ 1 3 = 1 × 2 3 × 2 = 2 6 4 6 = 4 × 1 6 × 1 = 4 6 Since, 4 6 > 2 6 If the fractions are unlike, first convert them into like fractions and compare them. Divide each strip of one whole into 2, 3, 4, 5, 6, 7and 8 equal parts as shown in the figure. 1. Three equivalent fractions of 1 2 are ............, ............ and ............. An equivalent fraction of 1 4 is ............. comparison of unlike fractions. Activity
Oasis School Mathematics Book-5 113 Arrange 1 4 , 5 6 and 3 3 in descending order. Solution: Given fractions 1 4 , 5 6 , 3 3 These are unlike fractions, L.C.M. of 4, 6 and 3 is 2 × 3 × 2 = 12 1 4 = 1 × 3 4 × 3 = 3 12 5 6 = 5 × 2 6 × 2 = 10 12 2 3 = 2 × 4 3 × 4 = 8 12 Since, 10 > 8 > 3 10 12 > 8 12 > 3 12 \ 5 6 > 2 3 > 1 4 example 2 I know ! Ascending order means increasing order and descending order means decreasing order. An equivalent fraction of 1 3 is ............. An equivalent fraction of 2 3 is ............. An equivalent fraction of 3 4 is ............. 2. Compare the fractions: 3. Write the fractions of 1 4 , 1 3 , 2 5 , 3 7 and 1 8 in ascending order. ............................................................................................................ 4. Write the fractions of 5 6 , 3 7 , 3 5 , 1 2 and 7 8 in descending order. .............................................................................................................
Oasis School Mathematics Book-5 114 Arrange 2 5 , 4 7 and 1 7 in ascending order: Arrange 2 3 , 4 5 and 1 2 in descending order: class Assignment 1. Observe the fractions and write >, < or = in the box. a. b. c. d. 2 3 4 7 1 3 3 7 12 15 13 15 11 17 11 17 e. f. g. h. 8 17 9 12 5 13 2 15 3 15 7 13 3 17 7 12 2. make the like fractions and compare them: 5 12 1 12 4 12 e. f. g. 3 8 3 9 4 9 and and and a. b. c. d. 2 5 1 2 3 5 1 4 3 4 2 3 5 6 1 5 and and and and Exercise 5.3 3. Arrange the following fractions in ascending order: 4. Arrange the following fractions in descending order: a. 2 7 , 1 7 , 5 7 b. 7 11, 2 11 , 9 11 c. 2 3 , 3 4 , 5 6 d. 1 2 , 3 4 , 7 12 a. 3 8 , 2 8 , 7 8 b. 3 11, 1 11, 6 11 c. 1 2 , 2 3 , 3 4 d. 3 8 , 1 4 , 5 6 Answers Consult your teacher.
Oasis School Mathematics Book-5 115 A fraction is said to be in its lowest term if only the common factor between the numerator and denominator is 1. We can convert a fraction into its lowest term by cancelling the common factors of both numerator and denominator. There are different ways of addition and subtraction of fractions depending upon its type. Let's be clear with the help of given examples. Express: 8 12 into its lowest term: Solution: 8 12 = 2 × 2 × 2 2 × 2 × 3 = 2 3 \ 8 12 = 2 3 Express: 15 8 56 into lowest term: Solution: 15 8 56 = 15 + 2 × 2 × 2 2 × 2 × 2 × 7 = 15 + 1 7 \ 15 1 7 example 1 example 2 2 8 2 2 2 2 12 2 6 3 I know ! how to factorize 2. express the following mixed number into improper fraction and convert them into their lowest term: b. 6 12 3 6 9 27 2 10 a. 4 12 c. 18 d. 30 f. 5 20 6 24 8 32 20 80 e. 25 30 g. 35 h. 50 1. express the following fractions into their lowest term: b. 9 12 h. 84 108 96 144 7 77 20 100 50 400 25 75 c. 15 20 i. d. 14 49 j. e. 27 81 k. l. f. 15 60 a. 6 8 g. Exercise 5.4 Fraction in its Lowest Term Answers 1. a) 3 4 b) 3 4 c) 3 4 d) 2 7 e) 1 3 f) 1 4 g) 7 9 h) 2 3 i) 1 11 j) 1 5 k) 1 8 l) 1 3 2. a) 9 2 b) 25 2 c) 55 3 d) 151 5 e) 101 4 f) 121 4 g) 141 5 h) 151 5
Oasis School Mathematics Book-5 116 Subtract: 8 9 – 3 9 = 8 – 3 9 = 5 9 example 1 8 9 3 9 5 9 look at one more example: Add: 2 1 3 + 5 2 3 Solution: 2 1 3 + 5 2 3 = 7 3 + 17 3 = 7 + 17 3 = 24 3 = 8 Steps: • Convert the mixed number into the improper fraction. • Keeping denominator same, add numerator. Alternative method: 2 1 3 + 5 2 3 = 2 + 5 + 1 3 + 2 3 = 7 + 1 + 2 3 = 7 + 3 3 = 7 + 1 = 8 Steps: • Separate the mixed number into whole number and proper fraction. • Add proper fractions. • Add the whole number with the sum of proper fractions. Subtract numerator, keep denominator same. 2 7 + 3 7 = 2 + 3 7 = 5 7 2 7 3 7 5 7 Addition and subtraction of fractions Add numerator, keep denominator same. Look at these examples properly and get the idea of addition and subtraction of like fractions. Difference of like fractions = Difference of the numerators Common denominator Sum of like fractions = Sum of the numerators Common denominator
Oasis School Mathematics Book-5 117 Subtract: 5 1 4 – 3 3 4 Solution: 5 1 4 – 3 3 4 = 21 4 – 15 4 = 21 – 15 4 = 6 4 = 3 × 2 2 × 2 = 3 2 Add: 2 3 5 + 3 1 5 + 4 4 5 Solution: 2 3 5 + 3 1 5 + 4 4 5 = 13 5 + 16 5 + 24 5 = 13 + 16 + 24 5 = 53 5 = 10 3 5 example 2 example 3 If the resultant fraction is improper, we have to convert it into mixed number. Exercise 5.5 1. Add the following and reduce them into lowest term if necessary: f. 4 g. h. 1 4 + 31 4 2 3 7 + 3 3 7 2 3 8 + 3 1 8 i. k. 1 5 12 + 4 5 12 15 7 12+12 1 12 a. b. c. d. e. 1 4 + 1 4 3 7 + 1 7 4 11 + 2 11 5 13 + 4 13 2 1 3 + 32 3 2. Subtract the following and reduce them into lowest term if necessary: f. g. h. i. j. 2 4 5 – 21 5 4 2 3 – 1 1 3 4 3 5 – 2 1 5 2 3 7 – 1 1 7 7 2 11 – 3 5 11 a. b. c. d. e. 5 6 – 1 6 3 4 – 1 4 6 7 – 2 7 5 11 – 1 11 6 13 – 2 13 3. Add the following and reduce them into lowest term if necessary: a. b. c. d. 1 7 + 2 7 + 3 7 5 11 + 2 11 + 1 11 2 9 + 3 9 + 1 9 2 2 3 + 51 3 + 31 3
Oasis School Mathematics Book-5 118 4. Simplify: a. d. b. e. c. f. 4 2 3 – 31 3 + 21 3 6 3 7 + 42 7 – 34 7 3 3 4 + 21 4 – 12 4 6 5 9 – 42 9 + 11 9 4 3 5 + 21 3 – 32 5 7 4 11 – 3 2 11 + 2 3 11 There are many situations in our daily life where addition and subtraction of like fraction takes place. Let's discuss one example. A man mixes 5 1 3 kg rice with 7 2 3 rice of another quality. If he sold 9 2 3 kg rice from the mixture, how much rice is left there? Hence, total weight of the mixture = (5 1 3 + 7 2 3 ) kg. If he sold 9 2 3 kg rice from in mixture, remaining quantity of rice = (5 1 3 + 7 2 3 – 9 2 3 ) = 16 3 + 23 3 – 29 3 = 16 + 23 – 29 3 = 39 – 29 5 kg = 10 3 kg = 3 1 3 kg. Answers 1. a) 1 2 b) 4 7 c) 6 11 d) 9 13 e) 6 f) 7 1 2 g) 56 7 h) 51 2 i) 55 6 j) 27 2 3 2. a) 2 3 b) 1 2 c) 4 7 d) 4 11 e) 4 13 f) 3 5 g) 3 1 3 h) 2 2 5 i ) 1 2 7 j) 3 8 11 3. a) 6 7 b) 8 11 c) 2 3 d) 111 3 e) 10 6 7 f) 131 5 g) 91 8 h) 125 8 4. a) 42 3 b) 41 2 c) 32 5 d) 71 7 e) 3 4 9 f) 6 5 11 e. f. g. h. 5 2 7 + 21 7 + 33 7 7 2 5 + 21 5 + 33 5 3 5 8 + 43 8 + 11 8 4 5 8 + 21 8 + 57 8 Verbal problems on Addition and Subtraction of Like Fractions
Oasis School Mathematics Book-5 119 example 1 In a fruit shop there are 5 2 7 kg apples 6 1 7 kg oranges and 7 2 7 kg grapes. What is the total weight of the fruits? Solution: Weight of apples = 5 2 7 kg Weight of oranges = 6 1 7 kg Weight of grapes = 7 2 7 kg. Total weight of the fruits = 5 2 7 kg + 6 1 7 kg + 7 2 7 kg = (37 7 + 43 7 + 51 7 ) kg. = 131 7 kg = 18 5 7 kg Hence, the total weight of the mixture is 18 5 7 kg. Example 2 A boy cut a cake into 12 equal pieces. He ate 4 pieces and gave 3 pieces to his brother and 2 pieces to his sister? What fraction of cake is eaten by each of them? What fraction of cake is eaten altogether? Solution: Total number of pieces of cake = 12. If he ate 4 pieces of cake, then the fraction of cake eaten by him = 4 12. His brother ate 3 pieces of cake. The fraction of cake eaten by his brother = 3 12. His sister ate 2 pieces of cake. The fraction of cake eaten by his sister = 2 12. Total fraction of cake eaten by them = 4 12 + 3 12 + 2 12 = 4 + 3 + 2 12 = 9 12 Hence, they ate 9 12 part of cake.
Oasis School Mathematics Book-5 120 Exercise 5.6 Solve the following verbal problems. 1. A man mixes 7 1 2 litres of milk with 2 1 2 litres of water. How many litre of mixture is there? 2. From 7 9 m ribbon, 2 9 m of ribbon is cut. Find the length of remaining part of ribbon. 3. A man mixes 4 9 litre of buffalo milk with 2 9 litre of cow milk. If he sold 3 9 litre of mixture, find, what fraction of milk is left to sell? 4. Among 5 3 7 kg of oranges 2 1 7 kg were rotten and 1 2 7 kg were sold. Find how many oranges are left to sold. 5. Saleem studied Maths for 1 1 3 hour, English for 2 3 hour and Nepali for 2 2 3 hours. How long did he study altogether? 6. A man travelled 5 3 7 km by bus, 9 2 3 km by car and 2 1 7 km by walking. Find the length of his total journey. 7. What will bethe result if the sum of 2 1 5 and 3 2 5 is added to the difference of 4 3 5 and 2 2 5 ? Answers 1. 101 2. 5 9 m 3. 3 9 litre 4. 2 kg 5. 42 3 hours 6. 166 7 km 7. 74 5 Project Work 1. Using transparent sheet show the addition and subtraction of like fraction and unlike fraction by diagram. 2. Collect 3/4 problems in our daily life where addition and subtraction of like fraction take place. Solve these problems in chart paper and present it in your classroom.
Oasis School Mathematics Book-5 121 To add or subtract unlike fractions they have to be first converted into like fractions. Let's see an example and get the idea about addition and subtraction of unlike fractions. Add: 2 3 + 3 4 L.C.M. of 3 and 4 is 3 × 4 = 12 2 3 × 4 4 + 3 4 × 3 3 = 8 12 + 9 12 = 8 + 9 12 = 17 12 = 1 5 12 example 1 - Convert all the fractions into like fractions. - Add the like fractions. Addition and Subtraction of Unlike Fractions Add: 5 6 – 1 4 L.C.M. of 6 and 4 is 2 × 3 × 2 = 12 Now, 5 6 – 1 4 = 5 × 2 6 × 2 – 1 × 3 4 × 3 = 10 12 – 3 12 = 10 - 3 12 = 7 12 example 2 Alternative method Add: 5 6 – 1 4 = 5 × 2 - 1 × 3 12 = 10 - 3 12 = 7 L.C.M. of 6 and 4 = 12 12 12 ÷ 6 = 2 \ 5 × 2 12 ÷ 4 = 3 \ 1 × 3 Alternative method Add: 2 3 + 3 4 = 2 × 4 + 3 × 3 12 = 8 + 9 12 = 17 12 = 1 5 12 L.C.M. of 3 and 4 = 12 12 ÷ 3 = 4 \ 2 × 4 12 ÷ 4 = 3 \ 3 × 3
Oasis School Mathematics Book-5 122 Subtract: 5 2 7 – 3 2 5 Solution: 5 2 5 – 3 2 5 = 37 7 – 17 5 = 37 7 × 5 5 – 17 5 × 7 7 Add : 2 1 3 + 43 4 + 15 6 Solution: L.C.M. of 3, 4 and 6 is 12 2 1 3 + 43 4 + 15 6 = 7 3 + 19 4 + 11 6 = 7 3 × 4 4 + 19 4 × 3 3 + 11 6 × 2 2 = 28 12 + 57 12 + 22 12 = 28 + 57 + 22 12 = 107 12 = 811 12 example 3 L.C.M. of 3, 4, 6 2 × 3 × 1 × 2 × 1 = 12 example 4 = 185 35 – 119 35 = 185 - 119 35 = 66 35 = 131 35 Alternative method Subtract: 5 5 6 – 3 1 4 Solution: 5 2 7 – 3 2 5 = 37 7 – 17 5 = 37 × 5 – 17 × 7 35 = 185 - 119 35 = 66 35 = 131 35
Oasis School Mathematics Book-5 123 1. Add the following and reduce them into the lowest term if necessary: 3. Simplify: a. b. c. d. e. 1 2 + 3 8 3 8 + 1 4 5 8 + 7 12 2 3 + 2 9 9 10 + 3 5 a. b. c. 1 2 + 3 4 – 5 6 5 9 – 3 6 + 5 12 5 8 – 1 4 + 3 2 d. e. f. 3 1 8 – 13 4 + 21 4 5 1 4 + 61 2 – 32 3 6 3 5 – 14 7 – 32 5 g. h. i. 5 1 2 + 63 4 + 25 6 6 3 4 – 31 8 – 11 4 5 1 2 – 32 3 + 23 4 f. g. h. i. j. 5 6 + 2 3 7 4 + 5 6 7 9 + 1 6 1 4 5 + 1 1 10 2 7 8 + 1 1 4 2. Subtract the following and reduce them into the lowest term if necessary: a. b. c. d. e. 1 2 – 3 8 3 8 – 1 4 5 6 – 7 12 2 3 – 2 9 9 10 – 3 5 f. g. h. i. j. 5 6 – 2 3 7 4 – 5 6 7 9 – 3 5 1 4 5 – 1 1 10 2 7 8 – 1 1 4 Exercise 5.7 Answers 1. a) 7 8 , b) 5 8 , c) 1 5 24 , d) 8 9 , e) 1 1 2 , f) 11 2 , g) 2 7 12, h) 17 18 , i) 2 9 10, j) 4 1 8 , 2. a) 1 8 , b) 1 8 , c) 3 12 , d) 4 9 , e) 3 10, f) 1 6 , g) 11 12, h) 8 45, i) 7 10, j) 1 5 8 , 3. a) 5 12, b) 17 36, c) 1 7 8 , d) 3 5 8 , e) 8 1 12, f) 2 1 35, g) 15 1 12, h) 2 3 8 , i) 4 7 12
Oasis School Mathematics Book-5 124 Let's take a whole number 5 and a fraction 1 3 . Take a whole number 6 and a fraction 1 4 . Let's subtract 1 4 from 6. 6 – 1 4 = 6 1 – 1 4 = 6 × 4 – 1 × 1 4 = 24 – 1 4 = 23 4 = 53 4 Add quickly: 5 + 1 4 = 3 + 2 3 = 10 + 1 4 = 6 + 2 3 = 15 + 1 7 = 20 + 3 10 = Let's add them 3 + 1 3 = 5 1 + 1 3 = 5 × 3 + 1 × 1 3 = 15 + 1 3 = 16 3 = 51 3 L.C.M. of 1 and 3 = 3 L.C.M. of 1 and 4 = 4 3) 1 6 (5 – 1 5 1 I understand ! I just have to remove + sign. 4) 2 3 (5 – 2 0 3 5 + 1 2 = 5 1 2 6 + 2 3 = 6 2 3 7 + 1 2 = 7 1 2 Quick method class Assignment Addition and Subtraction of a Whole Number and a Fraction
Oasis School Mathematics Book-5 125 = 185 35 – 119 35 = 185 - 119 35 = 66 35 = 131 35 1. Add the following and reduce them into the lowest term if necessary: 3. Simplify: a. b. c. d. e. 1 2 + 3 8 3 8 + 1 4 5 8 + 7 12 2 3 + 2 9 9 10 + 3 5 a. b. c. 1 2 + 3 4 – 5 6 5 9 – 3 6 + 5 12 5 8 – 1 4 + 3 2 d. e. f. 3 1 8 – 13 4 + 21 4 5 1 4 + 61 2 – 32 3 6 3 5 – 14 7 – 32 5 g. h. i. 5 1 2 + 63 4 + 25 6 6 3 4 – 31 8 – 11 4 5 1 2 – 32 3 + 23 4 f. g. h. i. j. 5 6 + 2 3 7 4 + 5 6 7 9 + 1 6 1 4 5 + 1 1 10 2 7 8 + 1 1 4 2. Subtract the following and reduce them into the lowest term if necessary: a. b. c. d. e. 1 2 – 3 8 3 8 – 1 4 5 6 – 7 12 2 3 – 2 9 9 10 – 3 5 f. g. h. i. j. 5 6 – 2 3 7 4 – 5 6 7 9 – 3 5 1 4 5 – 1 1 10 2 7 8 – 1 1 4 Answers 1. a) 7 8 , b) 5 8 , c) 1 5 24 , d) 8 9 , e) 1 1 2 , f) 11 2 , g) 2 7 12, h) 17 18 , i) 2 9 10, j) 4 1 8 , 2. a) 1 8 , b) 1 8 , c) 3 12 , d) 4 9 , e) 3 10, f) 1 6 , g) 11 12, h) 8 45, i) 7 10, j) 1 5 8 , 3. a) 5 12, b) 17 36, c) 1 7 8 , d) 3 5 8 , e) 8 1 12, f) 2 1 35, g) 15 1 12, h) 2 3 8 , i) 4 7 12 Exercise 5.8 Alternative method Subtract: 5 5 6 – 3 1 4 Solution: 5 2 7 – 3 2 5 = 37 7 – 17 5 = 37 × 5 – 17 × 7 35 = 185 - 119 35 = 66 35 = 131 35
Oasis School Mathematics Book-5 126 Remember ! Whole number part decimal point 1.4 decimal part Given figure is divided into ten equal parts. One part represents the fraction 1 10 . Given figure represents the decimal 0.1. Study the given figure and answer the questions given below. • In how many parts is the given figure divided into? • What fraction of the figure is shaded? • What part of decimal is shaded? 1 10 0.1 1 whole is shaded in the figure. 4 10 is shaded. i.e. 0.4 is shaded. The shaded part represents 1.4. As we know that 1 4 10 is shaded. So, we get the relation 1 4 10 = 1.4 Let's take one more example; If there is no whole number, we have to write 0 in the whole number position before decimal. 1.4 Again, Let's observe the given figure, Here, one whole is divided into 100 equal parts, one part represents 1 100 i.e. 0.01. Decimals UNIT 6 Review
Oasis School Mathematics Book-5 127 Write Read 1.6 one point six 1.07 one point zero seven 13.38 thirteen point three eight how to read the decimal number? 1. Write the following fractions in decimal and decimal into fraction. 2. Write the following decimal into fraction. 1 10 = 0.1 2 10 = 5 10 = 7 10 = 1 100 = 2 100 = 15 100 = 25 100 = 65 100 = 0.2 = 0.25 = 0.75 = 0.8 = 0.95 = 0.6 = 1 whole is shaded 7 parts out of 100 are shaded 1.07 1 10 = 0.1 1 100 = 0.01 2 10 = 0.2 3 100 = 0.03 25 100 = 0.25 63 100 = 0.63 78 100 = 0.78 20 100 = 0.20 In this figure, one whole is shaded and 7 part out of 100 is shaded. So, it is written as 1 7 100 , is also written as 1.07. So, 1 7 100 = 10.7. class Assignment
Oasis School Mathematics Book-5 128 Place Value of Decimal Numbers The fractions having denominators 10 are called tenths. 2 10 , 5 10 , 6 10 , etc. are tenths. 0.2, 0.5, 0.6, etc. are tenths. The fractions having denominators 100 are called hundredths. 3 100 , 5 100 , 6 100 , etc. are hundredths. 0.03, 0.05, 0.6, etc. are hundredths. The fractions having denominators 1000 are called thousandths. 2 1000, 3 1000, 6 1000, 12 1000, etc. are thousandths. 0.001, 0.003, 0.006, 0.012, are thousandths. = three - hundredths = 0.03 hundredths place tenths place = fifteen-thousandths = 0.015 thousandths place hundredths place tenths place tenths place 1 10 = one-tenth = 0.1 3 1000 15 1000 Let's see the place value chart of 432.675. Hundreds (H) 100 Tens (T) 10 Ones (O) 1 Decimal Tenths (t) Hundredths (h) Thousandths (h) 4 3 2 . 6 7 5 1 10 2 100 2 1000 Place value of 4 = 4 × 100 = 400 Place value of 3 = 3 × 10 = 30 Place value of 2 = 2 × 1 = 2 Place value of 6 = 6 × 1 10 = 6 10 = 0.6 Place value of 7 = 7 × 1 100 = 7 100 = 0.07 I know, 1 10 = 0.1, 1 100 = 0.01 1 1000= 0.001, 5 10 = 0.5 6 10 = 0.6
Oasis School Mathematics Book-5 129 expanded form and standard form of a decimal number 23.134 = 2 × 10 + 3 × 1 + 1 × 1 10 + 3 × 1 100 + 4 × 1 1000 = 2 × 10 + 3 × 1 + 1 × 0.1 + 3 × 0.01 + 4 × 0.001 Standard form Expanded form Place value of 5 = 5 × 1 1000 = 5 1000 = 0.005 Review Exercise 6.1 1. Write in decimal: a. c. d. e. b. 2. in the number 372.845, write the digit in the: a. tens place b. ones place c. hundreds place d. tenths place e. hundredths place f. thousandths place 3. Form decimal number with: a. 6 in ones place and 2 in tenths place. b. 7 in tens place, 5 in ones place, 3 in tenths place, 5 in hundredths place. c. 2 in tens place, 3 in ones place, 5 in tenths place, 3 in hundredths place and 4 is thousandths place. 4. Show the number 219.453 in the place value chart and write the place value of each digit. 5. Write these numbers in figure: a. Seven point two three b. Twelve point zero nine c. Twenty eight point one six d. Thirty seven point six three
Oasis School Mathematics Book-5 130 6. Write the number name of given number. a. 6.35 b. 19.64 c. 134.69 d. 235.92 e. 0.537 7. Write the following fractions in decimals: a. 2 10 b. 3 100 c. 4 1000 d. 6 10 e. 8 100 f. 12 100 g. 154 1000 h. 624 1000 i. 7 1000 j. 82 100 k. 4 3 10 l. 12 15 100 m. 56 17 100 n. 3 3 10 o. 129 253 1000 8. Write the given decimal numbers in expanded form. a. 0.6 b. 0.84 c. 12.63 d. 54.652 e. 37.185 9. Write the given decimal numbers in standard form. a. 2 × 10 + 5 × 1 + 6 × 0.1 + 5 × 0.01 b. 3 × 100 + 2 × 10 + 1 × 1 + 3 × 0.1 + 7 × 0.01 + 8 × 0.001 c. 4 × 1000 + 2 × 100 + 2 × 10 f+ 5 × 1 + 3 × 0.1 + 2 × 0.01 + 1 × 0.001 d. 5 × 100 + 4 × 10 + 2 × 1 + 6 × 1 10 + 7 × 1 100 + 8 × 1 1000 e. 4 × 1000 + 2 × 100 + 1 × 1 + 3 × 1 10 + 6 × 1 100 + 8 × 1 1000 Answers Consult your teacher.
Oasis School Mathematics Book-5 131 Let's see an example and get the idea of conversion of decimal into fraction. 0.85 = 85 100 17 20 = 17 20 Again, lets take one more example. 3.15 = 3 + 0.15 = 3 + 15 100 = 3 + 3 20 = 3 3 20 2 digits after decimal means I have to write two zeros after 1 in denominator. Steps: • Count the number of decimal places in the decimal. • Ignore the decimal point and write all the digits on the numerator of the fraction. • Write as many zeros after 1 in the denominator as there were decimal places in the fraction. • Reduce the fraction into its lowest term. convert the following decimals into fractions: 1.25 5.6 0.25 2.015 class Assignment Convert 2.05 into fraction. Solution: 2.05 = 2 + 0.05 = 2 + 5 100 = 2 + 1 20 = 2 1 20 example 1 Conversion of Decimals into Fractions Alternative method 2.05 = 2 5 100 1 20 = 2 1 20
Oasis School Mathematics Book-5 132 conversion of fractions into decimal We already know: i. When the denominator is 10, 100, 1000, etc. 2 10 = 0.2, 5 10 = 0.5, 7 10 = 0.7, etc. 3 100 = 0.03, 5 100 = 0.05, 9 100 = 0.09, etc. 7 1000 = 0.007, 3 1000 = 0.003, 6 1000 = 0.006, etc. I already know it ii. When the denominator is another number: Convert, 2 5 into decimal. 2 5 = 2 5 × 2 2 = 4 10 = 0.4 Let's convert 3 20 into decimal. 3 20 = 3 20 × 5 5 = 5 100 = 0.15 I have to convert denominator into 10, 100, 1000, etc. change the denominator of fraction into 10 or 100 and convert them into decimal. 4 10 = 1 100 = 2 100 = 3 100 = 6 100 = 3 5 11 20 1 2 16 25 class Assignment
Oasis School Mathematics Book-5 133 comparison of decimal Let's take any two numbers 23.84 and 15.23 Here, 23 > 15 \ 23.84 > 15.23 Compare 28.63 and 28.82 Solution: Here, Compare whole numbers, 28 = 28 Compare tenths 6 < 8 \ 28.63 < 28.82 example 1 Compare whole numbers first, then compare tenths, hundredths, thousandths etc. I understand ! We have to compare whole the number first then tenths, hundredths. 1. convert the following decimals into fractions: a. 0.8 b. 0.3 c. 0.12 d. 0.45 e. 2.5 f. 6.3 g. 8.5 h. 12.8 i. 5.25 j. 6.75 k. 12.95 l. 19.82 m. 3.14 n. 2.55 o. 150.14 p. 7.214 q. 25.306 r. 18.205 2. convert the following fractions into decimals: a. 3 2 10 b. 2 5 10 c. 1 3 100 d. 6 4 1000 e. 5 4 100 f. 2 25 100 g. 2 5 h. 3 5 i. 1 2 j. 4 5 k. 16 25 l. 11 2 m. 13 5 n. 71 2 o. 16 3 20 p. 417 25 q. 9 41 50 3. compare the given decimal numbers: a. 12.84 and 13.35 b. 163.28 and 47.12 c. 75.94 and 63.38 d. 18.61 and 18.54 e. 19.64 and 19.31 f. 34.27 and 34.23 g. 63.18 and 63.17 h. 15.312 and 15.314 i. 0.842 and 0.841 Exercise 6.2
Oasis School Mathematics Book-5 134 4. Arrange the following numbers in ascending and descending order: a. 3.14, 4.75, 2.69 b. 5.23, 5.27, 5.18 c. 6.572, 6.275, 6.752 d. 4.83, 4.75, 4.86 Answers Consult your teacher. 2.3, 3.57 and 8.164 are unlike decimals 5.12, 6.35, 2.50 are like decimals. If the number of digits after decimal point is same, such decimals are like decimals. If the number of digits after decimal points is not same, such decimals are unlike decimals. 2.3, 2.52 and 3.614 are unlike decimals 2.300, 2.520 and 3.614 are like decimals conversion of unlike decimals into like decimals 2.3 and 2.300 are same 2.52 and 2.520 are same Remember ! • Writing or removing zeros at the end of a decimal number does not change its value. Addition and subtraction of decimals Look at these examples properly and get the idea about addition and subtraction of decimals. Like and Unlike Decimal
Oasis School Mathematics Book-5 135 Add: 15.24 + 8.6 example 1 15.24 15.24 8.6 + 8.60 23.84 • Convert the decimals into like decimals. • Arrange the digits according to the place value so that the decimal points are exactly one below the other. • Start to add from hundredths. Carry over if needed. Subtract: 27.18 - 15.7 example 2 27.18 27.18 15.70 - 15.70 11.48 • Convert the decimals into like decimals. • Arrange the digits according to the place value so that the decimal points are exactly one below the other. • Start to subtract from hundredths, borrow if necessary. 1. identify whether the following decimals are like or unlike. a. 4.5 and 0.3 b. 2.56 and 3.5 c. 9.264 and 65.28 d. 0.001 and 524.12 e. 0.074 and 13.525 f. 0.1 and 23.3 2. Add: a. 24.16 + 5.8 b. 16.35 + 12.1 c. 46.25 + 6.4 d. 4.57 + 13.94 e. 13.63 + 15.95 f. 18.97 + 15.84 g. 13.742 + 18.217 h. 45.996 + 18.84 i. 12.64 + 7.5 + 18.372 j. 0.874 + 13.26 + 5.7 k. 18.64 + 15.736 + 5.9 l. 25.76 + 0.81 + 219.6 3. Subtract: a. 6.78 - 3.32 b. 8.69 - 7.42 c. 9.32 - 4.12 d. 14.6 - 3.84 e. 34.17 - 32.717 f. 28.654 - 13.82 g. 45.1 - 36.111 h. 536.3 - 442 .18 i. 8 - 5.376 j. 12 - 9.324 k. 200.26 - 97.865 l. 67.86 - 12.375 Exercise 6.3
Oasis School Mathematics Book-5 136 4. Simplify: a. 5.4 + 7 - 6.2 b. 4.7 + 2.6 - 3.8 c. 5.2 - 3.3 + 4.2 d. 4.63 + 2.32 - 3.9 e. 6.74 + 5.31 - 2.378 f. 48.93 + 50.05 + 20.007 g. 53.358 + 26.732 - 37.4 h. 105.38 + 3 6.79 - 46.372 i. 118.32 - 15.632 - 12.54 Answers Consult your teacher. There are many situations in our daily life when we have to add and subtract the decimals. Let's see an example and get an idea of addition and subtraction. • Read the questions properly • Decide what you have to do Ankit had Rs 25.65. His mother gave him Rs 23.80. How much money does he have altogether? Solution: Money that Ankit has = Rs 25.65 Money given by his mother = + Rs 23.80 Total money he has = Rs 49.45 example 1 1. a. What is the difference between 5.73 and 4.67? b. What should be added to 5.67 to make 13.64? c. What should be subtracted from 15.65 to make 8.432? d. From which number 15.37 should be subtracted to make 32.437? Exercise 6.4 Word Problems on Decimals
Oasis School Mathematics Book-5 137 2. a. Sandesh bought a book for Rs. 35.85, a pen at Rs. 17.95 and a pencil at Rs. 8.45. What is the total amount he spent? b. A milkman has 45.35l of milk. He sold 25.395l milk during the day. How much milk is left with him? c. Santosh bought a plate of Mo: Mo: worth Rs. 68.75 and a cold drink worth Rs. 15.35. He paid Rs. 100 note. How much change did he get back? d. A table costs Rs. 1450.65 and a chair costs Rs. 915.45. Find the total cost of a table and a chair. e. A milkman supplies 2.5 litre and 4.25 litre of milk to two customers. If he carries 7.25 litre of milk, how much milk will be left with him? f. A man deposited Rs. 275.35 in the bank. On the second day he deposited Rs. 325.65. Find the total amount deposited in the bank. 3. Find the perimeter of the given figure: b. 9.1 cm 8.62 cm 5 cm 7.81 cm 3.25 cm 5.62 cm 5.62 cm a. Project Work Collect some information from our daily life where addition and subtraction of decimals take place.
Oasis School Mathematics Book-5 138 Multiply: 0.374 × 100 Solution: 0.374 × 100 = 37.4 example 1 multiplication of decimal by 10, 100, 1000, etc: Let's learn the multiplication of a decimal number by 10, 100, 1000, etc. 3.174 × 10 = 31.74 4.374 × 100 = 437.4 5.624 × 1000 = 5624 Shift decimal point one step right Shift decimal point two steps right Shift decimal point three steps right I have to shift decimal point two steps right. 0.268 × 10 = .................... 1.205 × 10 = .................... 12.63 × 100 = .................... 256.2 × 100 = .................... 0.026 × 10 = .................... 5.125 × 100 = .................... 0.016 × 100 = .................... 0.0125 × 1000 = .................... 7.1723 × 1000 = .................... 72.65 × 10 = .................... example 2 multiplication of decimals by a whole numbers Let's learn multiplication of a decimal number by a whole number. 7.432 × 6 44.592 Multiplication of Decimals class Assignment multiply: • Perform the multiplication as if we are multiplying the two whole numbers. • Put the decimal point in the product to get as many decimal places in the multiplicand.
Oasis School Mathematics Book-5 139 multiplication of decimal by another decimals Let's learn the multiplication of two decimal numbers with the help of given example. Multiply: 9.85 × 4.6 Solution: 9.85 × 4.6 5910 39400 45.310 • Perform the multiplication as if we are multiplying two whole numbers. • Put the decimal point in the product to get as many decimal places in the product as there are in multiplicand and multiplier altogether. example 3 One kg of apples costs Rs 45.25. What is the cost of 9 kg of apples? Solution: Cost of 1 kg apples = Rs 45.25 Cost of 9 kg apples = Rs 45.25 × 9 Now, \ Cost of 9 kg of apples = Rs 407.25. 45.25 × 9 407.25 2. multiply: a. 0.7 × 5 b. 0.8 × 4 c. 2.6 × 3 d. 3.5 × 4 e. 4.7 × 5 f. 0.821 × 6 g. 1.372 × 7 h. 3.824 × 8 i. 4.721 × 9 j. 14.82 × 7 k. 6.52 × 12 l. 8.16 × 18 1. multiply: a. 0.36 × 10 b. 0.314 × 10 c. 0.014 × 10 d. 5.12 × 10 e. 6.37 × 10 f. 3.074 × 10 g. 0.367 × 100 h. 0.1082 × 100 i. 5.172 × 100 Exercise 6.5
Oasis School Mathematics Book-5 140 6. Find the area of given rectangles: 5.6 cm 4.5 cm 2.5 cm 3 cm a. b. Division of decimals by 10, 100 and 1000 We already know that, 2 ÷ 10 = 2 10 = 0.2 (two - tenths) 3 ÷ 10 = 3 10 = 0.3 (three- tenths) 5 ÷ 100 = 5 100 = 0.05 (five - hundredths) 12 ÷ 100 = 12 100 = 0.12 (twelve - hundredths) Shift decimal point one step left. Shift decimal point two steps left. 3 . multiply: a. 0.2 × 0.5 b. 1.2 × 0.4 c. 2.4 × 0.6 d. 1.8 × 0.8 e. 5.6 × 0.3 f. 3.4 × 0.25 g. 5.8 × 0.16 h. 3.957 × 0.9 4. a. If 1 kg of sugar costs Rs 55.35, what is the cost of 10 kg of sugar? b. If a bag contains 45.63 kg of rice, how much rice is contained in 100 such bags? 5. a. The cost of 1 m cloth is Rs 150.65. What is the cost of 9 m cloth? b. The cost of 1 kg of rice is Rs. 45.5. What is the cost of 0.3 kg of rice? Answers 1. Consult your teacher. 2. a) 0.35 b) 0.32 c) 7.8 d) 14 e) 23.5 f) 4.962 g) 9.604 h) 30.592 i) 42.489 j) 103.74 k) 78.24 l) 146.88 3. a) 0.01 b) 0.48 c) 1.44 d) 1.44 e) 1.68 f) 0.85 g) 0.928 h) 3.5775 4. a) Rs. 553.5 b) 4563 kg 5. a) Rs. 1355.85 b) 13.65 6. a) 16.8cm2 b) 11.25cm2 Division of Decimals
Oasis School Mathematics Book-5 141 Division of decimals by a whole number Let's learn the division of a decimal number by a whole number, Divide 12.645 by 5 Solution: \ 12.645 ÷ 5 = 2.529 example 1 4.543 ÷ 10 = 0.4543 36.18 ÷ 10 = 3.618 23.16 ÷ 100 = 0.2316 5614.34 ÷ 1000 = 5.61434 While dividing a number by 10, shift decimal point one step left. While dividing a number by 100, shift decimal point two steps left. While dividing a number by 1000, shift decimal point three steps left. 5 ) 12.645 ( 2.529 - 10 26 - 25 14 - 10 45 - 45 0 Division of a decimal number by another decimal number Let's learn to divide a decimal number by another decimal number. \ 52.2 ÷ 9 = 5.8 example 2 Divide: 5.22 ÷ 0.9 Here, 5.22 0.9 = 5.22 × 10 0.9 × 10 = 52.2 9 Now, 9 ) 52.2 ( 5.8 - 45 72 - 72 0 • Make divisor a whole number multiplying both numerator and denominator by appropriate number. • Divide as in the division of decimal number by a whole number. Division of the decimal number by a whole number is same as the division of a whole number by a whole number. Just we keep decimal after dividing the whole number.
Oasis School Mathematics Book-5 142 1. Divide: a. 16 ÷ 10 b. 523 ÷ 10 c. 23.16 ÷ 10 d. 628.24 ÷ 10 e. 738.06 ÷10 f. 18 ÷ 100 g. 726 ÷ 100 h. 57.68 ÷ 100 i. 723.84 ÷ 100 j.882.57 ÷ 100 k. 7.62 ÷ 100 l. 5.632 ÷ 100 m. 0.8234 ÷ 100 n. 28 ÷ 1000 o. 15.3 ÷ 1000 p. 17.82 ÷ 1000 q. 1.6543 ÷ 1000 r. 0.25 ÷ 1000 s. 235.894 ÷ 1000 t. 573.87 ÷ 1000 2. Divide: a. 0.42 ÷ 2 b. 0.45 ÷ 9 c. 0.56 ÷ 7 d. 1.26 ÷ 2 e. 8.42 ÷ 2 f. 1.255 ÷ 5 g. 0.728 ÷ 8 h. 13.2 ÷ 12 3. Divide: a. 5.1 ÷ 0.3 b. 1.25 ÷ 2.5 c. 0.216 ÷ 0.6 d. 8.64 ÷ 0.24 e. 3.35 ÷ 0.05 f. 7.385 ÷ 3.5 g. 57.6 ÷ 1.5 h. 0.765 ÷ 0.17 4. a. A rope of 3.92 m is cut into 4 equal parts. What is the length of each part? b. The cost of 5 pens is Rs 62.75. What is the cost of a pen? c. How many pieces of wire each of 3.5 cm can be cut from a wire of 17.5 cm? Exercise 6.6 Answers 1. Consult your teacher 2. a) 0.21 b) 0.05 c) 0.08 d) 0.63 e) 4.21 f) 0.251 g) 0.091 h) 1.1 3. a) 17 b) 0.5 c) 0.36 d) 36 e) 67 f) 2.11 g) 38.4 h) 4.5 4. a) 0.98 b) 12.55 c. 5
Oasis School Mathematics Book-5 143 Percent is composed of two words per and cent. Per means for every and cent means out of hundred. So percent means out of hundred. The symbol of percent is %. Discuss the following questions in your classroom. • How to represent the statement 20 out of100? • What is the meaning of 30 100 ? • What is the decimal value of 40 100 ? • What are the fractions of 0.6 and 0.75? For every Hundred Jubeda got 90 marks out of 100 full marks. The symbol of percent is % or p.c. Shankar got 85 marks out of 100 full marks. I got 90% marks I got 85% marks Percentage UNIT 7 Review
Oasis School Mathematics Book-5 144 1. Find the fraction and percentage of shaded part of the given figures having 100 squares: a. b. Fraction = Fraction = Percentage = Percentage = class Assignment 3. express the following fractions in percentage: a. 3 100 = b. 15 100 = c. 60 100 = d. 75 100 = e. 86 100 = 4. express the following percentage into fraction. a. 25% = b. 40% = c. 75% = d. 90% = 2. a. 65 students out of 100 are boys. What percentage of students are boys? b. Pooja scored 85 out of 100 full marks. What percent did she score? 82 100 25 100 60 100 = 82%, 82 100 75 100 52% = , 75% = , etc. Similarly, = 25%, = 60%, relation of Percent and Fraction In the given figure, a square is divided into 100 equal parts. Fraction represented by the shaded parts = 18 100 Here, 18 boxes out of 100 are shaded. So, percent of shaded part = 18%. Fraction represented by non shaded part = 82 100 Here, 82 boxes out of 100 are non shaded. So, percent of non-shaded part = 82%.
Oasis School Mathematics Book-5 145 relation of Percent with Decimal As we know that 9 100 = 0.09, 10 100 = 0.1, 15 100 = 0.15, 76 100 = 0.76 Again, we know that 86 100 = 1%, so we get the result 1% = 1 100 = 0.01 Similarly, 5% = 5 100 = 0.05 20% = 20 100 = 0.2 45% = 45 100 = 0.45 Conversely, 0.01 = 1 100 = 1% 0.50 = 50 100 = 50% 0.74 = 74 100 = 74% Steps: • Remove the symbol %. • Divide it by 100. • Convert the fraction into decimal. 1. convert the following percentage into decimal. 2. convert the following decimal into percentage. class Assignment • Convert decimal into fraction. • Convert fraction into percentage. a. 12% a. 0.03 = c. 0.32 = b. 0.15 = d. 0.86 = b. 60% c. 8% d. 85%
Oasis School Mathematics Book-5 146 example 2 Himal scored 20 out of 25 full marks. Find the percent of his marks. Solution: Marks obtained by Himal = 20 out of 25 His percentage = 20 25 4 5 × 100% 20 = 4 × 20% = 80% \ He scored 80% marks. conversion of fraction into percentage (if the denominator's other than 100) To convert fraction into percentage, follow the following steps: example 1 2 5 = 2 5 × 100% = 40% 3 10 = 3 10 × 100% = 30% • Multiply the fraction by 100. • Put the symbol %. Alternative method Marks obtained by Himal = 20 out of 25. \ He scored 80% marks. Now, 20 25 = 20 × 4 25 × 4 = 80 100 = 80% 3. express the following fractions in percentage: a. 3 10 b. 2 5 c. 3 4 d. 4 20 e. 3 50 1. express the following percentage in fraction: a. 20% b. 25% c. 30% d. 50% e. 35% f. 65% g. 40% h. 55% i. 75% j. 98% 2. express the following percentage in decimal: a. 25% b. 5% c. 50% d. 56% e. 72% Exercise 7.1 • Convert denominator to 100. • Convert fraction into percent. Alternative method 2 5 3 10 2 5 3 10 = = × = = × = 40% = 40% 40 100 20 20 30 100 10 10
Oasis School Mathematics Book-5 147 5 . Write the fraction of the given shaded figures and convert them into percentage: a. b. c. 6. marks obtained by 5 students of class V out of full marks 25 are given below. express their marks in percentage. Sumi : 18 Ruby : 22 Ranjan : 15 Asmin : 17 Pratik : 13 Answers Consult your teacher. f. 7 10 g. 19 20 h. 18 50 i. 7 20 j. 19 25 4. express the following decimal in percentage: a. 0.03 b. 0.26 c. 0.85 d. 0.87 e. 0.92 Project Work Collect the marks obtained by the students of your class out of hundred full marks in an examination. Show the marks in fraction, decimal and percentage. to find the value of percentage of the given quantity To find the value of the percentage of given quantity, we follow the following steps. example 1 Find the value of 15% of 300. Solution: 15% of 300 = 15 100 × 300 = 15 × 3 = 45 Steps: • Express the given percentage in fraction. • Multiply the fraction by given quantity.
Oasis School Mathematics Book-5 148 1. Find the value of: a. 20% of 180 b. 5% of 120 c. 15% of 600 d. 30% of 300 e. 40% of 240 f. 25% of 700 g. 60% of 200 h. 45% of 400 2. a. In a class, there are 40 students. If 10% students are absent, find the number of absent students. b. Out of Rs. 120, a boy had spent 40%. How much money did he spend? c. There are 900 students in a school. If 45% of them are girls, find the number of girls. d. A man earns Rs. 4000 in a month and he spends 20% of his income on food. Find how much money does he spend on food. Exercise 7.2 Answers 1. a. 36 b. 6 c. 90 d. 90 e. 96 f. 175 g. 120 h. 180 2. a. 4 b. 48 c. 405 d. 800 example 2 Out of 120 students in a class, 45% students are boys. Find the number of girls. Solution: Total students = 120 Percentage of boys = 45% Number of boys = 45 100 9 × 1206 = 54 Number of girls = 120 – 54 = 66 20 Project Work Collect the information from your guardians: • What is the monthly income of your family? • What is the approximate monthly expenditure in different title? • Calculate the expenditure in percentage.
Oasis School Mathematics Book-5 149 Choose the correct alternatives. 1. The fraction 7 3 is a (i) proper fraction (ii) improper fraction (iii) like fraction 2. The mixed number 2 3 7 is equal to (i) 23 7 (ii) 17 7 (iii) 7 6 3. The fractions having same denominators are called (i) equal fractions (ii) unlike fractions (iii) like fractions 4. 5 7 + 2 7 – 4 7 is equal to (i) 11 7 (ii) 3 7 (iii) 7 7 5. Fraction 1 10 is not equal to (i) 0.1 (ii) 10% (iii) 0.01 6. 1.35 is not equal to (i) 1 35 100 (ii) 1 7 10 (iii) 1 7 20 7. Above shaded figure represents the fraction. (i) 2 2 3 (ii) 3 2 3 (iii) 2 1 3 8. The meaning the number o.6 is same as the number (i) 0.60 (ii) 0.06 (iii) 6 9. 0.03 is equal to (i) 30% (ii) 3% (iii) 300% 10. Which of the following is not equal to 7 10 ? (i) 0.7 (ii) 70% (iii) 0.07 11. 20% of 500 is equal to (i) 10 (ii) 100 (iii) 200 12. Percentage of shaded part in the given figure is (i) 60% (ii) 40% (iii) 20%
Oasis School Mathematics Book-5 150 Full marks – 30 Attempt all the questions. 1. Covert the following improper fraction into mixed number 3 a. 26 5 b. 17 3 c. 46 9 2. Convert the following mixed number into improper fractions. 3 a. 5 2 3 b. 6 1 4 c. 5 2 7 3. Simplify: 4 a. 2 7 + 5 7 – 3 7 b. 2 2 9 + 5 1 9 – 3 1 9 4. Covert the following fraction into decimal. 3 a. 3 10 b. 7 10 c/ 15 10 5. Convert the following decimal into fraction and write in percentage. 3 a. 0.5 b. 0.6 c. 0.58 6. Convert the following fraction into percentage. 4 a. 56 100 b. 3 20 c. 12 20 d. 5 10 7. Add. 4 a. 0.65 + 5.86 b. 14.6 – 3.84 8. a. Among 25 students in a class, 16 students are present. Write the present students in fraction, convert the denominator into 100 and write the percentage of present students. 2 b. Out of 50 students in class, 10% students are present. What number of students are absent? 2 Unit Test