Grade 6 Natural and Whole Numbers

Transcription

1 ID : ae-6-natural-and-whole-numbers [1] Grade 6 Natural and Whole Numbers For more such worksheets visit Answer the questions (1) Find the successor of the given number: (2) If we write down all the numbers from 1 to 176 (including 1 and 176), how many digits will we write down? (3) Two brands of chocolates are available in the packs of 49 and 28, respectively. Adiba wants to buy the same number of chocolates of both the brands. What is the least number of packs of each brand of chocolates that she will need to buy? (4) Along a highway, there are electric poles on one side of the highway and telegraph poles on the other side. The electric poles are separated by 10 m and the telegraph poles are separated by 60 m. If an electric and a telegraph pole are both present at the point where the highway begins, after how much distance along the highway will they both be in front of each other again? (5) Ahmed ordered 13 cartons of erasers. Each carton holds 30 boxes and each box has 39 erasers. How many erasers did Ahmed order altogether? (6) Habib has two sheets of cloth. One sheet is 132 cm wide and the other sheet is 110 cm wide. He wants to divide the sheets into strips of equal width without wasting any cloth such that they are as wide as possible. How wide should he cut the strips? (7) A set of Biology, Chemistry and Physics books needs to be divided into multiple stacks of the same and highest possible height such that each stack contains books of only one subject. The number of Biology books is 666, that of Chemistry books is 396, and that of Physics books is 738. Assuming that all the books have uniform thickness, find the number of stacks of Physics books. (8) A lighthouse has two lights - one that flashes every 5 minutes and another that flashes every minutes. Suppose the lights flash together at noon. What is the first time after 1 PM when they will flash together again? (9) The average of Imam's marks in 4 subjects is 77. He got 57 marks in the 5 th subject. What is his average in all 5 subjects? Choose correct answer(s) from the given choices (10) The product of two 2-digit numbers is If the product of their units digits is 40 and that of their tens digits is 18, then the two numbers are : a. 29, 85 b. 25, 98 c. 28, 95 d. 89, 52

2 ID : ae-6-natural-and-whole-numbers [2] (11) (62 + 9) + 19 = 19 + (9 + 62) is an example of a. Closure Property b. Commutative Property c. Associative Property d. Distributive Property Fill in the blanks (12) The least common multiple (LCM) of 24 and 18 is. (13) = 96 Check True/False (14) Every whole number has a successor. True False (15) There is a whole number which does not change the value of any other whole number it is added to. True False 2017 Edugain ( All Rights Reserved Many more such worksheets can be generated at

3 Answers ID : ae-6-natural-and-whole-numbers [3] (1) We know that the successor of a given number is the one coming after it. Therefore, the successor of is = (2) 420 We need to find the total number of digits in all the numbers from 1 to 176. The range of numbers from 1 to 176 can be broken into numbers with 1, 2, and 3 digits, respectively: 1-digit numbers: 1 to 9: A total of = 9 numbers. Number of digits = 9 1 = 9 2-digit numbers: 10 to 99: A total of = 90 numbers. Number of digits = 90 2 = digit numbers: 100 to 176: A total of numbers = 77 numbers. Number of digits = 77 3 = 231 Total number of digits = Number of digits in the 1-digit numbers + Number of digits in the 2-digit numbers + Number of digits in the 3-digit numbers = = 420 Thus, the number of digits we would have written down if we wrote down all the numbers from 1 to 176 is 420.

4 (3) 4 packs of the first brand, 7 packs of the second brand. ID : ae-6-natural-and-whole-numbers [4] Adiba wants to buy equal number of chocolates of two brands, but she needs to buy them in the multiples of 49 and 28, respectively. Also, she wants to buy the least number of packs. Thus, the number of chocolates of each brand she needs to buy = L.C.M of 49 and 28. L.C.M of 49 and 28 = 196. Number of packs of the first brand Adiba needs to buy = Number of chocolates of the first brand Number of chocolates in one pack of the first brand = = 4 Number of boxes of the second brand Adiba needs to buy= Number of chocolates of the second brand Number of chocolates in one pack of the second brand = = 7 Hence, she needs to buy 4 packs of the first brand and 7 packs of the second brand. (4) 60 m Since an electric pole is there at every 10 m, it will be present at every multiple of 10. Similarly, a telegraph pole is there at every 60 m. It will thus be present at every multiple of 60. Now, the distance at which both types of poles will be present again, should be a multiple of both 10 and 60. Therefore, we need to find the Least Common Multiple (LCM) of 10 and 60 in order to find such a distance. LCM of 10 and 60 = 60 m Step 5 Therefore, both types of poles will be together again after a distance of 60 m.

5 (5) ID : ae-6-natural-and-whole-numbers [5] Each carton holds 30 boxes. He ordered 13 cartons. So, the number of boxes he ordered = = 390 boxes. Each box contains 39 erasers. He ordered 390 boxes. So, the number of erasers Ahmed ordered = = (6) 22 cm Let the width of strip be x cm. Since, no cloth should be wasted, 132 cm should be divisible by x cm. Similarly, 110 cm should be divisible by x cm. Also, we should remember that x has to be as large as possible. Therefore, x should be the HCF of 132 and 110. Hence, x = HCF(132, 110) = 22 cm. (7) 41 The number of Biology books is 666, the number of Chemistry books is 396 and the number of Physics books is 738. Since, all the books have uniform thickness and the height of each stack needs to be the same, the number of books each stack should contain will be equal to the H.C.F of 666, 396, and 738. All the prime factors of 666 : is a factor of is a factor of is a factor of is a factor of 37 1 Thus, 666 =

6 ID : ae-6-natural-and-whole-numbers [6] All the prime factors of 396 : is a factor of is a factor of is a factor of is a factor of is a factor of 11 1 Thus, 396 = Step 5 All the prime factors of 738 : is a factor of is a factor of is a factor of is a factor of 41 1 Thus, 738 = Step 6 Hence, the H.C.F of 666, 396, and 738 = = 18. Step 7 Now, we know that each stack of books will contain 18 books. Total number of Physics books = Therefore, the number of stacks of Physics books = = (8) 1:05 PM The first light flashes every 5 minutes and the other light flashes every minutes. Once the two lights flash together, the amount of time after which the two lights will flash together again is equal to the L.C.M of 5 minutes and minutes.

7 ID : ae-6-natural-and-whole-numbers [7] Before we calculate the L.C.M of 5 minutes and minutes, let us convert both the time periods into seconds. Since, 1 minute = 60 seconds, 5 minutes = 5 60 = 300 seconds, and minutes = = 150 seconds. Let us now calculate the L.C.M of 300 and 150. All the prime factors of 300: is a factor of is a factor of is a factor of is a factor of is a factor of 5 1 Thus, 300 = All the prime factors of 150: is a factor of is a factor of is a factor of is a factor of 5 1 Thus, 150 = Step 5 The L.C.M of 300 and 150 = = 300. Step seconds in minutes = minutes = 5 minutes. Step 7 Now, we know that the two lights flash together every 5 minutes. We have been told that the two lights flash together at noon. This means that times when they flash together again are 12:5, 12:10, 12:15, 12:20,... 1:05,... Therefore, the time after 1 PM when the two lights will flash together again = 1:05 PM.

8 (9) 73 ID : ae-6-natural-and-whole-numbers [8] We know that the average of marks in all the subjects = Sum of the marks in all the subjects Total number of subjects. The average of Imam's marks in 4 subjects = Sum of the marks in 4 subjects = 4 77 = 308 Sum of the marks in 4 subjects 4 = 77 Since, Imam got 57 marks in the 5 th subject, the average of Imam's marks in 5 subjects = Sum of the marks in 5 subjects 5 = Sum of the marks in 4 subjects + Marks in the 5th subject 5 = = = 73 Therefore, Imam's average in all the 5 subjects is 73.

9 (10) c. 28, 95 ID : ae-6-natural-and-whole-numbers [9] Let us assume that the two two-digit numbers are, 10 x 1 + y1 and 10 x 2 + y2, where y1 and y2 are their units digits and, x1 and x2 are their tens digits. Given : y1 y2 = (1) x1 x2 = (2) (10 x 1 + y1) (10 x 2 + y2) = (3) Now, we notice that there are four variables and only three equations have been specified. We know that four variables cannot be uniquely determined from three equations. Therefore, we will check the given options to find which of them satisfies the above three equations. On checking all the options carefully, we find that the option 28, 95 satisfies all the three equations. 8 5 = = = 2660 Step 5 Therefore, we can say that the two numbers are 28, 95. (11) c. Associative Property The word "associative" comes from "associate" or "group". The Associative Property is the rule that refers to grouping. For addition, the rule is "(a + b) + c = a + (b + c)". This means, "(62 + 9) + 19 = 19 + (9 + 62)" is an example of the Associative Property.

10 ID : ae-6-natural-and-whole-numbers [10] (12) 72 Let us find the LCM of 24 and 18: 2 24, , 9 2 6, 9 3 3, 9 3 1, 3 1, 1 The LCM is = = 72 (13) 82 If we multiply 82 with 96 or multiply 96 with 82, the result is the same. This is called the Commutative Law of multiplication and 96 82, both are equal to This means = Therefore, the answer is 82. (14) True We know that whole numbers are the numbers that are positive integers including '0' : 0, 1, 2, 3... So, if we have a whole number x, we can always find its successor by adding 1 to it. That is, if x is a whole number, x+1 is another whole number. Therefore, the answer is true.

11 (15) True ID : ae-6-natural-and-whole-numbers [11] We know that whole numbers are the numbers 0, 1, 2, 3... If we add the whole number '0' to any other whole number, we get that whole number itself as the sum. For example: = = 1 Hence, the answer is true.