ID : cn6integers [1] Grade 6 Integers For more such worksheets visit www.edugain.com Answer the questions (1) If a and b are two integers such that a is the predecessor of b, then what is the value of a b 11? (2) Find the sum of the following integers: A) 21517 and 50556 B) 21758 and 7242 C) 79592 and 9577 D) 43157 and 93694 (3) Find the sum of the following series if the number of terms is 146. 8 + (8) + 8 + (8) + 8 + (8) +... (4) Find the predecessor of each of the following integers: A) 12 = B) 65 = C) 73 = D) 35 = E) 14 = F) 0 = (5) Subtract : A) 94951 from 15463 B) 51289 from 29989 C) 99775 from 62607 D) 35684 from 94984 E) 84193 from 22636 F) 20652 from 70318 (6) Simplify : A) 1634 43 + 2720 40 + 3763 71 B) 2993 41 2624 64 + 5538 71 (7) Find the number of integers that lie between: A) 2 and 7 B) 5 and 7 C) 4 and 3 D) 2 and 0 Choose correct answer(s) from the given choices (8) The sum of any two negative integers will be : a. Positive, if the first number is larger b. Negative, if the first number is larger c. Positive integer d. Negative integer
(9) Choose the correct operator. 5 5 a. < b. > ID : cn6integers [2] c. = d. None of these Fill in the blanks (10) Find the value of the following : A) 11 ( 7 ) ( 8 ) 18 18 = B) 8 19 2 16 16 = Check True/False (11) a b = a b, where a and b are natural numbers and a > b. True False (12) Every negative number is greater than every natural number. True False (13) a b = a b, where a and b are natural numbers and a < b. True False (14) The additive inverse of a negative number is positive. True False (15) a + b = a + b, where a and b are integers and a > b. True False 2017 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : cn6integers [3] (1) 12 On looking at the question carefully, we notice that a is the predecessor of b. Therefore, a = b 1 Now, a b 11 = b 1 b 11...[Since a = b 1] = 1 11 = 12 Therefore, the value of a b 11 = 12. (2) A) 72073 According to the question, we have to find the sum of 21517 and 50556. Now, 21517 + (50556) = 21517 50556 = 72073 Therefore, sum of 21517 and 50556 = 72073 B) 14516 According to the question, we have to find the sum of 21758 and 7242. Now, 21758 + (7242) = 21758 7242 = 14516 Therefore, sum of 21758 and 7242 = 14516
C) 70015 ID : cn6integers [4] According to the question, we have to find the sum of 79592 and 9577. Now, 79592 + (9577) = 79592 9577 = 70015 Therefore, sum of 79592 and 9577 = 70015 D) 50537 According to the question, we have to find the sum of 43157 and 93694. Now, 43157 + 93694 = 50537 Therefore, sum of 43157 and 93694 = 50537 (3) 0 On carefully reading the question, we find that the given series is composed of alternate positive and negative terms. Therefore, if the number of terms are even, then there are equal number of positive and negative terms. Consequently, the sum of the series will be zero. Similarly, if the number of terms are odd, then the positive and negative terms are present in an unequal proportion. Consequently, the sum of the series is equal to the first term of the series. The number of terms in the given series is 146, which is even. Therefore, the sum of the given series is 0.
(4) A) 13 ID : cn6integers [5] All the positive numbers, negative numbers and zero are integers with the exception of fractions. So, we can write all the integers in the increasing order as: Integers =..., 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5,... Hence, the predecessor of 12 = 12 1 = 13. B) 66 All the positive numbers, negative numbers and zero are integers with the exception of fractions. So, we can write all the integers in the increasing order as: Integers =..., 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5,... Hence, the predecessor of 65 = 65 1 = 66. C) 74 All the positive numbers, negative numbers and zero are integers with the exception of fractions. So, we can write all the integers in the increasing order as: Integers =..., 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5,... Hence, the predecessor of 73 = 73 1 = 74. D) 36 All the positive numbers, negative numbers and zero are integers with the exception of fractions. So, we can write all the integers in the increasing order as: Integers =..., 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5,... Hence, the predecessor of 35 = 35 1 = 36.
E) 15 ID : cn6integers [6] All the positive numbers, negative numbers and zero are integers with the exception of fractions. So, we can write all the integers in the increasing order as: Integers =..., 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5,... Hence, the predecessor of 14 = 14 1 = 15. F) 1 All the positive numbers, negative numbers and zero are integers with the exception of fractions. So, we can write all the integers in the increasing order as: Integers =..., 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5,... Hence, the predecessor of 0 = 0 1 = 1. (5) A) 110414 Subtracting 94951 from 15463 = 15463 94951 = 110414 B) 21300 Subtracting 51289 from 29989 = 29989 (51289) = 29989 + 51289 = 21300 C) 162382 Subtracting 99775 from 62607 = 62607 99775 = 162382 D) 59300 Subtracting 35684 from 94984 = 94984 (35684) = 94984 + 35684 = 59300 E) 106829 Subtracting 84193 from 22636 = 22636 (84193) = 22636 + 84193 = 106829
F) 49666 ID : cn6integers [7] Subtracting 20652 from 70318 = 70318 (20652) = 70318 + 20652 = 49666 (6) A) 23 We can divide the two numbers by using the following steps : 1. Firstly, we will divide the mathematical signs of the numbers. We place a negative sign before the negative numbers and leave the positive numbers without any sign. We can divide the signs as shown below : + = + + + = = + 2. Now, we can divide the numbers as shown below. For example : 4 = 2, 2 4 2 4 2 4 2 = 2, = 2, = 2. Now, 1634 43 + 2720 40 + 3763 71 can be simplified as: 1634 43 + 2720 40 + 3763 71 = (38) + 68 + (53) = 23
B) 46 ID : cn6integers [8] We can divide the two numbers by using the following steps : 1. Firstly, we will divide the mathematical signs of the numbers. We place a negative sign before the negative numbers and leave the positive numbers without any sign. We can divide the signs as shown below : + = + + + = = + 2. Now, we can divide the numbers as shown below. For example : 4 = 2, 2 4 2 4 2 4 2 = 2, = 2, = 2. Now, 2993 41 2624 64 + 5538 71 can be simplified as: 2993 41 2624 64 + 5538 71 = (73) (41) + 78 = 46
(7) A) 8 ID : cn6integers [9] We know that the number of integers between any two integers is equal to a number one less than the difference between the two integers. Hence, the total number of integers that lie between 2 and 7 = 7 (2) 1 = 7 + 1 = 8 B) 11 We know that the number of integers between any two integers is equal to a number one less than the difference between the two integers. Hence, the total number of integers that lie between 5 and 7 = 7 (5) 1 = 7 + 4 = 11 C) 6 We know that the number of integers between any two integers is equal to a number one less than the difference between the two integers. Hence, the total number of integers that lie between 4 and 3 = 3 (4) 1 = 3 + 3 = 6 D) 1 We know that the number of integers between any two integers is equal to a number one less than the difference between the two integers. Hence, the total number of integers that lie between 2 and 0 = 0 (2) 1 = 0 + 1 = 1
(8) d. Negative integer ID : cn6integers [10] We know that negative numbers are less than '0' in magnitude and lie on its left hand side on the number line. The number line above shows two negative numbers a = 3 and b = 1. We must remember that when we add a positive number to a negative number, it shifts to the right side on the number line. Similarly, if we add a negative number, it shifts to the left side on the number line. For example, if we add b(1) to a(3), 'a' shifts further on the left side on the number line. Step 4 Since, the sum of any two negative numbers will always lie on the left side of '0' on the number line. Hence, the sum will always be negative. (9) c. = If we look at the numbers 5 and 5, we notice that 5 is equal to 5. Therefore, we can say that the correct operator is =.
ID : cn6integers [11] (10) A) 199584 We can multiply the two numbers in the following manner : 1. First of all, we have to multiply the mathematical signs of the given numbers. We place a negative sign before the negative numbers and leave the positive numbers without any sign. We can multiply the signs as follows: + + = + + = = + 2. Now, we have to multiply the numbers. For example : 3 2 = 6, 3 (2) = (6), (3) 2 = (6), (3) (2) = 6 So, in order to solve 11 ( 7 ) ( 8 ) 18 18, we have to multiply the two numbers first. Then, we will multiply the result with the next number and so on : 11 ( 7 ) ( 8 ) 18 18 = 77 ( 8 ) 18 18 = 616 18 18 = 11088 18 = 199584 Therefore, the value of 11 ( 7 ) ( 8 ) 18 18 is 199584.
ID : cn6integers [12] B) 77824 We can multiply the two numbers in the following manner : 1. First of all, we have to multiply the mathematical signs of the given numbers. We place a negative sign before the negative numbers and leave the positive numbers without any sign. We can multiply the signs as follows: + + = + + = = + 2. Now, we have to multiply the numbers. For example : 3 2 = 6, 3 (2) = (6), (3) 2 = (6), (3) (2) = 6 So, in order to solve 8 19 2 16 16, we have to multiply the two numbers first. Then, we will multiply the result with the next number and so on : 8 19 2 16 16 = 152 2 16 16 = 304 16 16 = 4864 16 = 77824 Therefore, the value of 8 19 2 16 16 is 77824.
(11) True ID : cn6integers [13] Let a = 4, b = 2.(Since a and b are natural numbers and a > b.) So, a b = + 4 2 = 2 We know that the absolute value of a number will always be positive. Therefore, L.H.S : a b = a b (a > b) a b = 2 = 2...(1) Now, let us look at the R.H.S. a = 4 = 4 b = 2 = 2 So, a b = 4 2 = 2...(2) Step 4 Therefore, a b = a b the given statement is true.
(12) False ID : cn6integers [14] We know that if a number is on the right hand side of another number on the number line, the first number is greater than the other number. Therefore, a > b as a is on the right hand side of b. We know that the numbers 1, 2, 3, 4,.. and so on, till infinity, are called natural numbers. The following picture shows that the negative numbers are on the left hand side of '0' on the number line, while all the natural numbers are on the right hand side of '0'. We can see that all the natural numbers are greater than all the negative numbers. Hence, the given statement is false.
(13) False ID : cn6integers [15] Let a = 2, b = 4.(Since a and b are natural numbers and a < b.) So, a b = + 2 4 = 2 We know that for a negative number (e.g. x), its absolute value will be positive (i.e. x). Therefore, L.H.S : a b = 1 ( a b) a b = 2 = 2...(1) Now, let us look at the R.H.S. a = 2 = 2 b = 4 = 4 So, a b = 2 4 = 2...(2) Step 4 As, a b = 2 and a b = 2 a b a b Hence, the given statement is false. (14) True We know that the additive inverse of a number a is the number which, when added to a, yields zero. In other words, the additive inverse is the opposite of a number. Therefore, the additive inverse of a positive number is negative and that of a negative number is positive. For example, the additive inverse of 14 is 14. The additive inverse of 5 is 5. Therefore, the given statement is true.
(15) False ID : cn6integers [16] To find out whether the given statement is true or false, let us pick certain values of the integers 'a' and 'b' such that one of these is a positive integer while the other one is a negative integer. For example, let us assume that a = 9 and b = 3. So, a + b = 9 + (3) = 6 = 6. Step 4 So, a + b = 9 + 3 = 9 + 3 = 12 Step 5 Since, 6 is not equal to 12. Hence, the given statement is false.