Grade 6 Integers. Answer the questions. Choose correct answer(s) from the given choices. For more such worksheets visit

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ID : cn6integers [1] Grade 6 Integers For more such worksheets visit www.edugain.

1 ID : cn6integers [1] Grade 6 Integers For more such worksheets visit 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) and B) and 7242 C) and 9577 D) and (3) Find the sum of the following series if the number of terms is (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) from B) from C) from D) from E) from F) from (6) Simplify : A) B) (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

2 (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 ) = B) = 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 ( All Rights Reserved Many more such worksheets can be generated at

3 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) According to the question, we have to find the sum of and Now, (50556) = = Therefore, sum of and = B) According to the question, we have to find the sum of and Now, (7242) = = Therefore, sum of and 7242 = 14516

4 C) ID : cn6integers [4] According to the question, we have to find the sum of and Now, (9577) = = Therefore, sum of and 9577 = D) According to the question, we have to find the sum of and Now, = Therefore, sum of and = (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.

5 (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.

6 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) Subtracting from = = B) Subtracting from = (51289) = = C) Subtracting from = = D) Subtracting from = (35684) = = E) Subtracting from = (84193) = =

7 F) ID : cn6integers [7] Subtracting from = (20652) = = (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, = 2, = 2. Now, can be simplified as: = (38) (53) = 23

8 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, = 2, = 2. Now, can be simplified as: = (73) (41) + 78 = 46

9 (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 = = 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 = = 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 = = 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 = = 1

10 (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 =.

11 ID : cn6integers [11] (10) A) 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 ) = 77 ( 8 ) = = = Therefore, the value of 11 ( 7 ) ( 8 ) is

12 ID : cn6integers [12] B) 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 , we have to multiply the two numbers first. Then, we will multiply the result with the next number and so on : = = = = Therefore, the value of is

13 (11) True ID : cn6integers [13] Let a = 4, b = 2.(Since a and b are natural numbers and a > b.) So, a b = = 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.

14 (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.

15 (13) False ID : cn6integers [15] Let a = 2, b = 4.(Since a and b are natural numbers and a < b.) So, a b = = 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.

16 (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 = = = 12 Step 5 Since, 6 is not equal to 12. Hence, the given statement is false.

Unit 2: Accentuate the Negative Name:

Unit 2: Accentuate the Negative Name: 1.1 Using Positive & Negative Numbers Number Sentence A mathematical statement that gives the relationship between two expressions that are composed of numbers and