Answers (1) A) 36 = - - = Now, we can divide the numbers as shown below. For example : 4 = 2, 2 4 = -2, -2-4 = -2, 2-4 = 2.
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1 Answers (1) A) 36 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: = (62) (98) = 36
2 B) 279 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: = (54) + (43) + (99) 83 =
3 (2) 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 116, which is even. Therefore, the sum of the given series is 0. (3) A) 5289 The sum of (153) and (859) : = (153) + (859) = = 706 Now, subtract (706) from (5995). = (5995) (706) = = 5289 Therefore, the answer is 5289.
4 B) The sum of (3571) and (4955) : = (3571) + (4955) = = 8526 Now, subtract (8526) from (8812). = (8812) (8526) = = Therefore, the answer is (4) A) We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of = B) We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of = C) We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of = 32555
5 D) We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of = E) We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of = F) 1 We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of 1 = 1 (5) (a 19) It is given that the value of 'a' is less than 19. So, the value of a 19 will be negative. Hence, the absolute value of a 19 is (a 19).
6 (6) 7 On looking at the question carefully, we notice that a is the predecessor of b. Therefore, a = b 1 Now, a b + 8 = b 1 b [Since a = b 1] = = 7 Therefore, the value of a b + 8 = 7. (7) 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 =.
7 (8) c. Negative integer 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) A) 17 We know that the absolute value (or modulus) of an integer x is x's numerical value without any regards to the mathematical sign placed before it. Therefore, the absolute value of 17 = 17.
8 B) 17 We know that the absolute value (or modulus) of an integer x is x's numerical value without any regards to the mathematical sign placed before it. Therefore, the absolute value of 17 = 17. C) 19 We know that the absolute value (or modulus) of an integer x is x's numerical value without any regards to the mathematical sign placed before it. Therefore, the absolute value of 19 = 19. D) 8 We know that the absolute value (or modulus) of an integer x is x's numerical value without any regards to the mathematical sign placed before it. Therefore, the absolute value of 8 = 8. E) 8 We know that the absolute value (or modulus) of an integer x is x's numerical value without any regards to the mathematical sign placed before it. Therefore, the absolute value of 8 = 8.
9 F) 6 We know that the absolute value (or modulus) of an integer x is x's numerical value without any regards to the mathematical sign placed before it. Therefore, the absolute value of 6 = 6. (10) A) 7 In case of negative numbers, the value of more negative number is smaller as compare to the less negative number or positive number,therefore 7 > 1 Now we can say that the larger number in pair 7, 1 is 7 B) 9 In case of negative numbers, the value of more negative number is smaller as compare to the less negative number or positive number,therefore 9 > 19 Now we can say that the larger number in pair 19, 9 is 19 C) 27 If you look at the pair 27, 6 carefully, you will notice that 27 > 6 Therefore you can say that the larger number in pair 27, 6 is 27
10 D) 23 If you look at the pair 6, 23 carefully, you will notice that 23 > 6 Therefore you can say that the larger number in pair 6, 23 is 23 E) 16 In case of negative numbers, the value of more negative number is smaller as compare to the less negative number or positive number,therefore 16 > 19 Now we can say that the larger number in pair 16, 19 is 16 F) 19 In case of negative numbers, the value of more negative number is smaller as compare to the less negative number or positive number,therefore 19 > 1 Now we can say that the larger number in pair 19, 1 is 19
11 (11) A) 9 a) We know that the division of a positive number by a negative number results in a negative number. For example : 4/(2) = (2) b) Similarly, the division of a negative number by a positive number results in a negative number. For example : (4)/2 = (2) c) Division of a negative number by a negative number results in a positive number. For example : (4)/(2) = 2 Let us divide 45 by 5, Dividend Divisor 5 ) 4 5 ( 9 Quotient 4 5 Remainder 0 Therefore, (45) (5) = 9
12 B) 30 a) We know that the division of a positive number by a negative number results in a negative number. For example : 4/(2) = (2) b) Similarly, the division of a negative number by a positive number results in a negative number. For example : (4)/2 = (2) c) Division of a negative number by a negative number results in a positive number. For example : (4)/(2) = 2 Let us divide 270 by 9, Dividend Divisor 9 ) ( 30 Quotient Remainder 0 Therefore, (270) (9) = 30
13 (12) A) negative a) We know that the multiplication of two positive integers results in a positive integer. For example : 4 5 = 20 b) Multiplication of two negative integers results in a positive integer. For example : ( 4) ( 5) = 20 c) Multiplication of two integers, one negative and other positive, results in a negative integer. For example : ( 4) 5 = ( 20) We must remember that if the number of negative integers are even, then the product of the integers will be positive. Otherwise, the product of the negative integers remains negative. So, the multiplication of 11 negative integers and 3 positive integers = (Multiplication of 11 negative integers) (Multiplication of 3 positive integers) = (Multiplication of 10 negative integers) (Negative integer) (Multiplication of 3 positive integers) = (Positive number) (Negative number) (Positive number) = Negative integer
14 B) negative a) We know that the multiplication of two positive integers results in a positive integer. For example : 4 5 = 20 b) Multiplication of two negative integers results in a positive integer. For example : ( 4) ( 5) = 20 c) Multiplication of two integers, one negative and other positive, results in a negative integer. For example : ( 4) 5 = ( 20) We must remember that if the number of negative integers are even, then the product of the integers will be positive. Otherwise, the product of the negative integers remains negative. So, the multiplication of 27 negative integers and 5 positive integers = (Multiplication of 27 negative integers) (Multiplication of 5 positive integers) = (Multiplication of 26 negative integers) (Negative integer) (Multiplication of 5 positive integers) = (Positive number) (Negative number) (Positive number) = Negative integer (13) Commutative We have been given the expression : A + B = B + A This represents the fact that changing the order of the addends (numbers being added) does not change the result of the addition,i.e., whether we add B to A or A to B, we get the same answer. For example : is same as as both are equal to 5. Such a property of an arithmetic operation, where the order of operands (numbers taking part in the arithmetic operation) does not change the results (answer) of the operation is called the commutative property. Addition operation satisfies the commutative property. Multiplication is another such operation which satisfies the property. For example : 2 3 = 3 2 Step 4 Therefore, we can say that A + B = B + A represents the commutative property of addition.
15 (14) False We know that the 'Absolute Value' is the value of the number itself without any regards to the mathematical sign placed before it. Therefore, this value is always a positive number. For positive numbers, the absolute value is same as the number itself. e.g. 5 = 5. For negative numbers, the absolute value is reverse of the number. e.g. 5 = 5. We can see that the absolute value of a number is either equal to the number (for positive numbers), or is larger than the number (for negative numbers). Hence the given statement "The absolute value of an integer is greater than the integer" is false. (15) True Let us assume that n is a positive number. Therefore, its negative = n. The sum of n and n = n + (n) = n n = 0 From the above calculation, we find that the sum of a number and its negative is zero. Hence, the answer is true.
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