ID : ae-7-integers [1] Grade 7 Integers For more such worksheets visit www.edugain.com Answer the questions (1) A railway company makes a profit of Dhs 1570 on per ticket of business class while loses Dhs 175 on every ticket in economy class. If the company sold 3718 tickets of business class and 41088 tickets of economy class in the month of July, what would be the total profit or loss company will make in that month. (2) Hani is in the process of making an ice cream. He has heated all the ingredients to 40 C and put them in refrigerator to freeze. If the cooling rate is 11 C per hour, what will be the temperature in freezer after 11 hours? (3) What is the absolute value of a + 9, if a is less than -9? (4) Cala made following transactions on her credit card account : Opening Balance : Dhs -7559 1) Credited Dhs 2002 2) Credited Dhs 746 3) Credited Dhs 4692 4) Debited Dhs 2512 5) Debited Dhs 126 If the starting balance on his credit card was Dhs -7559, what will be the final balance on her credit card account? (5) Find the additive inverse of each of the following integers: A) -23488 = B) 56213 = C) 86202 = D) -42053 = E) 14356 = F) 0 = (6) Find the sum of the following series if the number of terms is 163. 8 + (-8) + 8 + (-8) + 8 + (-8) +... (7) Find the sum of the following integers: A) 49086 and -57056. B) -19320 and 86278. C) 53622 and -35240. D) 97168 and -96304. E) -18153 and 69317. F) -15373 and -91711. (8) Find the larger number in the given pairs: A) -11, -13 B) -11, -24
C) -4, -15 D) -22, 13 ID : ae-7-integers [2] (9) An integer when divided by 6 gives a remainder 1. The resulting quotient when divided by 6 gives a remainder 2. The resulting quotient is then divided by 7 giving a quotient 1 and a remainder 5. What will be the final remainder, if the order of the divisors is reversed? Fill in the blanks (10) What will be the sign (answer : positive or negative) of the product if we multiply together : A) 26 negative integers and 10 positive integers = B) 7 negative integers and 7 positive integers = (11) If a > b, then (-a) will be than (-b). Check True/False (12) The additive inverse of a negative number is positive. True False (13) a + b = a + b, where a and b are integers and a > b. True False (14) a - b = a - b, where a and b are natural numbers and a < b. True False (15) The sum of a negative integer and a positive integer is always a positive integer. True False 2017 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : ae-7-integers [3] (1) Dhs -1353140 The company sold 3718 tickets of business class. Since the profit on per ticket of business class is Dhs 1570. Therefore the profit on 3718 tickets of business class = 3718 1570 = 5837260 The company sold 41088 tickets of economy class. Since the loss on per ticket of economy class is Dhs 175. Therefore the loss on 41088 tickets of economy class = 41088 175 = 7190400 Therefore the total profit or loss company will make in that month = 5837260-7190400 = Dhs - 1353140 (2) -81 C We know that when anything is heated, its temperature increases and if anything is cooled, then its the temperature decreases. If we look at the question carefully, we notice that the temperature of the ingredient is 40 C. Since, the cooling rate is 11 C per hour, therefore the temperature in freezer in 11 hours = (-11) 11 = -121 C Thus, the temperature in the freezer after 11 hours = Temperature of the ingredient + Temperature in the freezer in 11 hours = 40-121 = -81 C
(3) -(a + 9) ID : ae-7-integers [4] a + 9 = a + 9 if, a + 9 >= 0, a + 9 = -(a + 9) if, a + 9 < 0 We can write the above expression as, a + 9 = a + 9 if, a >= -9, a + 9 = -(a + 9) if, a < -9 Since it is given that a is less than -9, a + 9 = -(a + 9) (4) Dhs -2757 If you look at the question carefully, you will notice that the starting balance on Cala's credit card was Dhs -7559. total number of Dhs credited by Cala = 2002 + 746 + 4692 = Dhs 7440 total number of Dhs debited by Cala = 2512 + 126 = Dhs 2638 Now the final balance on her credit card = the starting balance on Cala credit card - total number of Dhs debited by Cala + total number of Dhs credited by Cala = -7559-2638 + 7440 = Dhs -2757 (5) A) 23488 We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of -23488 = 23488 B) -56213 We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of 56213 = -56213
C) -86202 ID : ae-7-integers [5] We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of 86202 = -86202 D) 42053 We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of -42053 = 42053 E) -14356 We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of 14356 = -14356 F) 0 We know that the additive inverse of a number is the opposite of the number. Therefore, the additive inverse of 0 = 0
(6) 8 ID : ae-7-integers [6] 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 163, which is odd. Therefore, the sum of the given series is 8. (7) A) -7970 Let us calculate the sum of 49086 and -57056 : = (49086) + (-57056) = - (57056-49086) Let us subtract 49086 from 57056. 5 7 0 5 6-4 9 0 8 6 7 9 7 0 Therefore, Sum = - (57056-49086) = -7970
B) 66958 ID : ae-7-integers [7] Let us calculate the sum of -19320 and 86278 : = (-19320) + (86278) = 86278-19320 Let us subtract 19320 from 86278. 8 6 2 7 8-1 9 3 2 0 6 6 9 5 8 Therefore, Sum = 86278-19320 = 66958 C) 18382 Let us calculate the sum of 53622 and -35240. = (53622) + (-35240) = 53622-35240 Let's subtract 35240 from 53622. 5 3 6 2 2-3 5 2 4 0 1 8 3 8 2 Therefore, Sum = 53622-35240 = 18382
D) 864 ID : ae-7-integers [8] Let us calculate the sum of 97168 and -96304. = (97168) + (-96304) = 97168-96304 Let's subtract 96304 from 97168. 9 7 1 6 8-9 6 3 0 4 8 6 4 Therefore, Sum = 97168-96304 = 864 E) 51164 Let us calculate the sum of -18153 and 69317 : = (-18153) + (69317) = 69317-18153 Let us subtract 18153 from 69317. 6 9 3 1 7-1 8 1 5 3 5 1 1 6 4 Therefore, Sum = 69317-18153 = 51164
F) -107084 ID : ae-7-integers [9] Let us calculate the sum of -15373 and -91711 : = (-15373) + (-91711) = - (15373 + 91711) Let us add 15373 and 91711. 1 5 3 7 3 + 9 1 7 1 1 1 0 7 0 8 4 Therefore, Sum = - (15373 + 91711) = -107084 (8) A) -11 We know that the value of a more negative number is smaller as compared to a less negative number or any positive number. Hence, we can say that the larger number in the pair -11, -13 is -11. B) -11 We know that the value of a more negative number is smaller as compared to a less negative number or any positive number. Hence, we can say that the larger number in the pair -11, -24 is -11. C) -4 We know that the value of a more negative number is smaller as compared to a less negative number or any positive number. Hence, we can say that the larger number in the pair -4, -15 is -4.
D) 13 ID : ae-7-integers [10] We know that the value of a more negative number is smaller as compared to a less negative number or any positive number. Hence, we can say that the larger number in the pair -22, 13 is 13.
(9) 4 ID : ae-7-integers [11] We know, Dividend = Quotient Divisor + Remainder Therefore, the dividend of third division: Dividend 3 = Quotient 3 Divisor 3 + Remainder 3 Dividend 3 = 1 7 + 5 Dividend 3 = 12 The dividend of the third division is actually the quotient of the second division. Therefore, Quotient 2 = Dividend 3 = 12 Step 4 Dividend of the second division, Dividend 2 = Quotient 2 Divisor 2 + Remainder 2 Dividend 2 = 12 6 + 2 Dividend 2 = 74 Step 5 Similarly, the dividend of the second division is actually the quotient of the first division. Therefore, Quotient 1 = Dividend 2 = 74 Step 6 Dividend of the first division: Dividend 1 = Quotient 1 Divisor 1 + Remainder 1 Dividend 1 = 74 6 + 1 Dividend 1 = 445 Step 7 Now, let us divide the number 445 in reverse order, 445 7 = 63, Remainder = 4 63 6 = 10, Remainder = 3 10 6 = 1, Remainder = 4 Step 8 Therefore, the final remainder is 4.
ID : ae-7-integers [12] (10) A) positive 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 26 negative integers and 10 positive integers = (Multiplication of 26 negative integers) (Multiplication of 10 positive numbers) = (Positive integer) (Positive integer) = Positive integer 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 7 negative integers and 7 positive integers = (Multiplication of 7 negative integers) (Multiplication of 7 positive integers) = (Multiplication of 6 negative integers) (Negative integer) (Multiplication of 7 positive integers) = (Positive number) (Negative number) (Positive number) = Negative integer
(11) Any 1 from the following 5 answers: less, small, smaller, lesser, < ID : ae-7-integers [13] If 'a' is greater than 'b', it means that 'a' lies on the right side of 'b' on the number line. For example, a = 8 and b = 2, a = 2 and b = -4, a = -1 and b = -7 Now, if we multiply a number by (-1), it shifts towards the opposite side of '0' by the same amount on the number line. a = -8 and b = -2, a = -2 and b = 4, a = 1 and b = 7 Therefore, we can see that after multiplying a number by (-1), the number that lies towards the left
ID : ae-7-integers [14] on the number line shifts more towards the right, and the number that lies towards the right on the number line shifts more towards the left. Hence, if a > b, then (-a) will be less than (-b). (12) 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. (13) False 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 = -8. So, a + b = 9 + (-8) = 1 = 1. Step 4 So, a + b = 9 + -8 = 9 + 8 = 17 Step 5 Since, 1 is not equal to 17. Hence, the given statement is false.
(14) False ID : ae-7-integers [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. (15) False Let us assume that n is a positive integer and -m is a negative integer. The sum of integers n and -m = n + (-m) = n - m If m is less than n, then the value of n - m is positive and, if m is greater than n, then the value of n - m is negative. Therefore, we can say that the sum of a negative integer and a positive integer is not always a positive integer. It will depend on the value of the integers. Step 4 Therefore, the answer is false.