ID : in-7-integers [1] Class 7 Integers For more such worksheets visit www.edugain.com Answer the questions (1) An integer is divided by 4 and gives a remainder of 3. The resulting quotient is divided by 5 and gives a remainder of 2. The resulting quotient is then divided by 9 giving a quotient of 1 and a remainder of 7. Find the number? (2) Subtract : A) 25430 from -75985 B) -7554 from -92655 C) -71881 from 89722 D) 86674 from -57396 E) 58964 from 76245 F) 36521 from 44637 (3) What is the absolute value of a - 5, if a is greater than 5? (4) Subtract the sum of : A) (9357) and (7355) from (-9062) B) (7501) and (-5929) from (9126) (5) An integer when divided by 6 gives a remainder 4. The resulting quotient when divided by 7 gives a remainder 6. The resulting quotient is then divided by 6 giving a quotient 1 and a remainder 3. What will be the final remainder, if the order of the divisors is reversed? (6) Find the smaller number in the given pairs : A) -23, -25 B) 28, 12 C) 12, 15 D) -20, 11 (7) Find the larger number in the given pairs: A) 13, -23 B) 5, -6 C) 22, 18 D) -12, 20 (8) Aditya is in the process of making an ice cream. He has heated all the ingredients to 60 C and put them in refrigerator to freeze. If the cooling rate is 12 C per hour, what will be the temperature in freezer after 11 hours? Choose correct answer(s) from the given choices (9) The sum of any two negative integers will be : a. Positive, if the first number is larger b. Negative integer c. Positive integer d. Negative, if the first number is larger Fill in the blanks
(10) What will be the sign (answer : positive or negative) of the product if we multiply together : ID : in-7-integers [2] A) 14 negative integers and 5 positive integers = B) 28 negative integers and 7 positive integers = (11) Divide : A) -350 by 14 = B) -77 by -11 = (12) Find the value of the following : A) ( -11 ) 8 + ( -1 ) 17 = B) ( -14 ) ( -9 ) 4 - ( -1 ) ( -3 ) 11 = (13) Find the value of the following : A) 6 4 4 = B) 1 ( -12 ) 0 = Check True/False (14) The additive inverse of a positive number is positive. True False (15) The sum of a number and its negative is zero. True False 2017 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : in-7-integers [3] (1) 331 According to the question, an integer is divided by 4 and gives a remainder of 3. Let us assume that the number or the dividend is x. Here, divisor = 4 Remainder = 3 We know that dividend = Divisor Quotient + Remainder Or, Dividend - Remainder Quotient = Divisor = x - 3 4 Since, the resulting quotient is divided by 5 and gives the remainder of 2, hence the resulting quotient works as the dividend. Dividend - Remainder New quotient = Divisor New quotient = ( x - 3 4 ) - 2 5 = x - 3-8 4 1 5 = x - 11 20 Since, the resulting quotient is divided by 9 giving the quotient of 1 and the remainder of 7, hence the resulting quotient works as the dividend. Dividend = Divisor Quotient + Remainder x - 11 = 9 1 + 7 20 x - 11 20 = 9 + 7 x - 11 = 16 20 x - 11 = 16 20 x = 320 + 11 x = 331
Step 4 Therefore, the number is 331. ID : in-7-integers [4] (2) A) -101415 Subtracting 25430 from -75985 = -75985-25430 = -101415 B) -85101 Subtracting -7554 from -92655 = -92655 - (-7554) = -92655 + 7554 = -85101 C) 161603 Subtracting -71881 from 89722 = 89722 - (-71881) = 89722 + 71881 = 161603 D) -144070 Subtracting 86674 from -57396 = -57396-86674 = -144070 E) 17281 Subtracting 58964 from 76245 = 76245-58964 = 17281 F) 8116 Subtracting 36521 from 44637 = 44637-36521 = 8116 (3) a - 5 It is given that the value of a is greater than 5. So, the value of a - 5 will be positive. Hence, the absolute value of a - 5 is a - 5.
(4) A) -25774 ID : in-7-integers [5] The sum of (9357) and (7355) : = (9357) + 7355 = 16712 Now, subtract 16712 from (-9062). = (-9062) - 16712 = -25774 Therefore, the answer is -25774. B) 7554 The sum of (7501) and (-5929) : = (7501) + (-5929) = 7501-5929 = 1572 Now, subtract 1572 from (9126). = (9126) - 1572 = 7554 Therefore, the answer is 7554.
(5) 3 ID : in-7-integers [6] We know, Dividend = Quotient Divisor + Remainder Therefore, the dividend of third division: Dividend 3 = Quotient 3 Divisor 3 + Remainder 3 Dividend 3 = 1 6 + 3 Dividend 3 = 9 The dividend of the third division is actually the quotient of the second division. Therefore, Quotient 2 = Dividend 3 = 9 Step 4 Dividend of the second division, Dividend 2 = Quotient 2 Divisor 2 + Remainder 2 Dividend 2 = 9 7 + 6 Dividend 2 = 69 Step 5 Similarly, the dividend of the second division is actually the quotient of the first division. Therefore, Quotient 1 = Dividend 2 = 69 Step 6 Dividend of the first division: Dividend 1 = Quotient 1 Divisor 1 + Remainder 1 Dividend 1 = 69 6 + 4 Dividend 1 = 418 Step 7 Now, let us divide the number 418 in reverse order, 418 6 = 69, Remainder = 4 69 7 = 9, Remainder = 6 9 6 = 1, Remainder = 3 Step 8 Therefore, the final remainder is 3.
(6) A) -25 ID : in-7-integers [7] In case of the negative numbers, the value of the greater negative number is smaller as compared to the less negative number or a positive number. Therefore, -25 < -23. Hence, we can say that the smaller number in the pair -23, -25 is -25. B) 12 If we look at the pair 28, 12, we will notice that 12 < 28. Therefore, we can say that the smaller number in the pair 28, 12 is 12. C) 12 If we look at the pair 12, 15, we will notice that 12 < 15. Therefore, we can say that the smaller number in the pair 12, 15 is 12. D) -20 We know that a negative number is always smaller than a positive number. Therefore -20 < 11. Hence, we can say that the smaller number in the pair -20, 11 is -20. (7) A) 13 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 13, -23 is 13.
B) 5 ID : in-7-integers [8] 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 5, -6 is 5. C) 22 Both the numbers, 22 and 18, are positive. On comparing the two numbers, we find that 22 > 18. Hence,the positive number 22 is larger than the positive number 18. D) 20 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 -12, 20 is 20. (8) -72 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 60 C. Since, the cooling rate is 12 C per hour, therefore the temperature in freezer in 11 hours = (-12) 11 = -132 C Thus, the temperature in the freezer after 11 hours = Temperature of the ingredient + Temperature in the freezer in 11 hours = 60-132 = -72 C
(9) b. Negative integer ID : in-7-integers [9] 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.
ID : in-7-integers [10] (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 14 negative integers and 5 positive integers = (Multiplication of 14 negative integers) (Multiplication of 5 positive numbers) = (Positive integer) (Positive integer) = Positive integer B) 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 28 negative integers and 7 positive integers = (Multiplication of 28 negative integers) (Multiplication of 7 positive numbers) = (Positive integer) (Positive integer) = Positive integer
ID : in-7-integers [11] (11) A) -25 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 350 by 14, Dividend Divisor 14 ) 3 5 0 ( 25 Quotient 2 8 7 0 7 0 Remainder 0 Therefore, (-350) (14) = -25
ID : in-7-integers [12] B) 7 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 77 by 11, Dividend Divisor 11 ) 7 7 ( 7 Quotient 7 7 Remainder 0 Therefore, (-77) (-11) = 7
ID : in-7-integers [13] (12) A) -105 We can multiply the two numbers by using the following steps: 1. Firstly, we will multiply 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 multiply the signs as shown below : + + = + + = = + 2. Now, we have to multiply the numbers. For example : 3 2 = 6, 3 (-2) = (-6), (-3) 2 = (-6), (-3) (-2) = 6 Therefore, ( -11 ) 8 + ( -1 ) 17 can be expressed as: ( -11 ) 8 + ( -1 ) 17 = (-88) + (-17) = -88-17 = -105 Hence, the value of ( -11 ) 8 + ( -1 ) 17 is -105.
ID : in-7-integers [14] B) 471 We can multiply the two numbers by using the following steps: 1. Firstly, we will multiply 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 multiply the signs as shown below : + + = + + = = + 2. Now, we have to multiply the numbers. For example : 3 2 = 6, 3 (-2) = (-6), (-3) 2 = (-6), (-3) (-2) = 6 Therefore, ( -14 ) ( -9 ) 4 - ( -1 ) ( -3 ) 11 can be expressed as: ( -14 ) ( -9 ) 4 - ( -1 ) ( -3 ) 11 = (504) - (33) = 471 Hence, the value of ( -14 ) ( -9 ) 4 - ( -1 ) ( -3 ) 11 is 471.
ID : in-7-integers [15] (13) A) 96 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 6 4 4, we have to multiply the two numbers first. Then, we will multiply the result with the next number and so on : 6 4 4 = 24 4 = 96 Therefore, the value of 6 4 4 is 96.
ID : in-7-integers [16] B) 0 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 1 ( -12 ) 0, we have to multiply the two numbers first. Then, we will multiply the result with the next number and so on : 1 ( -12 ) 0 = -12 0 = 0 Therefore, the value of 1 ( -12 ) 0 is 0. (14) False 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 false.
(15) True ID : in-7-integers [17] 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.