ID : ae-7-integers [1] Grade 7 Integers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Subtract : A) 21644 f rom 22642 B) -4505 f rom -83570 C) 133 f rom 16220 D) -56723 f rom -93861 E) -34450 f rom 26975 F) -72793 f rom 25486 (2) An arithmetic sequence is a sequence of numbers a 1, a 2, a 3,... where a n - a n-1 is the same value f or all n. For example 2, 4, 6, 8, 10,...is such a sequence where the dif f erence between adjoining numbers is 2. Given a, b, c, d and e are consecutive members of such a sequence, and that a + b + c + d + e = 70, what is the value of c? (3) The sum of two integers is 4075. If one of the integers is -4375, what is the other integer? (4) Which number in the f ollowing pairs is larger: A) 28, -27 B) -19, 17 C) -27, -30 D) -18, 5 Choose correct answer(s) f rom given choice (5) While doing the science experiment in the physics lab, Habiba had to take 4 measurements of the temperature and write the average of those as an answer. If the measurements of the temperature is 2, 0, -2, -4, what is the f inal answer of her experiment? a. -1 b. 0 c. -16 d. -4 (6) An airline company makes a prof it of Dhs 1016 on per ticket of business class while loses Dhs 127 on every ticket of economy class. If the company sold 30128 tickets of economy class, how many tickets should it sell f or business class to break even. a. -3826256 b. 3826256 c. 3766 d. 3850 Fill in the blanks (7) A + B = B + A represents the property of addition.
(8) Divide : A) 1925 by -55 = ID : ae-7-integers [2] B) 1998 by -54 = (9) Find the successor of each of the f ollowing integers: A) -5 = B) -61 = C) -56 = D) -13 = E) -94 = F) -20 = (10) Find the predecessor of each of the f ollowing integers: A) -3 = B) -41 = C) -23 = D) -33 = E) -40 = F) -17 = (11) Divide : A) -48 by -6 = B) -420 by 20 = (12) Find the value of f ollowing : A) ( -14 ) ( -16 ) 20 + ( -11 ) 6 ( -3 ) = B) 20 ( -5 ) ( -17 ) - ( -15 ) ( -12 ) = Check True/False (13) Zero is smaller than any negative number. True False (14) The absolute value of an integer is less than the integer. True False (15) Every negative number is less than every natural number. True False 2016 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) A) 998 Subtracting 21644 f rom 22642 = 22642-21644 = 998 B) -79065 Subtracting -4505 f rom -83570 = -83570 - (-4505) = -83570 + 4505 = -79065 C) 16087 Subtracting 133 f rom 16220 = 16220-133 = 16087 D) -37138 Subtracting -56723 f rom -93861 = -93861 - (-56723) = -93861 + 56723 = -37138 E) 61425 Subtracting -34450 f rom 26975 = 26975 - (-34450) = 26975 + 34450 = 61425 F) 98279 Subtracting -72793 f rom 25486 = 25486 - (-72793) = 25486 + 72793 = 98279
(2) 14 ID : ae-7-integers [4] If you look at the question caref ully, you will notice that a, b, c, d and e are consecutive members and the dif f erence between adjoining numbers is 2. Theref ore you can say that d = c + 2, b = c - 2, a = b - 2 = c - 2-2 = c - 4, e = d + 2 = c + 2 + 2 = c + 4 According to question a + b + c + d + e = 70 By putting the value of a, b, d and e (c - 4) + (c - 2) + (c) + (c + 2) + (c + 4) = 70 c - 4 + c - 2 + c + c + 2 + c + 4 = 70 c + c + c + c + c - 4-2 + 2 + 4 = 70 5c + 0 = 70 5c = 70 c = 70 5 c = 14 Now you can say that the value of c is 14. (3) 8450 The sum of two integers is 4075 One of the integer is -4375 T he other integer, = The sum of two integers - One of the integer = (4075) - (-4375) = 4075 + 4375 = 8450
(4) A) 28 ID : ae-7-integers [5] The value of more negative number is smaller as compared to a less negative number or any positive number. Thus, we can say that the larger number in the pair 28, -27 is 28. B) 17 The value of more negative number is smaller as compared to a less negative number or any positive number. Thus, we can say that the larger number in the pair -19, 17 is 17. C) -27 The value of more negative number is smaller as compared to a less negative number or any positive number. Thus, we can say that the larger number in the pair -27, -30 is -27. D) 5 The value of more negative number is smaller as compared to a less negative number or any positive number. Thus, we can say that the larger number in the pair -18, 5 is 5.
(5) a. -1 ID : ae-7-integers [6] If you look at the question caref ully, you will notice that Habiba had to take 4 measurements of the temperature and write the average of those as an answer. Since the measurements of the temperature is 2, 0, -2, -4, theref ore the f inal answer of her experiment = average of 2, 0, -2, -4, Sum of 2, 0, -2, -4, = Number of measurements of the temperature = -4 4 = -1 (6) c. 3766 The company sold 30128 tickets of economy class. Since the loss on per ticket of economy class is Dhs 127. Theref ore the loss on 30128 tickets of economy class = 30128 127 = Dhs 3826256 The break-even point is the point at which cost or expenses and revenue are equal, there is no net loss or gain. Theref ore the loss on 30128 tickets of economy class is equal to the prof it on 3766 tickets of business class. Now the prof it on 3766 tickets of business class = Dhs 3826256 Since the company makes a prof it of Dhs 1016 on per ticket of business class. Theref ore the number the tickets on which the company makes a prof it of Dhs 3826256 = 3826256 1016 = 3766 tickets Step 4 The company should sell 3766 tickets of business class to break even.
(7) Commutative ID : ae-7-integers [7] We have been presented with the expression A + B = B + A. This represents the f act that changing the order of addends (numbers being added) does not change the result of addition. Whether we add B to A or we add A to B, we get the same answer. For example, 2 + 3 is same as 3 + 2 as both are both 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 has commutative property. Multiplication is another type of operation which has commutative property. For example, 2 3 = 3 2. Step 4 Theref ore, we can say that A + B = B + A represents the commutative property of addition. (8) A) -35 Division of a positive number by a negative number results in a negative number. For example 4/(-2) = -2 Division of a negative number by a positive number results in a negative number. For example -4/2 = -2 Division of a negative number by a negative number results in a positive number. For example (-4)/(-2) = 2 Theref ore if we divide 1925 by -55, result will be negative 1925-55 = -35
B) -37 ID : ae-7-integers [8] Division of a positive number by a negative number results in a negative number. For example 4/(-2) = -2 Division of a negative number by a positive number results in a negative number. For example -4/2 = -2 Division of a negative number by a negative number results in a positive number. For example (-4)/(-2) = 2 Theref ore if we divide 1998 by -54, result will be negative 1998-54 = -37 (9) A) -4 The successor of -5 is = -5 + 1 = -4. B) -60 The successor of -61 is = -61 + 1 = -60.
C) -55 ID : ae-7-integers [9] The successor of -56 is = -56 + 1 = -55. D) -12 The successor of -13 is = -13 + 1 = -12. E) -93 The successor of -94 is = -94 + 1 = -93. F) -19 The successor of -20 is = -20 + 1 = -19.
(10) A) -4 ID : ae-7-integers [10] The predecessor of -3 is = -3-1 = -4. B) -42 The predecessor of -41 is = -41-1 = -42. C) -24 The predecessor of -23 is = -23-1 = -24. D) -34 The predecessor of -33 is = -33-1 = -34.
E) -41 ID : ae-7-integers [11] The predecessor of -40 is = -40-1 = -41. F) -18 The predecessor of -17 is = -17-1 = -18. (11) A) 8 Division of a positive number by a negative number results in a negative number. For example 4/(-2) = -2 Division of a negative number by a positive number results in a negative number. For example -4/2 = -2 Division of a negative number by a negative number results in a positive number. For example (-4)/(-2) = 2 Let's divide 48 by 6, Dividend Divisor 6 ) 4 8 ( 8 Quotient 4 8 Remainder 0 Theref ore (-48) ÷ (-6) = 8
B) -21 ID : ae-7-integers [12] Division of a positive number by a negative number results in a negative number. For example 4/(-2) = -2 Division of a negative number by a positive number results in a negative number. For example -4/2 = -2 Division of a negative number by a negative number results in a positive number. For example (-4)/(-2) = 2 Let's divide 420 by 20, Dividend Divisor 20 ) 4 2 0 ( 21 Quotient 4 0 2 0 2 0 Remainder 0 Theref ore (-420) ÷ (20) = -21
(12) A) 4678 ID : ae-7-integers [13] We can multiply two numbers by the f ollowing steps: 1. First of all we have to multiply sign of the numbers. we use negative sign bef ore the negative numbers and we can't use any sign bef ore the positive numbers. We can multiply sign as: + + = + + - = - - - = + 2. Now we have to multiply numbers. f or example 3 2 = 6, 3 (-2) = (-6), (-3) 2 = (-6), (-3) (-2) = 6. Now ( -14 ) ( -16 ) 20 + ( -11 ) 6 ( -3 ) can be expressed as: ( -14 ) ( -16 ) 20 + ( -11 ) 6 ( -3 ) = (4480) + (198) = 4678 Theref ore the value of ( -14 ) ( -16 ) 20 + ( -11 ) 6 ( -3 ) is 4678.
B) 1520 ID : ae-7-integers [14] We can multiply two numbers by the f ollowing steps: 1. First of all we have to multiply sign of the numbers. we use negative sign bef ore the negative numbers and we can't use any sign bef ore the positive numbers. We can multiply sign as: + + = + + - = - - - = + 2. Now we have to multiply numbers. f or example 3 2 = 6, 3 (-2) = (-6), (-3) 2 = (-6), (-3) (-2) = 6. Now 20 ( -5 ) ( -17 ) - ( -15 ) ( -12 ) can be expressed as: 20 ( -5 ) ( -17 ) - ( -15 ) ( -12 ) = (1700) - (180) = 1520 Theref ore the value of 20 ( -5 ) ( -17 ) - ( -15 ) ( -12 ) is 1520. (13) False We can see that on number line, negative numbers are on the lef t side of zero. Theref ore, negative numbers are smaller than 0. Since 0 is greater than the all negative values, the statement that 'Zero is smaller than any negative number', is f alse.
(14) False ID : ae-7-integers [15] Absolute Value is the value of the number without regards to its' sign. The value is always a positive number. For positive numbers, absolute value is same as number. e.g. 5 = 5. For negative numbers, absolute value is reverse of the number. e.g. -5 = 5. We can see that absolute value of a number if either equal to the number (f or positive numbers), or it is larger than the number (f or negative numbers). Hence the given statement "The absolute value of an integer is less than the integer" is f alse. (15) True We know that if a number is on right hand side of another number on number line, f irst number is greater other number. Theref ore a > b, as a is on right side of b. Following picture shows that negative numbers are on lef t hand side of 0 on number line, while natural numbers are on right hand side of 0 From above number line, we can see that natural numbers are greater than negative numbers. Theref ore, given statement is true