ID : ww-6-integers [1] Grade 6 Integers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Subtract : A) -8566 f rom 37583-73166 f rom 13448-62694 f rom 11073 57430 f rom -53545 E) 69449 f rom -74676 F) -20752 f rom -95012 Choose correct answer(s) f rom given choice (2) In a competitive exam, there are 40 questions. Students can score 2 marks f or each correct answer while 1 mark is deducted f or each incorrect answer. If Linda answered 18 questions correctly, how many marks did she get? a. 14 b. 36 c. 22 d. -26 Fill in the blanks (3) Which number in the f ollowing pairs is smaller : A) 17, 4 = -21, -2 = 23, -20 = 10, -9 = (4) Divide : A) -2016 by 42 = -2160 by 60 = (5) Find the sum of the f ollowing integers: A) -42602 and 87259 = 2492 and 41000 = -23631 and 56717 = 26865 and 54130 = (6) Which number in the f ollowing pairs is larger: A) 23, -13 = -3, -8 = 20, -28 =
ID : ww-6-integers [2] -27, -23 = E) 2, -5 = F) 24, 12 = (7) if a < b, -a will be than -b (8) Find the successor of each of the f ollowing integers: A) -78 = -93 = -5 = -67 = E) -34 = F) -16 = (9) Divide : A) 392 by -14 = 315 by -15 = Check True/False (10) The absolute value of an integer is greater than the integer. True False (11) The additive inverse of a positive number is positive. True False (12) The sum of a two negative integers can be a positive integer. True False (13) Zero is smaller than any negative number. True False (14) The sum of a negative integer and a positive integer is always a positive integer. True False (15) Zero is not an integer. True False 2016 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : ww-6-integers [3] (1) A) 46149 Subtracting -8566 f rom 37583 = 37583 - (-8566) = 37583 + 8566 = 46149 86614 Subtracting -73166 f rom 13448 = 13448 - (-73166) = 13448 + 73166 = 86614 73767 Subtracting -62694 f rom 11073 = 11073 - (-62694) = 11073 + 62694 = 73767-110975 Subtracting 57430 f rom -53545 = -53545-57430 = -110975 E) -144125 Subtracting 69449 f rom -74676 = -74676-69449 = -144125 F) -74260 Subtracting -20752 f rom -95012 = -95012 - (-20752) = -95012 + 20752 = -74260 (2) a. 14 The total number of questions in a competitive exam = 40, Marks obtained f or each correct answer = 2 and Marks deducted f or each incorrect answer = 1 Since Linda answered 18 questions correctly, Total marks obtained by Linda f or correct answers = 2 18 =36 Number of incorrect question answered by Linda = total number of questions in exam - number of correct questions answered by Linda = 40-18 = 22 Step 4 Now total marks obtained by Linda in exam = total marks obtained by Linda f or correct answers - total marks deducted f or incorrect answers = 36-22 = 14 Step 5 Theref ore Linda obtained 14 marks.
(3) A) 4 ID : ww-6-integers [4] If we look at the pair 17, 4, we will notice that 4 < 17. Theref ore, we can say that the smaller number in the pair 17, 4 is 4. -21 In case of negative numbers, the value of more negative number is smaller as compared to the less negative number or positive number. Theref ore, -21 < -2. Now, we can say that the smaller number in the pair -21, -2 is -21. -20 We know that a negative number is smaller than the positive number, theref ore - 20 < 23. Theref ore, we can say that the smaller number in the pair 23, -20 is -20. -9 We know that a negative number is smaller than the positive number, theref ore - 9 < 10. Theref ore, we can say that the smaller number in the pair 10, -9 is -9.
(4) A) -48 ID : ww-6-integers [5] 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 -2016 by 42, result will be negative -2016 42 = -48-36 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 -2160 by 60, result will be negative -2160 60 = -36 (5) A) 44657 If you look at the question caref ully, you will notice that you have to f ind the sum of -42602 and 87259 Now -42602 + 87259 = 44657 Theref ore the sum of -42602 and 87259 = 44657
43492 ID : ww-6-integers [6] If you look at the question caref ully, you will notice that you have to f ind the sum of 2492 and 41000 Now 2492 + 41000 = 43492 Theref ore the sum of 2492 and 41000 = 43492 33086 If you look at the question caref ully, you will notice that you have to f ind the sum of -23631 and 56717 Now -23631 + 56717 = 33086 Theref ore the sum of -23631 and 56717 = 33086 80995 If you look at the question caref ully, you will notice that you have to f ind the sum of 26865 and 54130 Now 26865 + 54130 = 80995 Theref ore the sum of 26865 and 54130 = 80995 (6) A) 23 In case of negative numbers, the value of more negative number is smaller as compare to the less negative number or positive number,theref ore 23 > -13 Now we can say that the larger number in pair 23, -13 is 23
-3 ID : ww-6-integers [7] In case of negative numbers, the value of more negative number is smaller as compare to the less negative number or positive number,theref ore -3 > -8 Now we can say that the larger number in pair -3, -8 is -3 20 In case of negative numbers, the value of more negative number is smaller as compare to the less negative number or positive number,theref ore 20 > -28 Now we can say that the larger number in pair 20, -28 is 20-23 In case of negative numbers, the value of more negative number is smaller as compare to the less negative number or positive number,theref ore -23 > -27 Now we can say that the larger number in pair -27, -23 is -27 E) 2 In case of negative numbers, the value of more negative number is smaller as compare to the less negative number or positive number,theref ore 2 > -5 Now we can say that the larger number in pair 2, -5 is 2 F) 24 If you look at the pair 24, 12 caref ully, you will notice that 24 > 12 Theref ore you can say that the larger number in pair 24, 12 is 24
(7) Any 1 f rom f ollowing 4 answers greater,bigger,larger,great ID : ww-6-integers [8] If a is less than b, it means that on number line, a is on the lef t side of b. For example, b = 8 and a = 2 b = 2 and a = -4, b = -1 and a = -7, Now, once we multiply a number by -1, on number line it shif ts on opposite side around 0 by the same amount. b = -8 and a = -2 b = -2 and a = 4, b = 1 and a = 7,
ID : ww-6-integers [9] So we can see that af ter multiplication by -1, on number line number which is in more lef t, goes to more right, and number which is on more right, goes to more lef t. Theref ore, if a < b, -a will be greater than -b (8) A) -77 All positive numbers, negative numbers and zero are integer, accept f ractions. we can write all integers in increasing order as: Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,... } The successor of -78 is = -78 + 1 = -77. -92 All positive numbers, negative numbers and zero are integer, accept f ractions. we can write all integers in increasing order as: Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,... } The successor of -93 is = -93 + 1 = -92. -4 All positive numbers, negative numbers and zero are integer, accept f ractions. we can write all integers in increasing order as: Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,... } The successor of -5 is = -5 + 1 = -4.
E) -33 ID : ww-6-integers [10] All positive numbers, negative numbers and zero are integer, accept f ractions. we can write all integers in increasing order as: Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,... } The successor of -34 is = -34 + 1 = -33. F) -15 All positive numbers, negative numbers and zero are integer, accept f ractions. we can write all integers in increasing order as: Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,... } The successor of -16 is = -16 + 1 = -15. (9) A) -28 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 392 by 14, Dividend Divisor 14 ) 3 9 2 ( 28 Quotient 2 8 1 1 2 1 1 2 Remainder 0 Theref ore (392) ÷ (-14) = -28
-21 ID : ww-6-integers [11] 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 315 by 15, Dividend Divisor 15 ) 3 1 5 ( 21 Quotient 3 0 1 5 1 5 Remainder 0 Theref ore (315) ÷ (-15) = -21 (10) False 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 greater than the integer" is f alse.
(11) False ID : ww-6-integers [12] The additive inverse of a number a is the number that, when added to a, yields zero. The additive inverse is the opposite of a number theref ore the additive inverse of a positive number is negative and a negative number is positive. For example, the additive inverse of 14 is 14. The additive inverse of 5 is 5. Theref ore the given statement is f alse. (12) False We know that negative numbers are less than 0 and are on lef t hand side of 0 on number line. Above number line shows two negative numbers a = -3 and b = -1 When we add a positive number, number on number line shif ts to the right and if we add a negative number, it shif ts to lef t on number line For example if we add b(-1) to a(-3), a shif ts to f urther lef t on number line, Step 4 Since sum of two negative numbers will be on lef t side of 0 on number line, sum will always be negative. Theref ore given statement is f alse.
(13) False ID : ww-6-integers [13] 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 Let us assume that n is a positive integer and -m is a negative integer. The sum of integer 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 the n, then the value of n - m is negative. Theref ore we can say that the sum of a negative integer and a positive integer is not always a positive integer. It will depends on the value of the numbers. Step 4 Theref ore the answer is f alse. (15) False Integers are the set of whole numbers (0, 1, 2, 3,...) and their opposites (0, -1, -2, -3,...). We can see that zero is an integer, theref ore given statement is f alse.