ID : ae-6-integers [1] Grade 6 Integers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Find the predecessor of each of the f ollowing integers: A) -98 = B) -63 = C) -8 = D) -3 = E) -24 = F) -23 = (2) Which number in the f ollowing pairs is smaller : A) -22, 17 B) 15, -28 C) -1, -30 D) -22, 13 (3) Which number in the f ollowing pairs is larger: A) 0, 27 B) -11, -7 C) -21, -22 D) 29, 17 (4) Subtract the sum of : A) 9958 and -946 f rom -9637 B) 4023 and 1443 f rom -9378 Fill in the blanks (5) Find the absolute value of f ollowing integers: A) B) -18 = -6 = C) 10 = D) 5 = E) -13 = F) 7 = (6) Find the value of f ollowing : A) ( -18 ) ( -4 ) + ( -16 ) 3 = B) 20 14 + 12 ( -14 ) = (7) The product of 2 given numbers is 294. The two numbers are each divisible by 7, but neither of them is 7. The larger of these two numbers =. (8) A + B = B + A represents the property of addition.
(9) ID : ae-6-integers [2] If a and b are two integers such that a is the predecessor of b, the value of a - b will be. (10) if a > b, -a will be than -b (11) Find how many integers are there between: A) -2 and 2 = B) -1 and 7 = C) -5 and 6 = D) -2 and 2 = (12) Simplif y : A) (5159 / -67) - (-2911 / -71) + (-3080 / 40) + (2480 / -62) = B) (-4140 / -69) + (5040 / -60) - (-2668 / -58) = (13) Find the value of f ollowing expression: A) 198-72 - ( -159 ) - 145-139 - ( -156 ) - 26-4 = B) ( -31 ) - ( -176 ) - 67-28 - ( -14 ) - ( -142 ) - ( -198 ) - ( -130 ) = Check True/False (14) The additive inverse of a positive number is positive. True False (15) The sum of a number and its negative number is zero True False 2016 Edugain (www.edugain.com). All Rights Reserved Many more such worksheets can be generated at www.edugain.com
Answers ID : ae-6-integers [3] (1) A) -99 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 predecessor of -98 is = -98-1 = -99. B) -64 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 predecessor of -63 is = -63-1 = -64. C) -9 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 predecessor of -8 is = -8-1 = -9. D) -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 predecessor of -3 is = -3-1 = -4.
E) -25 ID : ae-6-integers [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 predecessor of -24 is = -24-1 = -25. F) -24 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 predecessor of -23 is = -23-1 = -24. (2) A) -22 We know that a negative number is smaller than the positive number, theref ore - 22 < 17. Theref ore, we can say that the smaller number in the pair -22, 17 is -22. B) -28 We know that a negative number is smaller than the positive number, theref ore - 28 < 15. Theref ore, we can say that the smaller number in the pair 15, -28 is -28. C) -30 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, -30 < -1. Now, we can say that the smaller number in the pair -1, -30 is -30.
D) -22 ID : ae-6-integers [5] We know that a negative number is smaller than the positive number, theref ore - 22 < 13. Theref ore, we can say that the smaller number in the pair -22, 13 is -22. (3) A) 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 0, 27 is 27. B) -7 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 -11, -7 is -7. C) -21 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 -21, -22 is -21. D) 29 Both numbers 29 and 17 are positive. The positive number 29 is larger than the positive number 17.
(4) A) -18649 ID : ae-6-integers [6] The sum of 9958 and -946 9958 + (-946) = 9958-946 = 9012 Now subtract 9012 f rom -9637-9637 - 9012 = -18649 Step 3 Theref ore the answer is -18649 B) -14844 The sum of 4023 and 1443 4023 + 1443 = 5466 Now subtract 5466 f rom -9378-9378 - 5466 = -14844 Step 3 Theref ore the answer is -14844 (5) A) 18 The absolute value (or modulus) of a integer x is x's numerical value without regard to its sign. Theref ore the absolute value of -18 = 18. B) 6 The absolute value (or modulus) of a integer x is x's numerical value without regard to its sign. Theref ore the absolute value of -6 = 6.
C) 10 ID : ae-6-integers [7] The absolute value (or modulus) of a integer x is x's numerical value without regard to its sign. Theref ore the absolute value of 10 = 10. D) 5 The absolute value (or modulus) of a integer x is x's numerical value without regard to its sign. Theref ore the absolute value of 5 = 5. E) 13 The absolute value (or modulus) of a integer x is x's numerical value without regard to its sign. Theref ore the absolute value of -13 = 13. F) 7 The absolute value (or modulus) of a integer x is x's numerical value without regard to its sign. Theref ore the absolute value of 7 = 7.
(6) A) 24 ID : ae-6-integers [8] 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 ( -18 ) ( -4 ) + ( -16 ) 3 can be expressed as: ( -18 ) ( -4 ) + ( -16 ) 3 = (72) + (-48) = 72-48 = 24 Step 3 Theref ore the value of ( -18 ) ( -4 ) + ( -16 ) 3 is 24.
B) 112 ID : ae-6-integers [9] 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 14 + 12 ( -14 ) can be expressed as: 20 14 + 12 ( -14 ) = (280) + (-168) = 280-168 = 112 Step 3 Theref ore the value of 20 14 + 12 ( -14 ) is 112.
(7) 21 ID : ae-6-integers [10] Since numbers are divisible by 7, lets assume numbers are 7x and 7y. Also, since numbers are not equal to 7, x and y cannot be 1 It is given that their product is 294 (7x) (7y) = 294 49 xy = 294 xy = 294 49 xy = 6 Step 3 Since x and y cannot be 1, only possible f actors of xy = 6, are 3 and 2 Step 4 Theref ore numbers are (3 7 = 21) and (2 7 = 14) Step 5 Larger of two numbers = 21 (8) Commutative 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. Step 3 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.
(9) -1 ID : ae-6-integers [11] Because a is predecessor of b theref ore the value of a = b - 1 The value of a - b = b - 1 - b = b - b - 1 = -1
(10) Any 1 f rom f ollowing 4 answers less,small,smaller,lesser ID : ae-6-integers [12] If a is greater than b, it means that on number line, a is on the right side of b. For example, a = 8 and b = 2 a = 2 and b = -4, a = -1 and b = -7, Now, once we multiply a number by -1, on number line it shif ts on opposite side around 0 by the same amount. a = -8 and b = -2 a = -2 and b = 4, a = 1 and b = 7, Step 3
ID : ae-6-integers [13] 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 less than -b (11) A) 3 Number of integers between any two integers is equal to one less than the dif f erence between the two integers. Thus, the total number of integers that are there between -2 and 2 = 2 - (-2) - 1 = 2 + 1 = 3 B) 7 Number of integers between any two integers is equal to one less than the dif f erence between the two integers. Thus, the total number of integers that are there between -1 and 7 = 7 - (-1) - 1 = 7-0 = 7
D) 3 ID : ae-6-integers [14] Number of integers between any two integers is equal to one less than the dif f erence between the two integers. Thus, the total number of integers that are there between -2 and 2 = 2 - (-2) - 1 = 2 + 1 = 3 (12) A) -235 We can divide two numbers by the f ollowing steps: 1. First of all we have to divide 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 divide sign as: + + = + + - = - - - = + 2. Now we have to divide numbers. f or example 4 2 = 2, 4 (-2) = (-2), (-4) 2 = (-2), (-4) (-2) = 2. Now (5159 / -67) - (-2911 / -71) + (-3080 / 40) + (2480 / -62) can be simplif ied as: (5159 / -67) - (-2911 / -71) + (-3080 / 40) + (2480 / -62) = (-77) - 41 + (-77) + (-40) = -235
B) -70 ID : ae-6-integers [15] We can divide two numbers by the f ollowing steps: 1. First of all we have to divide 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 divide sign as: + + = + + - = - - - = + 2. Now we have to divide numbers. f or example 4 2 = 2, 4 (-2) = (-2), (-4) 2 = (-2), (-4) (-2) = 2. Now (-4140 / -69) + (5040 / -60) - (-2668 / -58) can be simplif ied as: (-4140 / -69) + (5040 / -60) - (-2668 / -58) = 60 + (-84) - 46 = -70 (13) A) 127 The given expression can be expressed as: 198-72 - ( -159 ) - 145-139 - ( -156 ) - 26-4 = 198-72 + 159-145 - 139 + 156-26 - 4 = 127 Theref ore the value of expression 198-72 - ( -159 ) - 145-139 - ( -156 ) - 26-4 is 127.
ID : ae-6-integers [16] (14) False 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. Step 3 Theref ore the given statement is f alse.