Mental Maths<\/strong><\/p>\n Question 1. Question 2. Question 3. Multiple Choice Questions<\/strong><\/p>\n Choose the correct answer from the given four options (4 to 19):<\/strong> Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. Question 14. Question 15. Question 16. Question 17. Question 18. Question 19. Value Based Questions<\/strong><\/p>\n Question 1. Question 2. Higher Order Thinking Skills (HOTS)<\/strong><\/p>\n Question 1. Question 2. Question 3.
\nFill in the blanks:
\n(i) ………… is the greatest negative integer.
\n(ii) ((-10) + 3) + (-12) = (-10) + (3 + …..)
\n(iii) The product of two negative integers and the product of two positive integers is a ………. integer.
\n(iv) The division of any integer by zero is ……..
\n(v) The integer whose product with (-1) is 22 is ………
\n(vi) (-15) \u00d7 …….. = 120
\n(vii) ……… \u00f7 (-6) = -12
\n(viii) (-10) \u00d7 ((-15) + 33) = ……. \u00d7 (-15) + (-10) \u00d7 33
\n(ix) ……… \u00f7 (-25) = 0
\n(x) ((-8) \u00d7 (-13)) \u00d7 27 = (-8) \u00d7 ((……) \u00d7 27)
\n(xi) 13 \u00d7 (-6) = -(……. \u00d7 ………) = …….
\n(xii) (-a) + b = b + additive inverse of ……….
\n(xiii) When we divide a negative integer by a positive integer, we divide them as whole numbers and put a ……… sign before the quotient.
\n(xiv) When -25 is divided by ……… the quotient is 5.
\n(xv) There are …….. pairs of integers satisfying a \u00f7 b = -1.
\n(xvi) The value of the expression ((-60) \u00f7 12) (-5) is ……….
\nSolution:
\n(i) -1 is the greatest negative integer.
\n(ii) [(-10) + 3] + (-12) = (-10) + (3 + ……..)
\n[(-10 + 3] + (-12) = (-10) + [3 + (-12)] (Associative law of addition)
\n(iii) The product of two negative integers and the product of two positive integers is a positive integer.
\n(iv) The division of any integer by zero is meaningless.
\n(v) The integer whose product with (-1) is 22 is -22. [\u2235 (-1) \u00d7 (-22) = 22]
\n(vi) (-15) \u00d7 ……. = 120
\n\\(\\frac { 120 }{ -15 }\\) = -8
\n(-15) \u00d7 (-8) = 120
\n(vii) …….. \u00f7 (-6) = -12
\n-6 \u00d7 (-12) = 72
\n72 \u00f7 (-6) = -12
\n(viii) (-10) \u00d7 {(-15) + 33} = ……… \u00d7 (-15) + (-10) \u00d7 33
\n= (-10) \u00d7 {(-15) + 33}
\n= (-10) \u00d7 (-15) + (-10) \u00d7 33 (Distributive law of multiplication)
\n(ix) 0 \u00f7 (-25) = 0 (\u2235 0 divided by every integer excepted is zero)
\n(x) {(-8) \u00d7 (-13)} \u00d7 27 = (-8) \u00d7 {(-13) \u00d7 27} (Associative law of mutliplication)
\n(xi) 13 \u00d7 (-6) = -(13 \u00d7 6) = -78
\n(xii) (-a) + b = b + additive inverse of a.
\n(xiii) When we divide a negative integer by a positive integer, we divide them as whole numbers and put a negative sign before the quotient.
\nquotient.
\n(xiv) When -25 is divided by (-5) the quotient is 5.
\n(xv) There are infinite pairs of integers satisfying a \u00f7 b = -1.
\n(xvi) The value of the expression ((-60) \u00f7 12) (-5) is 1.
\n{\u2235 \\(\\frac { -60 }{ 12 }\\) = -5 \u00f7 (-5) = \\(\\frac { -5 }{ -5 }\\) = 1}<\/p>\n
\nState whether the following statements are True (T) or False (F):
\n(i) For every integer a, |a| is either positive or zero.
\n(ii) The difference of two negative integers cannot be a positive integer.
\n(iii) We can write a pair of integers whose sum is not an integer.
\n(iv) Going 300 metres towards east first and then 100 m back is the same as going 100 m towards west first and then going 300 back.
\n(v) If we multiply an integer by (-1), then the result is the additive inverse of the integer.
\n(vi) If we divide an integer by (-1), then the result is the additive inverse of the integer.
\n(vii) 1 is the additive identity of integers.
\n(viii) (-17) \u00d7 6 is a whole number.
\n(ix) (-5) \u00d7 (-8) \u00d7 o is a positive integer.
\n(x) (-237) \u00d7 0 is same as 0 \u00d7 (-89).
\n(xi) The product of 5 negative integers is a negative integer.
\n(xii) Closure property holds for subtraction of integers.
\n(xiii) Commutative property does not hold for subtraction of integers.
\n(xiv) Associative property holds for subtraction of integers.
\n(xv) Closure property holds for division of integers.
\n(xvi) Commutative property does not hold for division of integers.
\n(xvii) (-1) is not a mutliplicative identity of integers.
\n(xviii) Multiplication fact (-8) \u00d7 (-12) = 96 is same as division fact 96 \u00f7 (-12) = -8.
\n(xix) [(-32 \u00f7 8] \u00f7 2 = (-32) \u00f7 (8 \u00f7 2)
\n(xx) For every integer a, a \u00f7 a = 1.
\n(xxi) The successor of 0 \u00d7 (-10) is 1 \u00d7 (-10).
\nSolution:
\n(i) For every integer a, |a| is either positive or zero. (True)
\n(ii) The difference of two negative integers cannot be a positive integer. (False)
\nCorrect:
\nDifference of -3 and -5 = -3 – (-5) = -3 + 5 = 2 which is positive
\n(iii) We can write a pair of integers whose sum is not an integer. (False)
\nCorrect:
\nAs sum of two integers is always an integer.
\n(iv) Going 300 metres towards east first and then 100 m back is the same as going 100 m towards west first and then going 300 back. (True)
\n(v) If we multiply an integer by (-1), then the result is the additive inverse of the integer. (True)
\n(vi) If we divide an integer by (-1), then the result is the additive inverse of the integer. (True)
\n(vii) 1 is the additive identity of integers. (False)
\nCorrect:
\n0 is a additive identity not 1.
\n(viii) (-17) \u00d7 6 is a whole number. (False)
\nCorrect:
\n(-17) \u00d7 6 = -102 is not a whole number as a whole numebr is zero or positive.
\n(ix) (-5) \u00d7 (-8) \u00d7 0 is a positive integer. (False)
\nCorrect:
\n(-5) \u00d7 (-8) \u00d7 0 which is neither positive nor-negative.
\n(x) (-237) \u00d7 0 is same as 0 \u00d7 (-89). (True)
\n(xi) The product of 5 negative integers is a negative integer. (True)
\n(xii) Closure property holds for subtraction of integers. (True)
\n(xiii) Commutative property does not hold for subtraction of integers. (True)
\n(xiv) Associative property holds for subtraction of integers. (False)
\nCorrect:
\nIt does not holds as
\n= 15 – 7 = 8
\n= 7 – 15 = -8
\nSo, 8 \u2260 (-8)
\n(xv) Closure property holds for division of integers. (False)
\nCorrect:
\nAs \\(\\frac { 15 }{ 5 }\\) = 3 but \\(\\frac { 5 }{ 15 }\\) = \\(\\frac { 1 }{ 3 }\\)
\nSo, 3 \u2260 \\(\\frac { 1 }{ 3 }\\)
\n(xvi) Commutative property does not hold for division of integers. (True)
\n(xvii) (-1) is not a mutliplicative identity of integers. (True)
\n(xviii) Multiplication fact (-8) \u00d7 (-12) = 96 is same as division fact 96 \u00f7 (-12) = -8. (True)
\n(xix) [(-32 \u00f7 8] \u00f7 2 = (-32) \u00f7 (8 \u00f7 2) (False)
\nCorrect:
\n[(-32) \u00f7 8} \u00f7 2 = -4 \u00f7 2 = -2
\nand (-32) \u00f7 (8 \u00f7 2) = -32 \u00f7 4 = -8
\nSo, it is false.
\n(xx) For every integer a, a \u00f7 a = 1. (False)
\nCorrect:
\nAs 0 \u00f7 0 \u2260 1
\n(xxi) The successor of 0 \u00d7 (-10) is 1 \u00d7 (-10). (False)
\nCorrect:
\nAs 0 \u00d7 (-10) = 0 and successor of 0 is 1 but 1 \u00d7 (-10) = -10<\/p>\n
\nState whether the following statements are true or false. Justify your answer.
\n(i) The sum of a positive integer and a negative integer is always a positive integer.
\n(ii) The sum of two integers is always greater than their difference.
\n(iii) For any two integers a and b, the inequality -a < b is always true.
\n(iv) The product of two integers is always greater than the sum of the integers.
\nSolution:
\n(i) The sum of a positive integer and a negative integer is always a positive integer. (False)
\nCorrect:
\nAs 3 + (-8) = 3 – 8 = -5 which is negative.
\n(ii) The sum of two integers is always greater than their difference. (False)
\nCorrect:
\nAs 3 + (-4) = -1 but 3 – (-4) = 3 + 4 = 7 and -1 < 7
\n(iii) For any two integers a and b, the inequality -a < b is always true. (False) Correct: Let a = -5 and b = 2, then -a = -(-5) = 5 and -a> b
\n(iv) The product of two integers is always greater than the sum of the integers. (False)
\nCorrect:
\nLet two integers be -2 and 3
\nThen product = -2 \u00d7 3 = -6
\nand sum = -2 + 3 = 1
\nBut -6 < 1
\nTheir product < Their sum.<\/p>\n
\nQuestion 4.
\nIf the integers 10, -7, 5, 3, -4 and 0 are marked on the number line, then the integer which lies on the extreme left is
\n(a) 10
\n(b) 0
\n(c) -7
\n(d) -4
\nSolution:
\nNumbers (Integers) 10, -7, 5, 3, -4 and 0 are marked on a number line.
\nThe integer on the extreme left will be -7. (c)<\/p>\n
\nOn the number line, the value of (-3) \u00d7 3 lies on the right hand side of
\n(a) -10
\n(b) -6
\n(c) 0
\n(d) 9
\nSolution:
\nValue of (-3) \u00d7 3 = -9 lies on the right side of-10 as (-10) < (-9) (a)<\/p>\n
\nThe vqlue of 5 \u00f7 (-1) does not lie between
\n(a) 0 and-10
\n(b) Oand 10
\n(c) -3 and -10
\n(d) -7 and 7
\nSolution:
\n5 \u00f7 (-1) = \\(\\frac { 5 }{ -1 }\\) = -5
\n-5 does not lie between 0 and 10
\nAs -5 is negative but 0 to 10 are positive integer.
\n0 and 10 (b)<\/p>\n
\nThe next number in the pattern -62, -37, -12, ……. is
\n(a) 25
\n(b) 0
\n(c) 13
\n(d) -13
\nSolution:
\n-62, -37, -12, …….
\nNext number is 0. (b)<\/p>\n
\nMultiplication of integers satisfies the property of
\n(a) closure
\n(b) commutativity
\n(c) associativity
\n(d) all of these
\nSolution:
\nMultiplication of integers satisfies the property of closure, commutative, associative i.e. all there properties. (d)<\/p>\n
\nClosure property does not hold in integers for
\n(a) multiplication
\n(b) division
\n(c) addition
\n(d) subtraction
\nSolution:
\nClosure property does not hold in the integers for the division. (b)<\/p>\n
\nThe number of integers between -20 and -10 are
\n(a) 8
\n(b) 9
\n(c) 10
\n(d) 11
\nSolution:
\nThe number of integers between -20 and -10 are 9
\n(-19, -18, -17, -16, -15, -14, -13, -12, -11) (b)<\/p>\n
\nIf the sum of two integers is -10 and one of them is 2, then the other is
\n(a) 8
\n(b) -8
\n(b) 12
\n(d) -12
\nSolution:
\nSum of two integers = -10
\nOne integers = 2,
\nthen Second integer will be = -10 – (2) = -12 (d)<\/p>\n
\nThe integer that must be subtracted from -5 to obtain -12 is
\n(a) 7
\n(b) -7
\n(c) 17
\n(d) -17
\nSolution:
\nThe integer will -12 if -5 is subtracted from that -5 – (……) = -12
\n12 – 5 = 7 (a)<\/p>\n
\nWhich of the following is not the additive inverse of a?
\n(a) -(-a)
\n(b) -a
\n(c) a \u00f7 (-1)
\n(d) a \u00d7 (-1)
\nSolution:
\nAdditive inverse of a is not a i.e. -(-a) (a)<\/p>\n
\n0 \u00f7 (-10) is equal to
\n(a) 0
\n(b) -1
\n(c) -10
\n(d) none of these
\nSol.
\n0 \u00f7 (-10) = \\(\\frac { 0 }{ -10 }\\) = 0 (a)<\/p>\n
\n(-33) \u00d7 102 + (-33) \u00d7 (-2) is equal to
\n(a) 3300
\n(b) -3300
\n(c) 3432
\n(d) -3432
\nSolution:
\n(-33) \u00d7 102 + (-33) \u00d7 (-2) = (-33) (102 – 2) = -33 \u00d7 100 = -3300 (b)<\/p>\n
\n(-25) (6 + 4) is not the same as
\n(a) -250
\n(b) (-25) \u00d7 10
\n(c) (-25) \u00d7 6 \u00d7 4
\n(d) (-25) \u00d7 6 + (-25) \u00d7 4
\nSolution:
\n(-25) (6 + 4) is not same as (-25) \u00d7 6 \u00d7 4
\n6 + 4 = 10 but 6 \u00d7 4 = 24 (c)<\/p>\n
\n101 \u00d7 (-1) + 0 \u00f7 (-1) is equal to
\n(a) -101
\n(b) 101
\n(c) -102
\n(d) 102
\nSolution:
\n101 \u00d7 (-1) + 0 \u00f7 (-1) = -101 + 0 = -101 (a)<\/p>\n
\nIf a and b are two integers, then which of the following may not be an integer?
\n(a) a + b
\n(b) a – b
\n(c) a \u00d7 b
\n(d) a \u00f7 b
\nSolution:
\na and b are two integers, then
\nBy closure proper a \u00f7 b is not an integer. (d)<\/p>\n
\nFor a non-zero integer a which is the following is not defined?
\n(a) a \u00f7 0
\n(b) 0 \u00f7 a
\n(c) a = 1
\n(d) 1 \u00f7 a
\nSolution:
\na is a non-zero integer, then
\na \u00f7 0 or \\(\\frac { a }{ 0 }\\) is not defined. (a)<\/p>\n
\nIn a competitive exam, 3 marks are given for every correct answer and 1 mark is deducted for every incorrect answer. Raju copied some answers from Reema and answered all the questions, he scored 20 marks though he got 10 correct answers. How many incorrect answers had he attempted? What values are promoted in the question?
\nSolution:
\nIn competitive exam
\n3 marks awarded for every correct answer.
\n1 mark is deducted for an incorrect answer.
\nRaju copied some answers from Reema.
\nHe scored 20 marks but he got 10 correct answers.
\nFor correct answer, his scores = 10 \u00d7 3 = 30
\nBut he scored 20 marks
\n30 – 20 = 10 marks were deducted
\nHe attempted 10 \u00f7 1 = 10 incorrect answers.
\nA student should not use unfair mean in the exam. It is a bad habit. He should work hard.<\/p>\n
\nIn a quiz, \u20b9 300 are awarded for every correct answer and a penalty of \u20b9 75 is put for every incorrect answer. Madhuri answered 15 questions out of which only 6 answers were correct. How much money is earned by Madhuri in the quiz?
\nIf she distributes the money earned by her to poor children in the neighborhood, what values are being promoted?
\nSolution:
\nIn a quiz,
\n\u20b9 300 are awarded for every correct answer.
\n\u20b9 75 is put as the penalty for every incorrect answer.
\nMadhuri scored 15 questions, but 6 questions were correct answers.
\nMoney earned for correct answer = 6 \u00d7 300 = \u20b9 1800
\nShe scored incorrect = 15 – 6 = 9
\nPenalty = \u20b9 75 \u00d7 9 = \u20b9 675
\nCorrect amount she got = \u20b9 1800 – \u20b9 675 = \u20b9 1125
\nSo, she got \u20b9 1125<\/p>\n
\nWrite a pair of integers whose product is -12 and there lies seven integers between them.
\nSolution:
\nProduct of two integers = -12
\nThe pairs can be possible
\n1 \u00d7 12, 2 \u00d7 6, 3 \u00d7 4
\nBut has 7 integers between them
\nThe pair can be -2 \u00d7 6 or -6 \u00d7 2
\nand seven integers between them will be
\n-1, 0, 1, 2, 3, 4, 5 or -5, -4, -3, -2, -1, 0, 1<\/p>\n
\nA water tank has steps inside it. A monkey is sitting on the first step. The water level is at the ninth step.
\n(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?
\n(ii) After drinking water, he wants to go back. For this, he jumps 5 steps up and then jumps back 3 steps down in every move. In how many jumps will he reach back the top of the tank?
\nSolution:
\nIn a tank,
\nMonkey is at first step and water level is at 9th step.
\n(i) Monkey jumps 3 steps down jumps back 2 steps
\nSo, he jumps 3 – 2 = 1 step in one attempt.
\n(ii) After drinking water, he jumps up 5 steps and then back 3 steps. So, he covers 2 steps in one jump.
\nSo, 9 – 5 = 4 + 1 = 5 jumps, he will come back at the first step of the tank.<\/p>\n
\nA shopkeeper earns a profit of \u20b9 2 by selling a pen and incurs a loss of 50 paise per pencil and loss of 15 paise per eraser while selling pencils and erasers of old stock. On a particular day, he earns a profit of \u20b9 10. If he sold 10 pens and the number of pencils and erasers he sold are in the ratio 7 : 10, then find the number of pencils and eraser she sold on that day.
\nSolution:
\nBy selling a pen, gain is \u20b9 2
\nand by selling a pencils, he loses 50 paise
\nand an eraser, he loses 15 paise
\nOn one day, he gains = \u20b9 10
\nOn that day he sold 10 pens and pencils and erasers in the ratio of 7 : 10
\nOn ten pens, his gain =10 \u00d7 2 = \u20b9 20
\nloss on penicls and erasers = \u20b9 20 – \u20b9 10 = \u20b9 10 = 1000 paise
\nRatio in pencil and erasers = 7 : 10
\nLet number of pencils = 7x, then eraser = 10x
\n7x \u00d7 50 + 10x \u00d7 15 = 1000
\n\u21d2 350x + 150x = 1000
\n\u21d2 500x = 1000
\n\u21d2 x = 2
\nNumber of pencils = 7 \u00d7 2 = 14
\nand number of erasers = 10 \u00d7 2 = 20<\/p>\nML Aggarwal Class 7 Solutions for ICSE Maths<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"