Grade 8 Rational Numbers

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Jasmine Blankenship
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1 ID : sg-8-rational-numbers [1] Grade 8 Rational Numbers For more such worksheets visit wwwedugaincom Answer t he quest ions (1) Is 003 the multiplicative inverse of ? Why or why not? (2) What is the smallest rational number that can be f ormed using 2 of the numbers below in the f orm of p q? (3) if -2 X = X 2 then X is a rational number (4) Find the 6 rational numbers between -5 8 and 3 10 (5) Reduce the rational number to the lowest f orm (6) If p q = p x m q x n then what is the relation between m and n? (7) What is the additive inverse of 8 5? (8) What is the value of? = 1 Choose correct answer(s) f rom given choice () Which property is ref lected by this expression = -10 ( -10 ) a Multiplicative Inverse b Distributive Property c Commutative Property d Multiplicative Identity

2 (10) Regarding rational numbers: A The quotient of two integers is always a rational number and ID : sg-8-rational-numbers [2] B 1 0 is not a rational number Which of the f ollowing statements is correct? a A is correct but B is incorrect b A is f alse but B is a correct explanation of A c Both A and B are f alse d A is correct and B is correct explanation of A (11) Which of the f ollowing statements is f alse: a Any rational number when multiplied by 2 is a rational number b Every rational number is an integer c Every negative number is a rational number d Every integer is a rational number () Which of the f ollowing is a rational number(s)? a 5-11 b -2 8 c d All of these (13) Which of the f ollowing statements is true f or a rational number a b a The denominator b cannot be a prime number b The denominator b cannot be 0 c The numerator a can be a decimal number d The denominator b can be a decimal number Fill in the blanks (14) The average of the middle two rational numbers if are arranged in ascending order is (15) Fill in the blank to make the two rational numbers equivalent A) 10 = 140 B) = 104 C) = 200 D) 13 = 54 78

4 Answers ID : sg-8-rational-numbers [4] (1) Yes - The product or f raction and its multiplicative inverse must be equal to 1 When we multiply a number by its Multiplicative Inverse we get 1 For example x 1 x = 1 [It means 1 x is a multiplicative inverse of x] According to the question we have to prove that 003 is the multiplicative inverse of To prove this we have to multiply the given number to the given multiplicative inverse and check if result is 1 or not Product = = = 1 It satisf ies the condition of product being equal to 1 Theref ore 003 is the multiplicative inverse of

5 ID : sg-8-rational-numbers [5] (2) 8 6 If you look at the question caref ully you will notice that you have to f ind out the value of smallest rational number that can be f ormed using 2 of the numbers below in the f orm of p q Rational number: A rational number is a number that can be written as a ratio That means it can be written as a f raction in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers For smallest rational number numerator (p) is the smallest number and denominator (q) is the largest number Now p = 8 and q = 6 8 Hence the smallest rational number is 6 Theref ore the smallest rational number that can be f ormed using 2 of the numbers is 8 6

6 (3) not ID : sg-8-rational-numbers [6] Rational numbers: A rational number is any number that can be expressed as the quotient or f raction p/q of two integers p and q with the denominator q not equal to zero Since q may be equal to 1 every integer is a rational number For example: reciprocal of p q is q p If you look at the question caref ully you will notice that you have -2 X = X 2 Now -2 X = X = X X -4 = X 2 X = -4-4 is not a rational number Theref ore X is not a rational number if -2 X = X 2 (4) (Answers can vary)

7 (5) 5 ID : sg-8-rational-numbers [7] 8 If you look at the question caref ully you will notice that the given number is Now Divide both numerator and denominator by 4 = 5 8 Theref ore the lowest f orm of rational number is 5 8

8 (6) m = n ID : sg-8-rational-numbers [8] If you look at the question caref ully you will notice that you have the relation p q = p x m q x n Now p q = p x m q x n p (q n) = q (p m) (p q) n = (q p) m n m = p q q p n m = p q p q n = 1 m n = m or m = n Theref ore the relation between m and n is m = n

9 (7) -8 ID : sg-8-rational-numbers [] 5 If you look at the question caref ully you will notice that you have to f ind out the additive inverse of 8 5 Additive inverse: The Additive Inverse of a number is the opposite of the number A number and its opposite add up to give zero They are called additive inverses of each other So by the help of def inition the additive inverse of 8 5 is -8 5 Theref ore the additive inverse of 8 5 is -8 5 (8) 2 According to question = = 1 1 = = = 1 = Now the value of is 2

10 () b Distributive Property ID : sg-8-rational-numbers [10] We have asked to f ind the property that ref lects in the f ollowing expression = -10 ( -10 ) Compare the expression with the a b a c = a(b c) By comparing we f ind that a b and c are and respectively a b a c = = a(b c) = -10 ( -10 ) = -10 ( ) 00 = 2376 T his property ref lects the distributive property Theref ore = -10 ( -10 ) ref lects the Distributive Property

11 (10) b A is f alse but B is a correct explanation of A ID : sg-8-rational-numbers [11] Rational Numbers: A rational number is a number that can be expressed as a f raction A rational number said to have numerator and denominator Condition f or rational number: The quotient of two integers is always a rational number provided the denominator is non-zero According to the condition of rational numbers the f irst statement that the quotient of the two integers is always a rational number is not satisf ied that is statement is f alse Step 4 1 is the example against the condition of rational numbers Theref ore rational number is not a Step 5 Theref ore A is f alse but B is a correct explanation of A (11) b Every rational number is an integer A rational number is a number that can be written as a ratio For example a/b where a and b are whole numbers All prime numbers are All natural numbers are All integers are Now you can say that the statement 'Every rational number is an integer' is f alse

12 () d All of these ID : sg-8-rational-numbers [] Rational numbers: A rational number is any number that can be expressed as the quotient or f raction p q of two integers p and q with the denominator q not equal to zero Now -2 8 is the rational number with p = -2 and q = is the rational number with p = 5 and q = -11 is the rational number with p = 5 and q = -14 Theref ore the correct option is the all of these (13) b The denominator b cannot be 0 If you look at the question caref ully you will notice that the given rational number is a b Definition of rational number : Rational numbers are terminating or recurring decimal numbers written in the f orm of f raction p q in which 'p' and 'q' are integers and the denominator 'q' not equal to zero Here denominator is b By the def inition denominator b cannot be zero Theref ore the correct answer is the denominator b cannot be 0

13 (14) 1 5 ID : sg-8-rational-numbers [13] To compare f ractions f irst we need to make sure that all denominators are same so we can just compare the numerators of f ractions The LCM of the denominators 10 6 and 2 = Now divide the LCM by the denominators and multiply the result with the numerator and denominator as f ollowing: or Step 4 Let s arrange the given numbers in ascending order we get: Step 5 Now the average of the middle two rational numbers = 3 2 = 1 2 = 1 5 Step 6 Thus the average of the middle two rational numbers is 1 5

14 (15) A) 17 ID : sg-8-rational-numbers [14] To make the two rational numbers equivalent f irst of all divide the given greatest numerator/denominator by the smallest numerator/denominator and divide the numerator/denominator which is in the f ront of blank by the result Now the number which make the rational numbers 10 and 140 equivalent is B) 24 To make the two rational numbers equivalent f irst of all divide the given greatest numerator/denominator by the smallest numerator/denominator and multiply the numerator/denominator which is in the f ront of blank by the result 6 Now the number which make the rational numbers and equivalent is C) 1 To make the two rational numbers equivalent f irst of all divide the given greatest numerator/denominator by the smallest numerator/denominator and multiply the numerator/denominator which is in the f ront of blank by the result Now the number which make the rational numbers 13 and equivalent is D) To make the two rational numbers equivalent f irst of all divide the given greatest numerator/denominator by the smallest numerator/denominator and divide the numerator/denominator which is in the f ront of blank by the result Now the number which make the rational numbers and 54 equivalent is 13 78

Grade 8 Rational Numbers

Grade 8 Rational Numbers ID : ae--rational-numbers [1] Grade Rational Numbers For more such worksheets visit wwwedugaincom Answer t he quest ions (1) Find the dif f erence between the greatest and the least numbers of - 4-24 9