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 21 (2) Write the rational number that does not have a reciprocal () Out of the three rational numbers -1-20 and - 15 which is greater? (4) If the sum of both the horizontal and vertical rows are the same f ind the missing rational number 9 5 Choose correct answer(s) f rom given choice (5) What is the relation of 9 to -9 described as a Additive Inverse b Multiplicative Inverse c Multiplicative Identity d Reciprocal
() Which of the f ollowing is a positive integer and a rational number? ID : ae--rational-numbers [2] a 29 22 b 2 c -4 d 42 () If p q = m n then which of the f ollowing is always true: a p x n = m x q b p n = m q c p x m = n x q d n m = p q () If p q = p x m q x n then which of the f ollowing statements is always true? a m = 1 n b m = 1 c m = n d m = 0 (9) -1 0 is a positive rational number b negative rational number c neither positive nor negative rational number d either positive or negative rational number (10) The average of the middle two rational numbers if -9-5 10 1 10 are arranged in ascending order a 1 b -1 10 c -2 15 d -2 5 (11) Regarding rational numbers: A The quotient of two integers is always a rational number and B 1 0 is not a rational number Which of the f ollowing statements is correct? a Both A and B are f alse b A is correct but B is incorrect c A is f alse but B is a correct explanation of A d A is correct and B is correct explanation of A
(12) Which of the statements below is f alse? a All negative numbers can be represented as rational numbers c There is no f raction that cannot be represented as a rational number ID : ae--rational-numbers [] b A negative decimal number cannot be a rational number d There is no integer that cannot be represented as a rational number () How many rational numbers are there between any two non equal rational numbers? a 50000 b 51 c 0 d Inf inite Fill in the blanks (14) Find the multiplicative inverse of the f ollowing A) 11 B) 9 4 (15) Fill in the blank to make the two rational numbers equivalent A) 9 B) = = C) 1 = 0 90 D) 1 = 221 201 Edugain (wwwedugaincom) All Rights Reserved Many more such worksheets can be generated at wwwedugaincom
Answers ID : ae--rational-numbers [4] (1) 2 First of all write - 4-24 9 21 in simplest f orm like as: -2 1 1-2 1 Let s arrange the given numbers in ascending order we get: -2 1 1 1-2 Now the f irst number is the least number and the last number is the greatest number Greatest number = 2 Least number = -2 1 Thus the dif f erence between the greatest and the least number = 2 - -2 1 = 2
(2) 0 ID : ae--rational-numbers [5] 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 2 is 2 Now 0 is a rational number a (where a is non-zero integer) reciprocal of 0 a is a 0 which is not a rational number because denominator is not equal to zero(0) in rational numbers T heref ore rational number zero(0) does not have a reciprocal () - 20 Let's f irst ignore the negative sign of the numbers and check the order of absolute values of the f ractions We know that if numerator of f ractions are same f raction with smaller denominator is larger T heref ore > > 15 1 20 We also know that f or negative numbers number with higher absolute value is smaller - 15 Or - 15 < - 1 < -1 < - 20 < - 20 Theref ore - 20 is greater than other two given f ractions
(4) 12 ID : ae--rational-numbers [] Let the missing rational number be x Sum of the numbers in the horizontal row = = 5 Sum of the numbers in the vertical row = x 9 5 = x 2 Step 4 It is given that the sum of the horizontal row is same as the sum of the vertical row That is = x 9 5 5 = x 2 x = 5-2 x = 12 Step 5 Theref ore the missing rational number is 12
(5) a Additive Inverse ID : ae--rational-numbers [] If you look at the question caref ully you will notice that you have to f ind out the additive inverse of 9 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 9 is -9 Theref ore the additive inverse of 9 is -9 () d 42 Rational Number :- A rational number is a real number that can be written as a simple f raction f or example 1 is a rational number Integer :- An integer is a number that can be written without a f ractional component For example all positive and negative integers are { - -2-1 0 1 2 } If you look at the all options caref ully you will notice that 42 is a positive integer it can be written as 42 and hence 42 is a rational number 1 Now you can say that 42 is a positive integer and a rational number
() a p x n = m x q ID : ae--rational-numbers [] If you look at the question caref ully you will notice that you have the relation p q = m n You have p q = m n By cross multiply p x n = m x q Theref ore p x n = m x q is always true () c m = n 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) c neither positive nor negative rational number ID : ae--rational-numbers [9] 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 -1 is not a rational number because denominator of the rational numbers can not be 0 zero(0) Theref ore -1 0 is neither positive nor negative rational number
(10) b -1 10 ID : ae--rational-numbers [10] 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 and 10 = Now divide the LCM by the denominators and multiply the result with the numerator and denominator as f ollowing: -9 1-5 1 1 1 10 1 10 or -9-15 Step 4 Let s arrange the given numbers in ascending order we get: -15-9 Step 5 Now the average of the middle two rational numbers = -9 2 = = - -1 10 1 2 Step Thus the average of the middle two rational numbers is -1 10
(11) c A is f alse but B is a correct explanation of A ID : ae--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 1 0 0 rational number is not a Step 5 Theref ore A is f alse but B is a correct explanation of A
(12) b A negative decimal number cannot be a rational number ID : ae--rational-numbers [12] A rational number is a number which can be written in the f orm p q where p and q both are integers and q is not equal to zero All integers can be written in the f orm of p/1 (where p is any integer) Hence all integers are rational numbers Theref ore the statement "There is no integer that cannot be represented as a rational number" is true All f ractions are rational numbers as they are represented in p q f orm where p and q are integers T heref ore the statement "T here is no fraction that cannot be represented as a rational number" is true Step 4 All integers (-ve or ve) can be written in the f orm p/1 where p is the integer Theref ore the statement "All negative numbers can be represented as rational numbers" is true Step 5 A negative decimal number can be written in p/q f orm if digits af ter decimal are either terminating or repeating T heref ore the statement "A negative decimal number cannot be a rational number" is false Step The f alse statement is "A negative decimal number cannot be a rational number" and hence the correct answer is b () d Inf inite Rational Number: A rational number is a number that can be expressed as a f raction A rational number is said to have numerator and denominator For example: 2 or 15 5 2 or 25 rational numbers between these two rational numbers are 151 152 15 154 152 1 and so on upto inf inite T heref ore Infinite rational numbers are there between any two non equal rational numbers
ID : ae--rational-numbers [] (14) A) 11 11 Multiplicative Inverse: When we multiply a number by its "Multiplicative Inverse" we get 1 Mathematically n 1 n = 1 The multiplicative inverse of 11 is 11 since 11 11 = 1 B) 9 4 4 9 Multiplicative Inverse: When we multiply a number by its "Multiplicative Inverse" we get 1 Mathematically n 1 n = 1 The multiplicative inverse of 9 4 is 4 9 since 9 4 4 9 = 1 (15) A) 15 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 and 9 equivalent is 15
B) 4 ID : ae--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 multiply the numerator/denominator which is in the f ront of blank by the result Now the number which make the rational numbers and equivalent is 4 C) 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 and 0 equivalent is 1 90 14 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 equivalent is 1 221