Class 8 Rational Numbers
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1 ID : in-8-rational-numbers [1] Class 8 Rational Numbers For more such worksheets visit wwwedugaincom Answer t he quest ions (1) Consider the f ollowing statement a b + c d = c d + a b What property is being described here? () Write the rational number that are equal to its negative (3) Name the property that is ref lected in the f ollowing expression: A) = 1 B) = = 14 4 (4) Write the rational number that does not have a reciprocal (5) What is the smallest rational number that can be f ormed using of the numbers below in the f orm of p q? 599, 749, 368, 964, 50, 445 (6) How many total number of rational numbers are there between any two non equal rational numbers? (7) Find the 5 rational numbers between 4 13 and -6 8 Choose correct answer(s) f rom given choice (8) Which of the f ollowing statement is true? a -1 > - b - < -8 8 c - > -8 8 d - = -8 8 (C) 0 Edugain (wwwedugaincom)
2 ID : in-8-rational-numbers [] (9) A rational number equivalent to -4-5 is a 8-10 b 8 10 c d None of these (10) What is the relation of 9 to - 9 described as a Additive Inverse b Multiplicative Inverse c Multiplicative Identity d Additive Identity (11) Consider the f ollowing statement a b + ( c d + e f ) = ( a b + c d ) + a b What property is being described here? a Associative property b Inverse c Additive property d Commutative property (1) If 3-8 = -9 X, then X = a 4 b -4 c d None of these Fill in the blanks (13) Find the multiplicative inverse of the f ollowing A) -13 B) 1 (14) Fill in the blank to make the two rational numbers equivalent A) = B) C) D) = (C) 0 Edugain (wwwedugaincom)
3 ID : in-8-rational-numbers [3] (15) The rational number that are equal to their reciprocals are & 0 Edugain (wwwedugaincom) All Rights Reserved Many more such worksheets can be generated at wwwedugaincom (C) 0 Edugain (wwwedugaincom)
4 Answers ID : in-8-rational-numbers [4] (1) Commutative property If you look at the question caref ully, you will notice that you have the f ollowing statement a b + c d = c d + a b According to the statement the sum of a b and c d is equal to the sum of c d and a b Which is similar to the commutative property Commutative property states that order of addition does not matter for example : 3 + = = 5 T heref ore the property of the statement is commutative property () 0 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 Rational number zero(0) is the only rational number that is equal to its negative Theref ore zero(0) is the only rational number that is equal to its negative (C) 0 Edugain (wwwedugaincom)
5 (3) A) Multiplicative Inverse ID : in-8-rational-numbers [5] We have asked to f ind the property that ref lects in the f ollowing expression, 6 9 = Compare the expression with the a 1 a = 1 By comparing we f ind that a is 6 9 and 1 a is = T his property ref lects the multiplicative inverse Theref ore, = 1 ref lects the Multiplicative Inverse B) Multiplicative Identity We have asked to f ind the property that ref lects in the f ollowing expression, = = 14 4 Compare the expression with the a 1 = 1 a = a By comparing we f ind that a is 14 4 T his property ref lects the multiplication identity Theref ore, = = 14 4 ref lects the Multiplicative Identity (C) 0 Edugain (wwwedugaincom)
6 (4) 0 ID : in-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 3 is 3 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 (C) 0 Edugain (wwwedugaincom)
7 ID : in-8-rational-numbers [7] (5) 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 of the numbers below in the f orm of p q 599, 749, 368, 964, 50, 445 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 = 50 and q = Hence, the smallest rational number is 964 Theref ore, the smallest rational number that can be f ormed using of the numbers is (6) 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: 3 or 15, 5 or 5 rational numbers between these two rational numbers are 151, 15, 153, 154, 15, and so on upto inf inite T heref ore, Infinite rational numbers are there between any two non equal rational numbers (7) , , -3 08, -3 60, -3 31, (Answers can vary) (C) 0 Edugain (wwwedugaincom)
8 ID : in-8-rational-numbers [8] (8) d - = -8 8 Let's look at all the options and see which one is correct >, is the wrong statement, because f or negative numbers, number with higher -1 - absolute value is smaller - - > -8 8 = -, is the wrong statement Because the numbers are equal Step < -8 8 = -, is the wrong statement Because the numbers are equal Step = -8 8 = -, is the right statement Because the numbers are equal Step 6 Theref ore, the correct option is - = -8 8 (C) 0 Edugain (wwwedugaincom)
9 ID : in-8-rational-numbers [9] (9) b 8 10 If we multiply numerator and denominator of given f raction by, -4-5 = = = Theref ore, 8 10 is equivalent to -4-5 (10) a Additive Inverse 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 (C) 0 Edugain (wwwedugaincom)
10 (11) a Associative property ID : in-8-rational-numbers [10] If you look at the question caref ully, you will notice that the f ollowing statement is given a + ( c + e ) = ( a + c ) + e b d f b d f According to the statement sum of a b + ( c d + e f ) is equal to the sum of ( a b + c d ) + e f Which is equal to the associative property Associative property is states that if you are adding or multiplying it does not matter where you put the parenthesisin other words, associative property states that you can add or multiply regardless of how the numbers are grouped By 'grouped' we mean 'how you use parenthesis' For example : + (3 + 5) = ( + 3) = 10 T heref ore the property of above statement is associative property (1) a 4 According to the question, we have to f ind the value of X in the given equation: 3-8 = -9 X Now, 3 = -9-8 X 3 X = X = 7 X = 7 3 X = 4 Theref ore the value of X is 4 (C) 0 Edugain (wwwedugaincom)
11 ID : in-8-rational-numbers [11] (13) A) Multiplicative Inverse: When we multiply a number by its "Multiplicative Inverse", we get 1 Mathematically, n 1 n = 1 The multiplicative inverse of -13 is -13, since = 1 B) 1 1 Multiplicative Inverse: When we multiply a number by its "Multiplicative Inverse", we get 1 Mathematically, n 1 n = 1 The multiplicative inverse of 1 is 1, since 1 1 = 1 (14) A) 38 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 (C) 0 Edugain (wwwedugaincom)
12 B) 35 ID : in-8-rational-numbers [1] 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 14 and 56 equivalent is C) 57 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 D) 07 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 3 07 (15) 1-1 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 Rational numbers 1 and -1 are the only numbers which are equal to their reciprocals Theref ore rational numbers 1 and -1 are equal to their reciprocals (C) 0 Edugain (wwwedugaincom)
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