1. Revision Description Reflect and Review Teasers Answers Recall of Rational Numbers:
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1 1. Revision Description Reflect Review Teasers Answers Recall of Rational Numbers: A rational number is of the form, where p q are integers q 0. Addition or subtraction of rational numbers is possible only when they have the same denominator. The Product of two rational numbers is obtained by multiplying the respective numerators denominators with each other. The Multiplicative Inverse or Reciprocal of a rational number is, where a b are non-zero integers. Dividing a rational number by another rational number is same as multiplying the dividend by the reciprocal of the divisor. 2. Properties of Rational Numbers To find the value of Since LCM of is 34, : 1) Reduce to stard form. 2) Find the product Description Reflect Review Teasers Answers Closure Property: 1. Addition: When two rational numbers are added, the sum is also a rational number. Hence, rational numbers are closed under addition. 2. Subtraction: When two rational numbers are subtracted, the difference is also a which is a which is a of 1) a) Multiply with additive inverse of. b) Add multiplicative inverse of ( ) 1) a) b) 1 2) a) b) 1) 2) 1
2 Hence, rational numbers are closed under subtraction. 2) a) What must be added to 3. Multiplication: When two rational numbers are multiplied, the product is also a Hence, rational numbers are closed under multiplication. 4. Division: When we divide two rational numbers except for division by zero (which is also a rational number), we get a So, rational numbers are not closed under division. But, if zero is excluded, we can say that the collection of other rational numbers is closed under division. which is a which is a to get the sum as zero? b) What must be multiplied to to get the product 1? Commutative Property: 1. Addition: For any two rational numbers a b, a + b b + a. Hence, addition of rational numbers is commutative. So, 2. Subtraction: For any two rational numbers a b, a - b b a. Hence, subtraction of rational numbers is not commutative. So, 3. Multiplication: For any two rational numbers a b, a b b a. Hence, multiplication of rational numbers is commutative. 4. Division: For any two rational numbers a b, So, 2
3 a b b a. Hence, division of rational numbers is not commutative. So, Associative Property: 1. Addition: For any three rational numbers a, b c, (a + b) + c a + (b + c). Hence, addition is 2. Subtraction: For any three rational numbers a, b c, (a b) c a (b c). Hence, subtraction is not 3. Multiplication: For any three rational numbers a, b c, (a b) c a (b c). Hence, multiplication is 4. Division: For any three rational numbers a, b c, (a b) c a (b c). Hence, division is not Additive Identity: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) For any rational number a, a a a. Hence, 0 is the additive identity for rational So, Multiplicative Identity: For any rational number a, 1 3
4 a 1 1 a a. Hence, 1 is the multiplicative identity for rational 1 So, Additive Inverse: If is a rational number, then there exists another rational number such that ( ) ( ) + + So, + + We say is the additive inverse of is the additive inverse of. Multiplicative Inverse: If is a (non-zero) rational number, then there exists a rational number, such that. So, We say is the multiplicative inverse or reciprocal of. Distributive Property: For all rational numbers a, b c, a ( b + c) (a b) + (a c) + ( ) ( ) ( ) So, + ( ) 4
5 3. Representation of Rational Numbers on the Number Line Description Rational numbers can be represented on the number line the same way as integers fractions. Reflect Review See below the table Teasers 1) Represent on the number line. Answers See below the table Reflect Review To represent on the number line Divide the whole number line between 0-1 into 7 equal parts the third point of division to the left of zero marked as A represents. A Answers 1) P
6 4. Rational Numbers between Two Rational Numbers Description Reflect Review Teasers Answers There are infinitely many rational numbers between two given rational To find 5 rational number between : Convert both the numbers into rational numbers with same denominator. LCM of 5 3 is 15. So, The rational numbers between are 1) Write 5 rational numbers between ) We can take any five of them as the solution. To find 3 rational numbers between 2 1: The mean of two rational numbers a b is given by. Here a -2, b 1 Mean Now, we can find the mean of -2. Mean [ ( )] ( ) Next, we can find the mean of. Mean [( ) ( )] ( ) ( ) 6
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