1 RATIONAL NUMBERS. Exercise Q.1. Using appropriate properties find: Ans. (i) (by commutativity)

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1 RATIONAL NUMBERS Exercise. Q.. Using appropriate properties find: 3 3 (i) (ii) Ans. (i) (by commutativity) (by distributivity)

2 (ii) (by commutativity) (by distributivity) Q.. Write the additive inverse of each of the following. (i) (ii) (iii) (iv) (v) Ans. (i) is the additive inverse of 8 8 because

3 (ii) (iii) 9 is the additive inverse of 9 because is the additive inverse of because (iv) (v) is the additive inverse of 9 because is the additive inverse of 9 because Q.3. Verify that ( x) x for: (i) x (ii) x Ans. (i) We have, x The additive inverse of x Since is x 3

4 The same equality + 0, shows that the additive inverse of or (ii) We have, x, i.e., ( x) x. 3 7 The additive inverse of x 3 7 Since The same equality , shows that the additive inverse of 3 7 or 3 3, i.e. ( x) x 7 7 is is x 3 7 is 3 7, Q.4. Find the multiplicative inverse of the following. (i) 3 (ii) 3 (iii) (iv) 7 Ans. (i) (v) 3 (ii) 7 3 (vi) is the multiplicative inverse of 3 is the multiplicative inverse of

5 (iii) (iv) (v) is the multiplicative inverse of is the multiplicative inverse of is the multiplicative inverse of (vi) is the multiplicative inverse of Q.. Name the property under multiplication used in each of the following. (i) (ii) (iii) 9 9 Ans. (i) is the multiplicative identity. So, the property used is property of multiplication. (ii) (iii) , i.e. a b b a Here, the property used is commutative property Here, property used is multiplicative inverse property.

6 Q.. Multiply 3 Ans. 7 by the reciprocal of 7. is the reciprocal of 7 product of 7 and 7 is., because the So, the required product Q.7. Tell what property allows you to compute as Ans. By associative property of multiplication We have, a (b c) (a b) c So by associative property of multiplication. We can complete Where a 3, b, c 4 3 Q.8. Is 8 9 the multiplicative inverse of? Why or 8 why not? Ans. No, because the product of 8 9 and

7 Q.9. Is 0.3 the multiplicative inverse of why not? Ans. Yes, 0.3 is the multiplicative inverse of ? Why or 3 3, because Q.0. Write. (i) The rational number that does not have a reciprocal. (ii) The rational numbers that are equal to their reciprocals. (iii) The rational number that is equal to its negative. Ans. (i) Zero is a rational number which has no reciprocal. (ii) and ( ) are the numbers which are equal to their reciprocals. (iii) Zero is the rational number which is equal to its negative. Q.. Fill in the blanks. (i) Zero has reciprocal. (ii) The numbers and are their own reciprocals. (iii) The reciprocal of is. (iv) Reciprocal of, where x 0 is. x (v) The product of two rational numbers is always a. (vi) The reciprocal of a positive rational number is. Ans. (i) Zero has no reciprocal. 7

8 (ii) The numbers and are their own reciprocals. (iii) The reciprocal of is. (iv) Reciprocal of, where x 0 is x. x (v) The product of two rational numbers is always a rational number. (vi) The reciprocal of a positive rational number is positive. Exercise. Q.. Represent these numbers on the number line. (i) 7 (ii) 4 Ans. (i) 7 means seven of four equal parts on the right of 0 on 4 the number line. (ii) means five of six equal parts on the left of 0 on the number line. 8

9 Q..Represent 9,, on the number line. 9 Ans. Location of rational numbers,, line are P, Q and R respectively. on the number 9 means, two of eleven equal parts on the left of 0. means, five of eleven equal parts on the left of 0. means, nine of eleven equal parts on the left of 0. Q.3. Write five rational numbers which are smaller than. Ans. Five rational numbers less than are,, 0,,. (Any number on the left of ) Because, number on the left side is always less than the number on the right side. Q.4. Find ten rational numbers between and. Ans. First convert and denominator. to rational numbers with the same 9

10 and Thus, we have 7 4 9,,, , - -, as the rational numbers between 8 and We can take any ten of these. Q.. Find five rational numbers between. (i) 4 3 and (ii) an d (iii) 3 3 Ans. (i) First convert and 3 same denominator. and and 4 to rational numbers with the Hence, the five rational numbers between 3 and 4 are: any five numbers between ,,,, (ii) First convert 3 and 3 same denominator. 4 47, 0 0 to rational numbers with the 0

11 and Hence, the five rational numbers between 3 and are: ,,,,. (Any five from and ) (iii) First convert and to rational numbers with the 4 same denominator and 3 Hence, the five rational numbers between and are : ,,,,. (Any five from and ) Q.. Write five rational numbers greater than. Ans. On a number line right side number is always greater than number on the left side. So five rational numbers greater than are 3, 0,, and of ). (Any five numbers on the right side

12 Q.7. Find ten rational numbers between 3 3 and 4. Ans. First convert 3 3 and to rational numbers with the same 4 denominator L.C.M of and 4 0. Convert the denominator with multiples of 0 i.e and Hence, the ten rational numbers between 3 3 and are any ten from,,,,,