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(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.

Answer :

(i) The rational number 0 has no reciprocal because there is no rational number which when multiplied with 0, gives 1.

(ii) We know that the reciprocal of 1 is 1 and the reciprocal of -1 is -1. Thus,1 and -1 are the only rational numbers which are their own reciprocals.

(iii) 0 is the rational number which equal to its negative.

- \( \frac{-2}{3} \)*\( \frac{3}{5} \)+\( \frac{5}{2} \)-\( \frac{3}{5} \)*\( \frac{1}{6} \)
- 1.Using appropriate properties find: (i)\(-\frac{2}3×\frac{3}5+\frac{5}2-\frac{3}5×\frac{1}6 \) (ii)\(\frac{2}5×(-\frac{3}7)-\frac{1}6×\frac{3}2+\frac{1}{14}×\frac{2}5 \)
- 2.Write the additive inverse of each of the following: (i)\(\frac{2}8 \) (ii)\(\frac{-5}9 \) (iii)\(\frac{-6}{-5} \) (iv)\(\frac{2}{-9} \) (v)\(\frac{19}{-6} \)
- 3.verify that -(-x)=x for (i)x=\(\frac{11}{15}\) (ii)x=\(\frac{-13}{17}\)
- 4.Find the multiplicative inverse of the following : (i)-13 (ii)\(\frac{-13}{19}\) (iii)\(\frac{1}5\) (iv)\(\frac{-5}8×\frac{-3}{7}\) (v)\(-1×\frac{-2}5\) (vi)-1
- 5.Name the property under multiplication used in each of the following: (i)\(\frac{-4}5×1=1×\frac{-4}5=\frac{-4}5\) (ii)\(\frac{-13}{17}×\frac{-2}7=\frac{-2}7×\frac{-13}{17}\) (iii)\(\frac{-19}{29}×\frac{29}{-19}=1\)
- 6.Multiply \(\frac{6}{13}\) by the reciprocal of \(\frac{-7}{16}\)
- 7.Tell what property allows you to compute \(\frac{1}3×(6×\frac{4}3)as (\frac{1}3×6)×\frac{4}3\)
- 8.Is \(\frac{8}9\) the multiplicative inverse of \(-1\frac{1}8\)? Why or why not?
- 9. Is 0.3 the multiplicative inverse of \(3\frac { 1 }{ 3 }\)? Why or why not?
- 11.Fill in the blanks : (i) Zero has ……………. reciprocal. (ii) The numbers ……………. and ………. are their own reciprocals. (iii) The reciprocal of – 5 is ……………. (iv) Reciprocal of \(\frac { 1 }{ x }\) , where \(x\neq 0\) is ……… (v) The product of two rational numbers is always a …………. (vi) The reciprocal of a positive rational number is ………..

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