Rational Numbers

Give an example of each, of two irrational numbers whose: (i) difference is a rational number. (ii) difference is an irrational number. (iii) sum is a rational number. (iv) sum is an irrational number. (v) product is a rational number. (vi) product is an irrational number. (vii) quotient is a rational number. (viii) quotient is an irrational number.

Fill in the blanks : (i) The product of two positive rational numbers is always……………...(ii) The product of two negative rational numbers is always …………… (iii) If two rational numbers have opposite signs then their product is always ………….. (iv) The reciprocal of a positive rational number is ………. and the reciprocal of a negative raitonal number is …………… (v) Rational number 0 has ………….. reciprocal. (vi) The product of a rational number and its reciprocal is ……….. (vii) The numbers ……….. and ……….. are their own reciprocals. (viii) If m is reciprocal of n, then the reciprocal of n is …………

Show that (-216)/(42875) is the cube of a rational number. Also find the rational number.

Fill in the blanks : The product of two positive rational number is always .. The product of a positive rational number and a negative rational number is always .... The product of two negative rational numbers is always ...... The reciprocal of a positive rational number is ...... The reciprocal of a negative rational number is ...... Zero has .... reciprocal The product of rational number and its reciprocal is ....... The numbers.... and .... are their own reciprocal If a is reciprocal of b, then the reciprocal of b is .... The number 0 is .... the reciprocal of any number. Reciprocal of 1/a , a\ !=0\ i s ddot (17 x 12)^(-1)=17^(-1)x

Every rational number is ?

Every rational number is a fraction.

Every rational number is an integer.

If tanalpha=sqrt(a) , where a is a rational number whch is not a perfect square, then which of the following is a rational number?

Fill in the blanks : (iv) The reciprocal of a positive rational number is…………..and the reciprocal of a negative rational number is……………….

In each of the following state if the statement is true (T) or false (F): (i) The quotient of two integers is always an integer. (ii) Every integer is a rational number. (iii) Every rational number is an integer. (iv) Every fraction is a rational number. (v) Every rational number is a fraction. (vi) If a/b is a rational number and m any integer, then a/b=(axxm)/(bxxm) (vii) Two rational numbers with different numerators cannot be equal. (viii) 8 can be written as a rational number with any integer as denominator. (ix) 8 can be written as a rational number with any integer as numerator. (x) 2/3 is equal to 4/6dot