Rational Numbers Practice Questions and Step-by-Step Solutions

1) Write the following rational numbers in the standard form a) 8 −36 b) ) 68 −119 c) ) 91 −78 d) ) −36 27 2) Which of the following are equivalent a) −13 7 , 39 −21 b) ) 3 −8 , −6 16 c) 9 4 , −36 16 3) Write the additive inverse of the following a) 3 −8 b) −19 16 c) −3 −8 d) 17 21 4) Write the reciprocal of the following a) -16 b) −13 19 c) 3 −7 × 4 9 d) -1× −2 5 5) Verify the property (a x b) x c = a x ( b x c) by taking a= −3 7 , b= 7 12 , c= −6 16 6) Verify the property x × (y + z) = x × y + x × z for x = −5 4 , y = −16 7 , z = -5 7) Verify the following a) −2 5 + [ 3 4 + −7 10 ] = [ −2 5 + 3 4 ] + −7 10 8) Using suitable property solve the following a) 2 3 + −4 5 + −2 3 + −11 15 b) −6 15 × 4 7 - −7 20 × 4 7 + 3 4 c) 5 4 × −3 7 + 5 4 × 9 13 9) Find 5 rational numbers which lies between a) −1 3 and 2 5 b) 1 4 and 1 2 c) -2 and -1 10) Solve: a) The product of two rational numbers is −40 3 . If one of them is −5 2 , find the other. b) By what rational number should we multiply11 5 to get −33 25 ? **************