its not right answerbut may help u in giving idea if its not helpful plz dont blame or report mebcaz atleast i triedStep-by-step explanation:Exercise 1.1Question 1:Using appropriate properties, find:(i) -2/3 * 3/5 + 5/2 – 3/5 * 1/6 (ii) 2/5 * (3/-7) – 1/6 * 3/2 + 1/14 * 2/5Answer:(i) -2/3 * 3/5 + 5/2 – 3/5 * 1/6 = -2/3 * 3/5 – 3/5 * 1/6 + 5/2 [Using associative property] = 3/5 * (-2/3 – 1/6) + 5/2 [Using distributive property] = 3/5 * {(-4 - 1)/6} + 5/2 [LCM (3, 2) = 6] = 3/5 * (-5/6) + 5/2 = -3/6 + 5/2 = -1/2 + 5/2 = (-1 + 5)/2 = 4/2 = 2 (ii) 2/5 * (3/-7) – 1/6 * 3/2 + 1/14 * 2/5 = 2/5 * (-3/7) + 1/14 * 2/5 – 1/6 * 3/2 [Using associative property] = 2/5 * (-3/7 + 1/14) – 1/2 * 1/2 [Using distributive property] = 2/5 * {(-6 + 1)/14} – 1/4 [LCM (7, 14) = 14] = 2/5 * (-5/14) – 1/4 = -1/7 – 1/4 = (-4 -7)/28 [LCM (7, 4) = 28] = -11/28Question 2:Write the additive inverse of each of the following:(i) 2/8 (ii) -5/9 (iii) -6/-5 (iv) 2/-9 (v) 19/-6Answer:We know that additive inverse of a rational number a/B is (-a/b) such that a/b + (-a/b) = 0(i) Additive inverse of 2/8 = -2/8 (ii) Additive inverse of -5/9 = 5/9 (iii) -6/-5 = 6/5Additive inverse of 6/5 = -6/5 (iv) 2/-9 = -2/9Additive inverse of -2/9 = 2/9 (v) 19/-6 = -19/6Additive inverse of -19/6 = 19/6Question 3:Verify that -(-x) = x for:(i) x = 11/15 (ii) x = -13/17Answer:(i) Putting x = 11/15 in -(-x) = x, we get=> -(-11/15) = 11/15=> 11/15 = 11/15=> LHS = RHSHence, verified.(i) Putting x = -13/17 in -(-x) = x, we get=> -{-(-13/17)} = -13/17=> -(13/17) = -13/17=> -13/17 = -13/17=> LHS = RHSHence, verified.Question 4:Find the multiplicative inverse of the following:(i) -13 (ii) -13/19 (iii) 1/5 (iv) (-5/8)*(-3/7) (v) -1 * (-2/5) (VI) -1Answer:We know that multiplicative inverse of a rational number a is 1/a such that a * 1/a = 1(i) Multiplicative inverse of -13 = -1/13 (ii) Multiplicative inverse of -13/19 = -19/13 (iii) Multiplicative inverse of 1/5 = 5 (iv) (-5/8)*(-3/7) = (5 * 3)/(8 * 7) = 15/56Multiplicative inverse of 15/56 = 56/15 (v) -1 * (-2/5) = 2/5Multiplicative inverse of 2/5 = 5/2 (vi) Multiplicative inverse of -1 = 1/-1 = -1Question 5:Name the property under multiplication used in each of the following:(i) -4/5 * 1 = 1 * -4/5(ii) -13/17 * -2/7 = -2/7 * -13/17(iii) -19/29 * 29/-19 = 1Answer:(i) 1 is the multiplicative identity.(ii) Commutative property.(iii) Multiplicative Inverse property.Question 6:Multiply 6/13 by the reciprocal of -7/16Answer:The reciprocal of -7/16 = -16/7Now, 6/13 * (-16/7) = -(6 * 16)/(13 * 7) = -96/91Question 7:Tell what property allows you to compute 1/3 * (6 * 4/3) as (1/3 * 6) * 4/3Answer:By using associative property of multiplication, a * (b * c) = (a * b) * cQuestion 8:Is 8/9 the multiplicative inverse of -1? Why or why not?Answer:SINCE multiplicative inverse of a rational number a is 1/a if a * 1/a = 1Therefore, 8/9 * (-1) = 8/9 * -9/8 = -1But its product must be positive.So, 8/9 is not multiplicative inverse of (-1)Question 9:Is 0.3 the multiplicative inverse of 3? Why or why not?Answer:Since multiplicative inverse of a rational number a is 1/a if a * 1/a = 1Therefore, 0.3 * 3 = 3/10 * 10/3 = (3 * 10)/(10 * 3) = 30/30 = 1So, 0.3 is the multiplicative inverse of 3Question 10: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.Answer:(i) 0 (ii) 1 and -1 (iii) 0Question 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 1/x where x ≠ 0 is _______________.(v) The product of two rational numbers is always a _______________.(vi) The reciprocal of a positive rational number is _______________.Answer:(i) No (ii) 1, -1 (iii) -1/5 (iv) x(v) Rational Number (vi) Positive rational number