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## Chapter 1 Rational Numbers Exercise 1.1

Question 1: Using appropriate properties find.
(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6

= (-2/3 × 3/5) + 5/2 - (3/5 × 1/6)
= -6/15 + 5/2 - 3/30
= -2/5 + 5/2 - 1/10
LCM of 2, 5 = 10
= -2/5 × 2/2 = -4/10, 5/2 × 5/5 = 25/10
= -4/10 + 25/10 = -4 + 25/10 = 21/10
= 21/10 - 1/10 = 21 - 1/10 = 20/10 = 2

(ii) 2/5 × (-3/7) - 1/6 × 3/2 + 1/14 × 2/5

= [2/5 × (-3/7)] - [1/6 × 3/2] + [1/14 × 2/5]
= -6/35 - 3/12 + 2/70
= -6/35 - 1/4 + 1/35
LCM of 4, 35, 35 = 120
= -6/35 × 4/4 = -24/120, 1/4 × 35/35 = 35/120, 1/35 × 4/4 = 4/120
= -24/120 - 35/120 + 4/120 = -24 - 35 + 4/120 = -55/120 = -11/28

Question 2: Write the additive inverse of each of the following
(i) 2/8
Additive inverse of 2/8 is – 2/8

(ii) -5/9
Additive inverse of -5/9 is 5/9

(iii) -6/-5 = 6/5
Additive inverse of 6/5 is -6/5

(iv) 2/-9 = -2/9
Additive inverse of -2/9 is 2/9

(v) 19/-16 = -19/16
Additive inverse of -19/16 is 19/16

Question 3: Verify that: -(-x) = x for.
(i) x = 11/15

x = 11/15, -x = -11/15
= 11/15 + (-11/15) = 0
-x = -(-11/15), x = 11/15
= -(-11/15) + 11/15 = 0
Therefore, -(-x) = x.

(ii) x = -13/17

x = -13/17, -x = 13/17
= (-13/17) + 13/17 = 0
-x = 13/17, x = -13/17
= 13/17 + (-13/17) = 0
Therefore, -(-x) = x.

Question 4: Find the multiplicative inverse of the
(i) -13
-1/13

(ii) -13/19
-19/13

(iii) 1/5
5

(iv) -5/8 × (-3/7)
56/15

(v) -1 × (-2/5)
5/2

(vi) -1
-1

Question 5: Name the property under multiplication used in each of the following.
(i) -4/5 × 1 = 1 × (-4/5) = -4/5
1 is multiplicative identity.

(ii) -13/17 × (-2/7) = -2/7 × (-13/17)
Commutativity

(iii) -19/29 × 29/-19 = 1
Multiplicative inverse

Question 6: Multiply 6/13 by the reciprocal of -7/16

Reciprocal of -7/16 = 16/-7 = -16/7
= 6/13 × (-16/7) = -96/91

Question 7: Tell what property allows you to compute 1/3 × (6 × 4/3) as (1/3 × 6) × 4/3
Associativity

Question 8: Is 8/9 the multiplication inverse of 1 1/8? Why or why not?
No, 8/9 is no the multiplicative inverse of -1 1/8 because 8/9 × -7/8 ≠ 1

Question 9: If 0.3 the multiplicative inverse of 3 1/3? Why or why not?
Yes, 0.3 is the multiplicative inverse of 3 1/3 because 3/10 × 10/3 = 30/30

Question 10: Write
(i) The rational number that does not have a reciprocal.
0

(ii) The rational numbers that are equal to their reciprocals.
1 and (-1)

(iii) The rational number that is equal to its negative.
0

Question 11: Fill in the blanks.
(i) Zero has
no reciprocal.
(ii) The numbers
1 and -1 are their own reciprocals
(iii) The reciprocal of -5 is
5.
(iv) Reciprocal of 1/x, where x ≠ 0 is
x.
(v) The product of two rational numbers is always a
rational number.
(vi) The reciprocal of a positive rational number is
positive.