## Chapter 1 Rational Numbers Exercise 1.1

**Question 1: Using appropriate properties find.**

(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6

Answer:

(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6

Answer:

= (-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**

Answer:

Answer:

= [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

Answer:Additive inverse of 2/8 is – 2/8

(i) 2/8

Answer:

**(ii) -5/9**

Answer:Additive inverse of -5/9 is 5/9

Answer:

**(iii) -6/-5 = 6/5**

Answer:Additive inverse of 6/5 is -6/5

Answer:

**(iv) 2/-9 = -2/9**

Answer:Additive inverse of -2/9 is 2/9

Answer:

**(v) 19/-16 = -19/16**

Answer:Additive inverse of -19/16 is 19/16

Answer:

**Question 3: Verify that: -(-x) = x for.**

(i) x = 11/15

Answer:

(i) x = 11/15

Answer:

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**

Answer:

Answer:

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

Answer:-1/13

(i) -13

Answer:

**(ii) -13/19**

Answer:-19/13

Answer:

**(iii) 1/5**

Answer:5

Answer:

**(iv) -5/8 × (-3/7)**

Answer:56/15

Answer:

**(v) -1 × (-2/5)**

Answer:5/2

Answer:

**(vi) -1**

Answer:-1

Answer:

**Question 5: Name the property under multiplication used in each of the following.**

(i) -4/5 × 1 = 1 × (-4/5) = -4/5

Answer:1 is multiplicative identity.

(i) -4/5 × 1 = 1 × (-4/5) = -4/5

Answer:

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

Answer:Commutativity

Answer:

**(iii) -19/29 × 29/-19 = 1**

Answer:Multiplicative inverse

Answer:

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

Answer:

Answer:

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**

Answer:Associativity

Answer:

**Question 8: Is 8/9 the multiplication inverse of 1 1/8? Why or why not?**

Answer:No, 8/9 is no the multiplicative inverse of -1 1/8 because 8/9 × -7/8 ≠ 1

Answer:

**Question 9: If 0.3 the multiplicative inverse of 3 1/3? Why or why not?**

Answer:Yes, 0.3 is the multiplicative inverse of 3 1/3 because 3/10 × 10/3 = 30/30

Answer:

**Question 10: Write**

(i) The rational number that does not have a reciprocal.

Answer:0

(i) The rational number that does not have a reciprocal.

Answer:

**(ii) The rational numbers that are equal to their reciprocals.**

Answer:1 and (-1)

Answer:

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

Answer:0

Answer:

**Question 11: Fill in the blanks.**

(i) Zero has

(i) Zero has

__no__

**reciprocal.**

(ii) The numbers

(ii) The numbers

__1__

**and**

__-1__

**are their own reciprocals**

(iii) The reciprocal of -5 is

(iii) The reciprocal of -5 is

__5__

**.**

(iv) Reciprocal of 1/x, where x ≠ 0 is

(iv) Reciprocal of 1/x, where x ≠ 0 is

__x__

**.**

(v) The product of two rational numbers is always a

(v) The product of two rational numbers is always a

__rational number__

**.**

(vi) The reciprocal of a positive rational number is

(vi) The reciprocal of a positive rational number is

__positive__

**.**

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