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\ 06-Jan-2025 Surender Singh Routhan Proof-2 Reader’s Sign _______________________ Date __________

Answers

Chapter 1: Rational Numbers Practice Time 1C
Let’s Recall 1. (a) 7 (b) 1 (c) −13 (d) 29
72
1. (a) 7 (b) 0 (c) −3 (d) 14 8 −2 10 17 28
−33
−3
1 1 1 1 2. (a) (b) (c) (d)
40
2. (a) 8 (b) 1 (c) 10 (d) 124 15 43 42 8
4
−1
3. (a) 4. (a) (b) (c)
–1 0 3 1 5 88 12
5 5. (a) −47 (b) 23 (c) 1
(b) 72 72 6
–1 −7 0 1 Think and Answer
10 2,272.5 km
(c) Think and Answer
–1 0 2 1
7 1 and (–1)
(d) Practice Time 1D
0 1 2 11 3 1. (a) 1 (b) −1 (c) −2 (d) 3
5 8 3 3 4
7 1 −8
4. (a) 1 (b) (c) (d) 13 22 1
48 25 3 2. (a) −13 18 (b) 8 (c) −1 35 (d) −16 2
Think and Answer
P = −9 , Q = 11 , R = −8 3. (a) −11 (b) 27
24
5 7 3
Practice Time 1A 4. (a)   −13   (b) (–19) (c) 11 (d)   −35  
1. (a) 12 (b) −16 (c) 28 (d) −8  9  9  16 
15 −20 35 −10 5. (a) 6 (b) 2 (c) −105
2. No, since in the standard form of a rational number, the denominator is 7 11 44
always positive. 6. (a) Commutative Property (b) Associative Property
3. (c) Multiplicative Inverse (d) Distributive Property
–1 −3 0 1 1 −8 −5 −1
8 4 10. (a) 5 ; Reciprocal = 8 (b) 6 ; Reciprocal = –6
4. ; 2 3
–3 −12 –2 –1 0 1 2 12 3 (c) 3 ; Reciprocal = 2
5 5
Yes, these points are equidistant. Practice Time 1E
5. (a) = (b) > (c) < (d) < 1. (a) −5 (b) 22 (c) 11 (d) −1
1
1
6. (a) −7 < 1 < < 3 (b) −4 < −7 << 2 2 − 15 20 10
11 4 3 5 5 11 7 5 2. (a) −77 (b) 25 (c) −5
1 3 − 3 − 9 2 1 7 − 4 90 28 28
7. (a) 1 > > > (b) 1 > 1 > >
3 4 5 11 5 7 11 5 3. (a) −4 (b) 1
8. 17 39 11 49 27 (Answer may vary) 15 6
,
,
,
,
96 192 48 192 96 4. (a) 4 (b) 10 5. −2
9. 1.225, 1.25, 1.275 (Answer may vary) 5 5
10. −2 , −1 , −1 , −1 0 ,, 1 , 1 , 1 , 1 , 2 (Answer may vary) Practice Time 1F
21 21 14 28 56 28 14 21 21 11 5 5 5 2
Quick Check 1. 5 60 hours 2. 19 12 kg 3. 304 12 km 4. 45 16 m
−2 24 −9
1. Additive Identity: 0; Additive Inverse: 5. 6. 84 7.
3 49 14
2
2. Additive Identity: 0; Additive Inverse: 3 8. 218 2 km/h; 3 hours
7 11 3
4 Brain Sizzlers
3. Additive Identity: 0; Additive Inverse:
7 260 630
−3 1. 2.
4. Additive Identity: 0; Additive Inverse: 49 13
Practice Time 1B 7 Chapter Assessment
−1 −11 5 −17 A. 1. (a) 2. (d) 3. (c) 4. (b) 5. (a)
1. (a) (b) (c) (d) 6.
4 14 12 36 (a) 7. (d) 8. (a) 9. (c) 10. (b)
(e) −3 (f) −41 (g) 0 B. 1. (a) 2. (b) 3. (a)
56 120 C. 1. positive 2. order 3. −3 4. −3 5. –5 and –6
2. (a) Commutative Property (b) Associative Property 3 3 2 5 11
(c) Existence of additive identity (d) Existence of additive inverse D. 1. ` 205 2. ` 23 3. 7 full circles; 2 32 cm 2
4
4
−  4
3. (a)    7   (b) 0 (c) 3 5 (d) −4 4. (a) 60 students (b) 30 students
9
8. 0 (c) 240 more students are rewarded with Grade B than with Grade C.
361 Answers