BOOK FOUR

Exercise 1a Pages1 & 2 5. 8 0 0 2. c = 264 (294 - 30)

d = 395 (365 + 30)
1. 8 0 0 , 3 2 0 0 6. 1 0 0 0
3. e = 18 (30 - 12)
2. 3000, 4000 7. 1 5 0 f = 42 (30 + 12)
3. 1500, 6000 8. 9 0 0 4. g = 71 (72 - 1)
4. 6000, 9000 9. 3 0 0 0 h = 84 (83 + 1)
5. 5400, 7200
10. 400 5. i = 5.0(5.5 - 0.5)
6. 2000, 4000 j = 9.0(8.5 + 0.5)
11.8 0 0
7. 5100, 6800
1 2. 7 0 0 Exercise 2b Page 6
8. 600, 1800 (Time Measurement)
1 3. 9 0 0
9. 2500, 10000 Example:
1 4. 2 0 0 0
10. 6600, 8800 24s
2m
1 5. 3 0 0 96s
1 1 . 1800, 3600 60s = 1m
1 6. 5 0 0 60m = 1h
1 2 . 1800, 5400
24s
13.13500,54000 1 7. 9 0 0 0 60s = 1m
96s 2
1 8. 1 1 0 0 120sec
1 4 . 2500, 5000 120s = 120
60
1 5 . 1075, 2150 1 9. 1 0 0 0
= 2m
1 6 . 9450, 12600 2 0. 9 5 0 145m
3h
1 7 . 1560, 2340 35m
Exercise 2a Page 5
1 8 . 1390, 5560 145m 60m = 1h
Example: 35m 3
1 9 . 1838, 3676 180m 1 8 0 m= 180
2 0 . 4200, 5600 66 72 79 60
= 3h
77 83 90

Exercise 1b Pages 3 & 4 66 + 11 = 77 47s

4m
72 + 11 = 83 193s
1. 4000
79 + 11 = 90 47s
2. 1 6 0 60s = 1m
193s 4

3. 5 0 0 240s 2 4 0 s = 240
1 . a = 37 (45 - 8) 60
4. 8 0 0 b = 26 (18 + 8) = 4m

40
 1. 5s (1m - 55s) 13. I (I - G) Exercise 4b Pages 10 &11
2. 2h (78m + 42m) 14. I (K + E) Division, Mulitiplication,
3. 69s (2m - 51s) 15. C (B + H) Subtraction and Addition
4. 176s (4m - 64s) 16. M (I + J + H) Example:
5. 20m (7h - 400m) 17. H (A + K + J)
6. w240m(10h-360m) 18. J (E + I + J) 1. 48 6 8
7. 1m (29s + 31s) 19. L (K + H + G) (6 x 8 = 48)
8. 2h (66m + 54m) 20. M (H + I + J)
9. 20s(12m -700s)
10. 560m(11h -100m) Exercise 4a Page 9 2. 15 19 4
Improper Fractions (15 + 4 = 19)
Exercise 3a Page 7 Example:
(Next Roman Numeral) 7 13/4
Example: 4 3. 14 294 21
1. ix x 2. v vi 13/4 = (4 x 1) + 3 (14 x 21 = 294)
4
9 10 5 6 4+3 7
1. V 11. XL 4 = 4
2. XII 12. LI 4. 52 65 13
3. XIV 13. XXIII 17 (65 - 13 = 52)
52/3
4. XVIII 14. XXIX 3
5. XXVI 15. II 52/3 = (3 x 5) + 2
6. XXIX 16. XLVIII 3 5. 408 102 4
7. LIII 17. XLVI 15 + 2 17
= =
3 (408 ÷ 102 = 4)
8. XLVI 18. XXIV 3
9. II 19. XXIV
10. VI 20. III 1. 21/4 6. 302 504 202

2. 22
/5 (302 + 202 = 504)
Exercise 3b Page 8
Alphanumeric line 3. 71/3
1. M(L + H) 7. 9 108 12
45
4. /7 (108 ÷ 9 = 12)
2. J (M + D)
3. I (K + E) 5. 92/3
4. E (G - I) 8. 50 440 390
13
5. F (K - L) 6. /6
6. I (H + H) (50 + 390 = 440)
7. 111/2
7. F (L - M)
8. G (F + H) 12 9. 75 15 5
8. /11
9. M (L + H) (75 ÷ 15 = 5)
10. H (L + C) 9. 8 7/8
11. I (L + D) 77
12. A (G - M)
10. /6 10. 16 112 7
(16 x 7 = 112)

41
 1. a = 72 (60 + 12)
11. 191 500 309 3 3 x 5 = 15
b = 36 (48 - 12) 15 18 15 + 3 = 18
(500 - 309 = 191) 2. c = 40 (30 + 10) 5
15 + 5 = 20
d = 10 (20 - 10) 20
12. 2000 200 10 3. e = 100 (70 + 30)
(200 x 10 = 2000) f = 90(120 - 30) 1. 8(24 ÷ 3)
4. g = 8 (6 + 2) 2. 20 (16 + 4)
13. 77 693 9 h = 3(5 - 2) 3. 40 (8 x 5)
(77 x 9 = 693) 5. i = 2 (1 + 1) 4. 7(56 ÷ 8)
j = 8 (9 - 1) 5. 33(30 + 3)
14. 23 144 121 Exercise 5b Pages13 6. 35( 30 + 5)
Equivalent Fractions 7. 27 (3 x 9)
(144 - 23 = 121)
Example: 8. 40 (32 + 8)
15. 136 2 68 3 6 9. 4 (28 ÷ 7)
(68 x 2 = 136) 5 10 10. 2(22 ÷ 11)
3 x 2 = 6
16. 15 225 15 5 x 2 10 Exercise 6a Page 15
(225 ÷ 15 = 15) Example:
5 10 18.22cm 11.45cm
17. 169 471 302 6 12
5 x 2
(169 + 302 = 471) = 10
6 x 2 12 29.67cm
18. 597 3 199 2
1. /10 18.22cm + 11.45cm =
(199 x 3 = 597) 2. 2/7 29.67cm
3. 6/16 29.67cm - 18.22cm =
19. 100 5000 50 4. 5/7 11.45cm
(100 x 50 = 5000) 5. 8/10 29.67cm - 11.45cm =
6. 3/4 18.22cm
20. 189 3 63 7. 10/24
(189 ÷ 63 = 3) 8. 5/7 14.28kg 9.70kg
9. 14/24
10. 1/6
Exercise 5a Page 12
Example: 23.98kg
Exercise 5c Page 14
Example: 14.28kg + 9.70kg =
30 45 55
23.98kg
15 30 40 2 2 x 2 = 4 23.98kg - 14.28kg =
4 6 4 + 2 = 6 9.70kg
2
30 - 15 = 15 4 + 2 = 6 23.98kg - 9.70kg =
6
45 - 15 = 30 14.28kg
55 - 15 = 40

42
1. 39.64cm (22.16cm Exercise 6c Page 17 200 10 2000
+ 17.48cm) Multiplication
2. 33.09cm (48.42cm - 200 x 10 = 2000
Example: 2000 ÷ 200 =100
15.33cm)
3. 27.14cm (62.25cm - 2000 ÷ 10 = 200
24 2x4 =8
35.11cm)
4. 9.38cm (5.12cm + 81 8x1 =8 380 15 5700
4.26cm) 380 x 15 = 5700
5. 18.77cm0(15.32cm 36 3 x 6 = 18 5700 ÷ 380 =15
+ 3.45cm) 92 9 x 2 = 18 5700 ÷ 15 = 380
6. 13.35kg (31.50kg -
18.15kg) 1. 5200 (650 x 8)
7. 7.24kg (46.38kg - 44 4 x 4 = 16
2. 12 (3600 ÷ 30)
39.14kg) 28 2 x 8 = 16
8. 21.48kg (82.60kg - 3. 420 (6300 ÷ 15)
61.12kg) 4. 2600 (13 x 20)
9. 19.07kg (55.51kg - 1. 2 (3 x 4 = 12) 5. 11(616 ÷ 56)
36.44kg) (6 x 2 = 12) 6. 100 (3200 ÷ 32)
10. 39.21kg (20.19kg + 2. 1 (10 x 2 = 20) 7. 2100(50 X 42)
19.02kg) ( 1 x 20 = 20) 8. 11 (1925 ÷ 175)
3. 2 ( 2 x 14 = 28) 9. 150(7500 ÷ 50)
Exercise 6b Page 16 (7 x 4 = 28) 10. 25(10000 ÷ 400)
Example: 4. 4 (12 x 4 = 48)
2 4 (16 x 3 = 48) Exercise 7b Page 19
20 8 5. 8 (16 x 4 = 64) Example:
( 8 x 8 = 64)
2 x2 = 4 2 3
6. 1 ( 1 x 100 = 100) 16
2 x4 = 8 (10 x 10 = 100) 5 2
22 + 42 = 4+16 = 20 22 = 4
7. 22 (4 x 11 = 44)
5 10 ( 22 x 2 = 44) 52 = 25 (1)
125 50 8. 2 (5 x 12 = 60) 32 = 9 (2)
(30 x 2 = 60) 22 = 4
5 x 2 = 10 9. 2 (12 x 2 = 24) 4 + 25 = 29
5 x10 = 50 9 + 4 = 13
(4 x 6 = 24)
52 +102 =25+100 = 125 29 - 13 = 16
10. 0 ( 0 x 1 = 0)
1. 320(82 + 162) (0 x 0 = 0)
3 1
2. 12(6 x 2) 5
3. 450 (15 x 30) 1 2
4. 3(18 ÷ 6) 32 = 9 (1)
Exercise 7a Page 18
5. 605(112 + 222) 12 = 1
Example:
6. 20(10 x 2) 12 = 1
7. 338 (13 x 26) 150 12 1800 (2)
22 = 4
8. 20 (800 ÷ 40) 150 x 12 =1800 9 + 1 = 10
9. 720 (122 + 242) 1800 ÷ 150 = 12 1+4 =5
10. 648(18 x 36) 1800 ÷ 12 = 150 10 - 5 = 5

43
 5 4
30 8. 5 (81 - 6) ÷ 15) 15. 132(66 x 4 ÷ 2)
5 2 9. 146(20 x 7) + 6) 16. 10(500 x 2 ÷ 100)
52 = 25 (1) 10. 4(134 - 6) ÷ 32)
52 = 25 17. 12(48 x 2 ÷ 8)
11. 123(13 x 9) + 6)
42 = 16
(2) 12. 256 (25 x 10) + 6) 18. 5(40 x 2 ÷ 16)
22 =4
13. 3 (69 - 6) ÷ 21) 19. 60(24 x 5 ÷ 2)
14. 906 (90 x 10) + 6) 20. 70(105 x 2 ÷ 3)
25 + 25 = 50
16 + 4 = 20 15. 20(106 - 6) ÷ 5)
50 - 20 = 30 16. 97(13 x 7) + 6) Exercise 8b
17. 69(21 x 3) + 6) Pages 22 & 23
1. 27(40 - 13)
2. 111(200 - 89) 18. 1(106 - 6) ÷ 100) Example:
3. 2 (74 - 36 = 19. 118 (16 x 7) + 6)
38 - 34 = 4, 4 ) 20. 30(126 - 6) ÷ 4) 2
4. 2 (81 - 18 = 63,
67 - 63 = 4, 4 )
Exercise 8a Page 21 4 16
5. 0 (32 - 32)
Example: 2
6. 1(25 - 4 = 21- 20 2 =4
= 1, 1 ) 6x 3 ÷ 2 = 9 42 = 16
7. 6 (50 - 36 = 14, 10 x 5 ÷ 2 = 25
22 +14 = 36, 36 8
12 x 5 ÷ 2 = 30
8. 60(80 - 20)
9. 9(265 - 100 = 1. 40 (8 x 10 ÷ 2)
165 -84=81, 81) 64 4096
10. 0 (9 - 4 = 5 - 5 = 2. 5 (30 x 2 ÷ 12)
82 = 64
0, 0 ) 3. 21(14 x 3 ÷ 2) 642 = 4096
4. 4(50 x 2 ÷ 25)
Exercise 7c Page 20 1. 8 1 ( 9 2 )
Example: 5. 10(90 x 2 ÷ 18)
2. 6 2 5 ( 2 5 2 )
8 x 4 z = 38 6. 9(36 x 2 ÷ 8)
3. 10000(1002)
z = 6 7. 52.5(35 x 3 ÷ 2)
8 x 4 = 32 + 6 = 38 4. 2 5 6 ( 1 6 2 )
8. 96(32 x 6 ÷ 2 5. 2 4 0 1 ( 4 9 2 )
1. 256 (50 x 5) + 6) 9. 0(0 x 2 ÷ 60) 6. 1 2 9 6 ( 3 6 2 )
2. 6 (366 - 6) ÷ 60
10. 10 (65 x 2 ÷ 13) 7. 6 5 6 1 ( 8 1 2 )
3. 78(8 x 9) + 6)
4. 330(54 x 6) + 6 11. 189(42 x 9 ÷ 2) 8. 1 4 6 4 1 ( 1 2 1 2 )
5. 7(90 - 6) ÷ 12 12.144(72 x 4 ÷ 2) 9. 5 0 6 2 5 ( 2 2 5 2 )
6. 237(21 x 11) + 6) 13. 45 (45 x 2 ÷ 2) 1 0 . 1 6 0 , 0 0 0 ( 4 0 0 2)
7. 12 (78 - 6) ÷ 6) 14. 69(23 x 6 ÷ 2)

44
Exercise 8c Page 24 Exercise 10a Page 27 4. BEEF
Example: Example: Study the 5. 4155
25 35 65 example 6. 388458
0 1 2 3 4 5 6 7. 7815
5 7 13 a b c d e f g 8. FELL
25 ÷ 5 = 5 7 8 9 9. 612
35 ÷ 5 = 7 h i j 10. LEAF
that is, a = 0; b = 1; 11. FAY
65 ÷ 5 = 13
c = 2 etc 12. 6158
1. a = 2(1x 2) b = 7(14 ÷ 2) 13. BEAM
1. 21 + 45
2.c =20(5x4) d =11(44 14. I98
2. 69 - 30
÷ 4) 15. LAY
3. 5 x 9
3. e = 100(10 x 10) f = 16. BELL
4. 0+ 8
6(60 ÷ 10) 17. BAY
4. g = 96(8 x 12) h = 5. 56 ÷ 2 18. 5164
11(132 ÷ 12) 6. 99 + 1 19. 216
5. i = 1(1 x 1) j = 2( 2 ÷ 1) 7. 10 x 5 20. FAX
8. 33 ÷ 1
Exercise 9a Page 25 9. 22 x 4 Exercise 11a
(Study the example) 10. 70 - 1 Pages 29 & 30
1. 19 11. 209 11. fg ÷ c Fractions
2. cj 12. ddj Example:
12. ej + ba
3. 57 13. eea 1
13. ia + j /4
4. haj 14. 440
14. jxa
5. 123 15. 579 15. bf - c 1
6. 309 16. bba 16. bf x e 3
7. hhb 17. 360
/4
17. hh + bi
8. 108 18. gai 18. fg - cb 1
/4 + 3/4 = 4/4
9. jaa 19. 7459
19. ja - ha
10. 100 20. 8024 1+3
20. ef ÷ g 4
= 1
Exercise 9b Page 26
Exercise 10b Page 28
1
1. 1 8 6 11.1445 Example: /3
2. f e d 12.hide X A B Y L M 5
3. 5 8 6 13.7867 /9
9 1 4 2 5 6
4. c a b 14.2054 Z E F 2
/9
5. 1 0 6 15.beef 7 8 3 5
6. b e d 16.d a d that is, x = 9, A = 1; /9 - 2/9 = 3/9
7. 7 0 3 17.7 0 3 B = etc
8. d e a d 1 8 . f i b 5-2 3 1
1. FEEL = 9 = 3
9. 3 4 0 5 1 9 . h i d 9
2. 5172
10.bib 20.7403 3. FEMALE

45
 1
/6 Exercise 11b 16. 1
/20 (4/5 - 3/ 4 )
Pages 31 & 32
5
/6 Example: 17. 3
/14 (5/7 - 1/2 )
2
/3 1
/6 18. 7
/30 (5/6 - 3/ 5 )
5
/6 - 1/6 = 4/6 1 19. 9
/28 (3/4 - 3/ 7 )
1
/2 /3
5-1 4 = 4 = 2 20. 13
/30 (3/5 - 1/6 )
= 1
9 6 6 3 1
/2 - 1/3 = 3 - 2 =
6 6
7
1. /10 (1/2 + 1/5 )
3
/9
2. 2
/3 (11/12 - 1/4 ) Exercise 11c
1
Pages 33&34
3. 3
/5 (2/5 + 1/5 ) 7
/8 /2 Example:
4. 1/7 (9/14 - 1/2 ) 7
/8 - 1 /2 = 7 - 4 = 3 1
/2
8 8 3
1 5 1
5. /4 ( /12 - /6 )
1. 1/6 (2/3 - 1/2) 7
/8 3
/8
6. 1/3 (13/21 - 2/7 ) 7 4
5 3 1
2. /12 ( /4 - /3) 7
7. 19
/28 (3/7 + 1/4 ) 7 /8 - 4 3 /8 =
1 1 2
3. /10 ( /2 - /5)
8. 1/4 (7/12 - 1/3 ) 7-3 4
3 8 = 38
4. 3/20 (3/4 - 3/5)
9. 9
/10 (2/5 + 1/2 ) 1
5 = 32
5. /21 (2/3 - 3/7)
10. 1/4 (9/20 - 1/5 ) 3
6. 3/10 (1/2 - 1/5 ) 1 /4
13 2 1
11. /20 ( /5 + /4 )
7. 1/20 (1/4 - 1/5 ) 1 1
12. 1/5 (11/30 - 1/6 ) 3 /4 1 /2
3 4 1
8. /10 ( /5 - /2 ) 1
13. 3/4 (11/12 - 1/6 ) 3 /4 - 11/2 =
7 3 1
9. /12 ( /4 - /6 )
14. 8/15(1/3 + 1/5 ) 1-2
10. 1/12 (5/6 - 3/4 ) 2 =
4
15. 1/2 (5/6 - 1/3 )
5 - 2 = 13
11. 3/28 (6/7 - 3/4) 1 4
16. 3/4 (19/20 - 1/5 ) 4
12. 5/12 (2/3 - 1/4 )
17. 1/3 (14/15 - 3/5 ) 1. 11/4 (31/2 - 21/4)
13 2 1
13. /24 ( /3 - /8 )
18. 5/8 (3/8 + 1/4 ) 2. 11/8 (31/4 - 21/8)
1 3 2
14. /4 ( /4 - /4 )
19. 2
/9 (5/9 - 1/3 ) 3. 23/8 (11/8 + 11/4)
1 3 1
15. /10 ( /5 - /2 )
20. 1/3(11/24 - 1/8 ) 4. 11/4 (25/8 - 13/8)

46
 4. 15 (50 + 10 = 60) 7. 35 (45 - 10)
5. 11/4 (23/4 - 11/2)
(4 x 15 = 60) 8. 159 (154 + 5)
6. 31/3 (11/6 + 21/6) 5. 81(3 x 3 = 9) 9. 310 (300 + 10)
(81 ÷ 9 = 9) 1 0 . 19 (29 - 10)
7. 11/2 (35/8 - 21/8) 1 1. 76 (66 + 10)
6. 12(3 x 4 = 12)
1 2 . 62 (31 x 2)
8. 12/3 (35/6 - 21/6) (144 ÷ 12 = 12) 1 3 . 101 (96 + 5)
9. 31/2 (23/8 + 11/8) 7. 2 (8 x 8 = 64) 1 4 . 80(90 - 10)
( 2 x 32 = 64) 1 5 . 39 (29 + 10)
10. 11/6 (21/3 - 11/6) 8. 0 (20 - 20 = 0) 1 6 . 80 (70 + 10)
( 0 x 20 = 0) 1 7 . 135(130 + 5)
11. 11/4 (23/4 - 11/2)
9. 10 (2 x 2 = 4) 1 8 . 134 (67 x 2)
12. 35/6 (11/3 + 21/2) (40 ÷ 10 = 4) 1 9 . 123 (118 + 5)
10. 5 (75 - 50 = 25) 2 0 . 60 (70 - 10)
13. 11/6 (22/3 - 11/2)
(125 ÷ 5 = 25)
14. 31/3 (51/2 - 21/6) Exercise 13a Page 38
Exercise 12b 1. amount
15. 45/6 (21/3 + 21/2) Pages 36&37 2. June
Example: 3. March
16. 21/8 (51/4 - 31/8) 4. 2 inches (2”)
50
5. 16 inches (16”)
17. 31/10 (51/2 - 22/5)
40 80 85 6. June and July
18. 43/4 (25/8 + 21/8) 7. 2 inches (2”)
50 - 10 = 40 8. 12 inches (12”)
40 x 2= 80 + 5 = 85 9. April and August
Exercise 12a Page 35
10. 14 inches (14”)
Example: 38
Exercise 13b Page 39
5+4 3x3 28 56 61 (Study the pattern and
5+4=9 find out the difference
38 - 10 = 28
3x3=9 between the members)
28 x 2=56 + 5 = 61
60 1. 17 6. 2 1
24 - 4 4x5 2. 85 7. 4
24 - 4 = 20 50 100 105 3. 14 8. 6 0
4 x 5 = 20 60 - 10=50 4. 45 9. 8
50 x 2=100+5=105 5. 28 10.9
1. 15 (5 x 7 = 35)
(20 + 15 = 35) 1. 30 (15 x 2) Exercise 14a Page 40
2. 4 (30 - 6 = 24) 2. 70 (60 + 10) Example:
(96 ÷ 4 = 24) 3. 185 (180 + 5)
4 7
4. 75 (85 - 10)
3. 10 (2 x 5 = 10) 11 20 5 14
5. 64(32 x 2)
(100 ÷ 10 = 10) 6. 30(20 + 10) 5 2

47
5 x 4 = 20 7 x 2 = 14 6. 72(8 x 9) Exercise 15a Page 43
5+4=9 7+2=9 7. 8(64 ÷ 8) Example:
20 - 9 =11 14 - 9 = 5
8. 11(33 ÷ 3) 19 15 5
5
39 55 9. 26(78 ÷ 3) 19 - 5 = 14
11 10. 200(25 x 8) 14 + 1 = 15
5 x 11 = 55
5 + 11 = 16 6 4 3
55 - 16 = 39 Exercise 14c Page 42 6 -3=3
Example: 3 + 1 = 4
1. 2 (4x2) - (4+2)
2. 64 (8 x 8) 20
10 3 8
3. 9 (72 ÷ 8) 400
10 - 8 = 2
4. 4 (96 ÷ 24) 400 = 20 2 + 1 = 3
5. 99 (9 x 11) 202 = 400 1. 50(56 - (7 - 1)
6. 2 (4 ÷ 2) 2. 16(25 - 10) + 1)
8 3. 36(18 + 19) - 1)
7. 47(5x13)-(5+13)
64 4. 31(30 + 1)
8. 250 (25 x 10)
5. 19(19 + 1) - 1)
9. 64 (128 ÷ 2) 64 = 8 6. 4(10 - (7 - 1)
10. 80(10x10)-(10+10) 2
8 = 64 7. 4(3 - 0) + 1)
8. 69(92 - (24 - 1)
16 9. 120(100 + 21) - 1)
Exercise 14b Page 41
256 10. 11(21 - 11) + 1)
Example:
256 = 16
32 Exercise 15b Page 44
32 ÷ 8 = 4 162 = 256
4 Example:
8 x 4 =32
8 1. 6 ( 36 )
x
2. 8 1 ( 9 2 ) 4 2 3 2 2 6
25
25 ÷ 5 = 5 3. 12( 144 )
+
5 5 x 5 = 25 4. 225 (15 2 )
5 5. 361 (19 2 ) 2 + 2 = 4
6. 13 ( 169 ) 3 x 2 = 6
100 7. 22( 484 )
100 ÷ 5 = 20 x
5 8. 121 (11 2 ) 8 5 4 7 3 28
20 x 5 =100 9. 49 (7 2 )
20 +
1 0 . 10( 100)
1. 9(36 ÷ 4) 5 + 3 = 8
2. 125(5 x 25) 4 x 7 = 28
3. 13(91 ÷ 7)
4. 12(108 ÷ 9)
5. 81(9 x 9)

48
 x Exercise 15d Page 46 1. 12(10 + 2)
13 8 1 6 5 6 Example: 2. 2(16 ÷ 8)
+
3. 48(16 x 3)
8 + 5 = 13 3 5 2 1 6 5
1 x 6 = 6 7 1 = 28 0 4. 12(144 ÷ 12)
4 0
3 x 2 = 6 5. 5(35 ÷ 7)
1. 14 (7 x 2) 5 x 1 = 5 6. 63(7 x 9)
2. 0 (12 x 0) 7 x 4 = 28 7. 56(48 + 8)
3. 6 (3 + 3) 1 x 0 = 0 8. 7(21 ÷ 3)
4. 4 (32 ÷ 8)
1. 3(9 ÷ 3), 2(12 ÷ 6) 9. 12(120 ÷ 10)
5. 3 (8 - 5)
10(20 ÷ 2), 20(4 x 5) 1 0 . 169(13 x 13)
6. 1/2 (1 - 1/2)
7. 20 (16 + 4) 2. 60(12 x 5), 0(5 ÷ 0)
8. 65 (5 x 13) Exercise 16b Page 48
2(14 ÷ 2), 5(45 ÷ 9) Example:
9. 20 (6 + 14), 9(81 ÷ 9)
3. 5(15 ÷ 3), 44(11 x 4)
10. 1(61 - 60) 25 5
/2(1/4 ÷ 1/2), 30(2 x 15)
1
10
Exercise 15c Page 45 4. 250(25 x10),1(2÷ 2) 15 5
Example: 1(1/3 ÷ 1/3),10(2 x 5) 5 + 5 = 10
8 2 5 x 5 = 25
25 10 Exercise 16a Page 47 10 + 5 = 15
7 Example:
8 + 2 = 10 42 6
6 13
8 + 7 + 10 = 25
2 9 20 7
4 3
12 6 + 7 = 13
31 16 6 + 3 = 9
6 x 7 = 42
3 6 ÷ 2 = 3 13 + 7 = 20
12 + 4 = 16
3 x 2 = 6
12 + 16 + 3 = 31 1. 22(13 + 9)
1. 0(25 - (10 + 15) 15 2. 8(19 - 11)
2. 6(12 - 6) 3. 54(18 x 3)
3. 120(60 + 40 + 20) 5
3
18 4. 9(63 ÷ 7)
4. 12(44 - (25 + 7) 5. 23(19 + 4)
5. 10(8 + 2) 15 + 3 = 18 6. 11(7 + 4)
6. 60(80 - 20) 15 ÷ 5 = 3 7. 31(28 + 3)
7. 87(54 + 6 + 27) 3 x 5 = 15 8. 12(24 - 12)
8. 19(19 - 0) 9. 72(9 x 8)
9. 29(53 - (18 + 6) 10. 18(11 + 7)
10. 35(20 +15)

49
Exercise 16c Page 49 Exercise 17a Page 50 Exercise 17c Page 52
1. KE + IN Example: Example:
53 + 67 = 120
2. BR 12 5 5 12 12 ÷ 3 = 4
= = 2 10 15 5
I 6 15 ÷ 5 = 3
5 x 5 = 25 3
3. BREAK = 12345 4- 3=1
5 + 5 = 10
4. R X G = 2 X 8 = 16 25
5. RAKE = 2453 60 ÷ 6 = 10
8 3 60
6. AK - = 22 11 16 4 16 ÷ 4 = 4
45 - = 22 8 x 3 = 24 6 10 - 4 = 6
45 - 22 = 23 8 + 3 = 11
24
23 = = RE 1. 4(24 ÷ 6)
1. 6(13 - 7)
2. 13(8 + 5) 2. 16(8 ÷ 2)
7. G ÷ A = ÷E 3. 12(15 - 3) 3. 150(25 x 6)
8÷4 = ÷3 4. 63(7 x 9) 4. 9(81 ÷ 9)
5. 18(16 + 2)
8 5. 2(14 ÷ 7),1(2-1)
= 6. 9(14 - 5)
4 3 7. 8(16 - 8) 6. 2(50 ÷ 25),4(6-2)
2 8. 50(10 x 5) 7. 6(3 ÷ 0.5),3(6-3)
8 x 3 9. 20(12 + 8)
= 6
4 1 0 . 5(12 - 7) 8. 1(1 ÷ 1),0(1-1)
1
9. 20(600 ÷ 30),
= 6 = I
10(20 - 10)
Exercise 17b Page 51
Example: 10. 4(2 ÷ 0.5),1(5-4)
∴ G÷A = I ÷ 26 16
E
11 7
8. 8
10 5 2 7
I A = 64 = 64 10 + 5 + 11 2+7+7 Exercise 17d Page 53
RXA 2X4 81 = 26 = 16 Example:
= 8 1. 1(24 - (10 + 13) 2 8
2. 5 (22 - (2 + 15)
9.KING - BEAK=
3. 30 (60 - (17+13) 20
5678 - 1345 = 4333 4. 59 (25+16+18)
4 6
10. B x A x R = 5. 0 (33 - (22 + 11)
1x4x 2 = 8 6. 43(100- (47+10) 2 + 8 = 10
7. 7(92 - (81 + 4) 4 + 6 = 10
8. 5 (56 - (35 + 16) 10 + 10 = 20
9. 43(105 - (41+21)
1 0 . 95(20 + 32 + 43)

50
 6. 100(24 + (77-1) Exercise 18d Pages
6 3
7. 40(43 - ( 4 - 1) 57-58
18 8. 19(17 + (3 - 1) Example:
9. 38(62 - 25) + 1
4 5 16
10.120(100+(21 - 1)
6 + 3 = 9 4 8 2
4 + 5 = 9 Exercise 18b Page 55 2
9 + 9 = 18 Example: 4 x 2 = 8; 8 x 2 = 16
11 7 + 4 = 11 8 ÷ 2 = 4; 16÷ 2 = 8
1. 3( 11 - 8) 7
28 3 + 4= 7 1. 2(10 ÷ 5)
2. 20(2 + 8) + (15 + 5)
4 7 x 4 = 28
3. 6(15 - 9) 2. 6(3 x 2)
3 7 - 4 = 3
4. 40(12 + 8) + (15 + 5) 3. 36(4 x 9)
11 - 7 = 4
5. 3( 9 - 6) 4. 2(12 ÷ 6)
6. 13( 25 - 12) 1. 21(25 - 4)
5. 6(42 ÷ 7)
7. 0( 11 - 11) 2. 0(0x 6)
6. 100(10 x 10)
8. 38(1 + 18) + (9 + 10) 3. 14(28 ÷ 2)
9. 12( 17 - 5) 7. 4(8 ÷ 2)
4. 12(7 + 5)
10. 2( 14 - 12) 5. 3(30 - 27) 8. 8(8 x 1)
6. 2(16 - 14) 9. 8(4 x 2)
Exercise 18a Page 54
7. 24(20 + 4) 1 0 . 3(3 ÷ 1)
Example: 8. 144(12 x 12) 1 1 . 3(12 ÷ 4)
44 31 14 9. 10(90 ÷ 9) 1 2 . 11(33 ÷ 3)
1 0 . 19(22 - 3)
1 3 . 2(24 ÷ 12)
Exercise 18c Page 56 1 4 . 144(24 x 6)
= (44 - 14) + 1 = 31
Example:
8 3 6 12 d 3 = 12 x 3 = 18 Exercise 19a Page 59
2
1. 15(6 x 5 ÷ 2) Example:
= (8 - 6) + 1 = 3 5
2. 8(36 x 2 ÷ 9)
20 11 10 10 2
3. 10(50 x 2 ÷ 10)
4. 27(18 x 3 ÷ 2) 12 17
= (20 - 10) + 1 = 11
5. 5(50 x 2 ÷ 20)
12 - 10 = 2
1. 55 (72 - 18) + 1 6. 8(20 x 2 ÷ 5) 10 + 5 + 2 = 17
2 . 20 (35 - (16 - 1)
3 . 40 (30 + (11 - 1) 7. 24(24 x 2 ÷ 2) 5 x 2 = 10
4. 33 (55 - (23 - 1) 8. 6(27 x 2 ÷ 9) 10 ÷ 2 = 5
5. 1 (81 - 81) + 1 10 + 2 = 12
9. 30(15 x 4 ÷ 2)
12 - 7 = 5
1 0 . 8(32 x 2 ÷ 8)

51
 1. 20(15 + 5) 14. 12(9 + 27) ÷ 3)
5 180
2. 55(45 + 10)
3. 4(16 - 12) =139 15. 5(50 ÷ 10)
4. 11(6 + 2 + 3) 6 30 16. 8(49 + 7) ÷ 7)
5. 25(30 - 5) 5 x 6 = 30 17. 2(16 ÷ 8)
6. 44(55 - 11) 6 x 30 = 180
18. 27(9 x 3)
7. 3(31 - 28) 5 + 6 + 30 = 41
8. 20(18 + 2) 180 - 41 = 139 19. 8(64 ÷ 8)
9. 2(32 - 30) 20. 9(12 + 6) ÷ 2)
1 0 . 10(50 - 40) 1. 3(12 ÷ 4)
2. 27(54 - (3+6+18)
Exercise 19b Page 60 Test 1 Page 63
3. 125 (5 x 25)
Example: 1. 16; 18
36m 4. 71(100 - (4+5+20) 2. 129; 130
9m 13m 5. 198(245-(5+7+35) 3. 100; 105; 110
6. 4(16 ÷ 4) 4. 800; 900; 1000
4m 7. 2 (18 ÷ 9) 5. 719; 720;721
9m x 4m = 36m 8. 116(147- (3+7+21) 6. 1,300; 1,400; 1,500
9m + 4m = 13m 7. 895, 900; 905
9. 15 (5 x 3)
13m - 9m = 4m 8. 416; 418; 420
10. 161(240-(15+4+60) 9. 710; 715; 720;
36m ÷ 9 = 4m
10. 4,219; 4,220; 4,221
1. 3m(39m ÷ 13m) Exercise 19d Page 62 11. 9,400; 9,500; 9,600
2. 44m(42m + 2m) 12. 282; 284; 286
10 - 2 - 20
3. 18m(72m ÷ 4m) 13. 500; 600; 700
4. 49m(7m x 7m) 15 14. 1,185; 1,190, 1,195
5. 54m(9m x 6m) 15. 25; 30; 35
10 x 2 = 20 16. 197; 198; 199
6. 15m(10m + 5m)
7. 56m (8m x 7m) 10 + 20 ÷ 2 = 15 17. 185; 187; 189; 191
20 ÷ 10 = 2 18. 755; 765; 770
8. 15m(45m ÷ 3m)
19. 840;850
9. 18m(11m + 7m) 20. 2,220; 2,222
6 - 3 - 18
10. 4m(100m ÷ 25m)
8 Test 2 Pages 64&65
Exercise 19c Page 61 1. 77, 103, 79
Example: 6 x 3 = 18
2. 600, 500, 500, 400,
2 32 6 + 18 ÷ 3= 8 300
= 18 18 ÷6 = 3 3. 21, 24, 27, 30, 33
4 8 4. EE5; FF6; GG7;
2x4=8 HH8
11. 2(8 ÷ 4) 5. 20T; 22V; 24X; 26Z
4 x 8 = 32 12. 6 (6 x 1)
2 + 4 + 8 = 14 6. 20, 14, 22, 15
32 - 14 = 18 13. 5(25 ÷ 5) 7. 17Q; 16P; 15O; 14N

52
 8. 23, 4, 22 4. g = 2.5 (1 x 2.5) B. 32 = 9
9. klm, 11, 12, 13, 5
h = 3(7.5 ÷ 2.5) 42 = 16
nop, 14, 15, 16 5. i = 120 (30 x 4) 5 9 + 16 = 25
10. 30, 20, 10 3 4 25 5
11. 43, 6, 53, 7 j = 7(28 ÷ 4) 51 = 5
12. 72, 70, 68, ........56 4 82 = 64
13. 22, 21, vu; c Test 4 Pages 68 & 69
22 = 4
14. 11, 7, 8; 12, 9, 10 17
Example : 8 2 64 +174 = 68
15. 701, 710, 801 68
16. 3, 28, 4 A. 5 8 4 1 = 17
17. 480, 380, 280
2 13 72 = 49
18. 30, 70, 35 3 4
42 = 16
19. 30, 71, 40 5 + 3 = 8 5
20. 46, 51, 52, 57 7 4 49 + 516 = 65
8 ÷ 2 = 4 65
131 = 5
Test 3 Pages 66 & 67 3 12
1. 10 1. 2(25 + 9) ÷ 17)
2. 20 9 3 4 2. 25 (100 + 25) ÷ 5)
3. 15 3 + 9 = 12 3. 6 ( (12 x 6) - 36)
4. 19
5. 25
12 ÷ 3 = 4 4. 5.28 ( (4.1x 9) - 9)
6. 55 5. 16 (144 + 16) ÷ 10)
8 14
7. 60 6. 2 ( 9 + 1) ÷ 5)
8. 49 6 2 7 7. 0 ( (1 x 4 ) - 4 )
8 + 6 = 14 8. 1 ( (2 x 1) - 1 )
14 ÷ 2=7 9. 5 (64 + 16) ÷ 16)
B. Example:
1. 3(9 ÷ 3) 10. 2 (121 + 25) ÷ 73)
32 24 12 11. 8 ( (29 x 5) - 81)
8 6 3 2 . 9(18 - 9)
12. 3 ( (6 x 3) - 9)
32 ÷4 = 8 3 . 32(16 + 16)

24 ÷4 = 6 4 . 50(100 ÷ 2) Test 5 Pages 70&71

12 ÷ 4 = 3 5 . 5(30 - 25) A. Example:

1. a = 9 (3 x 3)
6 . 2(24 ÷ 12) 30 16
7 . 6(12 - 6) 10 4
b = 9 (27 ÷ 3) 20 12
2. c = 300 (12 x 25) 8 . 9(18 - 9) 8
d = 3 (75 ÷ 25) 9 . 7(14 ÷ 2) 30 - 10 = 20
3. e = 120(10 x 12) 16 - 4 = 12
1 0 . 4 (20 - 16)
f = 12 (144 ÷ 12) 20 - 12 = 8

53
 1 1. 20(60 - (15 + 25) 1 . 2(24 -18 = 6 ÷ 3)
11 6 1 2 . 26(82 - (42 + 14)
2 3 2 . 195 (75 + 120)
1 3 . 32(86 - (33 + 21)
9 3
1 4 . 17(25 - 8) 3 . 6(91 - 49 = 42 ÷ 7)
6
1 5 . 49(93 - 44) 4. 1 (24 - 16 = 8 ÷ 8)
11 - 2 = 9 1 6 . 18(56 - (18 + 20) 5 . 100(40 + 60)
6- 3 =3 1 7 . 24(18 + 6)
9- 3=6 1 8 . 33(96 - (42 + 21)
6 . 5(180 ÷ (24 + 12)
1 9 . 74 (33 + 24 + 17) 7 . 1/2 (15 ÷ (24 + 6)
9 7
20.42 (97 - 55) 8 . 99(90 + 9)
5 6
4 1 9. /3(27-18 = 9 ÷ 27)
1

3 Test 6 Pages 72&73 10. /2 (5/12 ÷ (1/3 + 1/2)

1

9- 5 =4 A. Example:
7- 6 =1 9
4- 1 =3
B. Example:
1. 5 (9 - 4) 5 56
2 . 18 (15 + 3) 3
5 x 4= 20 8 2
3 . 28 (14 + 14) 9 x 4 =+36 6
4
4 . 60 (84 - 24) 56 10
or
5 . 19 (29 - 10) 8 + 2 = 10
6 . 12 (8 + 4) 9 + 5 =14
3 x2 =6
7 . 8 (21 - 13)
10
56 ÷ 14=4
8 . 34 (42 - 8) 6
9 . 33 (66 - 33) 9 4
8 36 12
1 0 . 9 (10 - 1)
8 x 2 = 16 13
B. Example: 2 10 x 2=+20
9 + 4 = 13
or 36
2 6 6 x 2 = 12
5 10 + 8 = 18
11. 30 (50 - 20)
36 ÷ 18 = 2
40 12. 14 (28 ÷ 2)
6 9 4 14 13. 100 (50 ÷ 2)
20 120
6 + 2 + 6 = 14 14. 106 (64 + 42)
9 - 5 =4
15. 19 (62 - 43)
5 14 2 20 x 2 = 40
8 16. 200(100 x 2)
40 x 2 =+80
120 17. 80 (58 + 22)
or
18. 150 (300 ÷ 2)
7 27 19 26 40 + 20= 60
19. 50 (92 - 42)
7 + 5 + 14 = 26 120 ÷ 60=2
20. 17 (80 - 63)
27 - 8 = 19

54
Test 7 Pages 74&75 1. 30(3 x 10) Test 9 Pages 78&79
A. 2. 8(5 + 3) A. Example for 1-10
1. 17km 3. 3(9 - 6)
64 36
2. 32km 4. 4(8 - 4)
3. 8km 5. 4(7 - 3) 64 = 8
6. 12(12 + 0) 14
4. 37km 36 = 6
5. 48km 7. 128(8 x 16) 8 + 6=14
6. Mowe to Ikeja 8. 2(9 - 7)
25 4
7. Ikoyi 9. 7(10 - 3)
1 0 . 22(2 x 11) 25 = 5
B. Example for 8 - 17 7 4 =2
5+2=7
6 3 7 21 B. Example page 77
49 81
6÷2 = 3 1
3 x 7 = 21 49 = 7
1
16
1
/2 /2 81 = 9
8 4 4 16 7 + 9 = 16
1
8÷ 2 = 4 /2 + 1/2 = 1 + 1/2
1. 12 ( 4 + 100 )
4 x 4 = 16 = 2/ 2 = 1 2. 121( 20 - 81)2
8. 24(6 x 4) 3. 25 (10 - 25)2
1 1/ 2
9. 6(48 ÷ 8)
4. 9 (7 - 16 )2
1 0 . 18(9 x 2) 3
3
/4 /4 5. 13 ( 36 + 49 )
1 1 . 4(52 ÷ 13)
1 2 . 32(16 x 2) 3
/4 + 3/4 = 3 + 3/4 6. 144 (15 - 9 )2
1 3 . 13(65 ÷ 5) or 2 1 7. 14( 9 + 121)
= 6/ 4 = 1 / 4 2
(26 ÷ 2) 8. 4 (10 - 64 )2
1 4 . 4(64 ÷ 16) = 1 1/2
9. 81(18 - 81) 2
1 5 . 72(8 x 9)
2 1 1
1 6 . 40(20 x 2) 1 1. /3 ( /3 + /3 ) 10. 4 ( 4 + 4 )
1 7 . 63(9 x 7) 1 2 . 5/6 (1/2 + 1/3 )
B. Example for 11 - 20
Test 8 Pages 76&77 1 3 . 3/4 (13/12 - 1/3 )
2 m 3 = 2x3 = 3
A. Examples for 1 - 10 2
1 4 . 3/4 (1/2 + 1/4 )
50 12 m 3 = 12 x 3
5 + 5 = 10 1 5 . 1/5 (13 /15 - 2/3 ) = 18
5 10 2
5 x 10 = 50
5
16. 10
/21 (1/7 + 1/3) 1 1. 30 (12 x 5 ÷ 2)
16
6 8 6 + 2 = 12 1 7 . 5/12 (13 /12 - 2
/3 ) 1 2 . 7 (21 x 2 ÷ 6)
2 2 x 8 = 16 1 3 . 10 (50 x 2 ÷ 10)
1 8 . 1 3 /4 (5 /6 + 11
/12 )
45 1 11 2 1 4 . 54 (12 x 9 ÷ 2)
4 9 4+ 5= 9 1 9 . /4 ( /12 - /3 )
5 5 x 9 = 45 2 0 . 1/3 (5/6 - 1/2) 1 5 . 8 (32 x 2 ÷ 8)

55
1 6 . 5(15 x 2 ÷ 6) 4. t x t
1 7 . 48(48 x 2 ÷ 2) 5. ei ÷ u

1 8 . 5(35 x 2 ÷ 14) 6. ii ss ÷
7. ib + ib
1 9 . 36(18 x 4 ÷ 2) 8. ie - u
2 0 . 12(18 x 2 ÷ 3) 9. ss + b
1 0 . tb ÷ ib
Test 10 Page 80 1 1. 64 + 31
Examples for 1 - 20 1 2 . 60 + 8
then = 6358, 13.16 ÷ 4
those=63275, 1 4 . 34 + 6
g=9 t=6 h=3 1 5 . 48 + 0
e=5 n=8 1 6 . 60 x 4
1 7 . 10 x 3
something = 1 8 . 38 + 4
721563489
o=2 s=7
÷4
1 9 . 60
20.88 + 10
m =1 i =4
1. 7215 11. him Test 12 Pages 82&83
2. his 12. 635 25 12345678901
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3. 325 13. them 12345678901
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Number of children

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4. hen 14. 3215 20 12345678901
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6. set 16. 15652 15 12345678901
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Test 11 Page 81 0 10 20 30 40 50
Substitute represents dogs
cats birds rabbits none
6306414348
Number of Pets
s = 6, u = 3, b =0,
t = 4, i = 1, e = 8 1. 5 6. 100(10+20+30+40)
e.g 40 + 4 = tb + t 2. 25 7. 50(30+20)
st ÷ e = 64 ÷ 8 3. 20 8. 50
4. 70(30 + 40) 9. 60(20+30+10)
1. st ÷ t 5. 30(10 + 20) 10.125(5+10+15+20+25+50)
2. tb + e
3. u x b

56
 Test 13 Pages 84&85
Birthdays
12
10
123456
1234567 123456
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Number of children

8 123456
1234567
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0 J M A M J J A S O
F N D
Months of the year 5 14 3 x14 =42
1. 4 6. 2(8 - 6)
7 5 x 7 =35
2. May, June & Dec. 7. 26(6+2+2+6+2+8)
3. 14(2 + 4 + 8) 8. 32(4+2+4+6+8+8) 3 7 42 - 35=7
4. 8 (2 + 2 + 2 + 2) 9. 6(32 - 26)
1. 2 (6 - 4)
5. 20(4 + 2 + 6 + 8) 1 0 . 58 (32 + 26)
2. 5 (56 - 26) ÷ 6)
Test 14 Page 86
1. 4 1 1 .1 0 1 0
1. 51 11. 32 3. 5 (54 + 6) ÷ 12)
2. 81 12. 10
2. 7 3 4 1 2 .2 5 6
13. 16
4. 3 (32 - 14) ÷ 6)
3. 3 3 3 1 3 .6 2 5 3. 9
4. 8 9 1 4 .4 1 4. 9 14. 30 5. 9 (19 + 8) ÷ 3)
5. 7 0 15. 31,32, 33 5. 4 15. 3 6. 19(75 - 56)
6. 1 8 1 6 .7 2 9 6. 94 16. 2
7. 1(5 - 4)
7. 9 7 1 7 .4 0 7. 3 17. 34
8. 7 8 1 8 .5 6 7 8. 2 18. 4 8. 1
/2 (1/9 + 5/36) ÷ 1/2)
9. 1 0 1 9 .4 5 9 9. 441 19. 6 9. 0 (2 - 2) ÷ 7)
1 0 .1 6 2 0 .6 0 0 20. 72
10. 0 10. 0 (1 - 1)
Test 16 Pages 88 & 89
Test 15 Page 87 Examples for 11 - 20
Example: Example for 1 - 10
3 x 5 = 51, 7 * 4 = 14 3 5 4 x 5 =20 22
20
4 x 6 = 42, 9 * 6 = 27 2 3 x 6 =18
14
3 x 5 = 15 = 51 4 6 20 -18 =2 6 8
7 x 4 = 28 = 14 6 + 8 = 14
2 6 + 14 = 20
12 11 9 x 11=99
4 x 6 = 24 = 42
3 12 x 8=96 8 + 14 = 22
9 x 6 = 54 = 27
2 8 99 - 96=3
9

57
 19 17 3 x 3 x 2 = 18 6 . 729 (9 x 81)
12 5 4 7 . 144 (12 2 )
7 5 40
7 + 5 = 12 8 . 1 ( 1)
7 + 12 = 19 2
5 + 12 = 17 9 . 11 ( 121)
4 x 2 x 5 = 40
33 30 10. 64 (82)
6. 24 (2 x 3 x 4)
21 7. 9 (108 ÷ (3 x 4)
12 9
12 + 9 = 21 8. 168 (6 x 4 x 7) B. Example
12 + 21 = 33
9 + 21 = 30 9. 1/4 (1/16 ÷ (1/2 x 1/2) 10 20 25
10. 2 (80 ÷ (8 x 5)
1 1. 26 (18 + 8)
12. 9 (23 - 14)
Test 18 Page 91 & 92 2 4 5
13. 27 (16 + 11)
14. 25 (47 - 22) A. Example 5 x 2 = 10
15. 50 (19 + 31) 5 x 4 = 20
3 32 = 9 5 x 5 = 25
16. 85 (34 + 51) 9 x 3 = 27 or
17. 65((40 + 25) 27 or 10 ÷ 5 = 2
18. 7(28 - 21) 9 = 3 20 ÷ 5 = 4
19. 33( 66 - 33) 9 25 ÷ 5 = 5
3 x 9 = 27
20. 41(28 + 13)
21 27 30
Test 17 Page 90 5 52 = 25
Examples for 1-5 25 x 5 = 125
A x B= 125 or 7 9 10
A x B 25 = 5
25 5 x 25 = 125 3 x 7 = 21
2
3 x 4= 3 x 9 = 27
6 3 x 10 = 30
3 x 4 12 = 6 22 = 4 or
= 2
2 21 4 x 2 = 8 21 ÷ 3 = 7
1. 15 (5 x 6 ÷ 2) 8 or 27 ÷ 3 = 9
4 = 2 30 ÷ 3 = 10
2. 0.008 (.2 x .08 ÷ 2) 4 2 x 4 = 8
3. 0.05 ( /8 x /15 ÷ 2)
3 4 1. 8(48 ÷ 6)
2. 10(40 ÷ 4)
4. 8 (12 x 2 ÷ 3) 1. 216 (36 x 6)
3. 3(27 ÷ 9)
5. 6 (27 x 2 ÷ 9) 2 . 10 ( 100)
4. 12(24 ÷ 2)
B. Examples for 6-10 3 . 49 (7 2 = 49) 5. 63(9 x 7)
2 3 4 . 8( 64) 6. 32(4 x 8)
18 7. 80(8 x 10)
5 . 16 (4 2 )
3 8. 121(11 x 11)

58
Test 19 Page 93 3. 6 (17 - 14 = 3) 5. 21
(3 + 3 = 6) 3 x 7 x 1/4 x 8 = 1/2
3 2 1 6
5 4 9 3 4. 22 (21 - 2 = 19) 6. 12 x 3/5 x 32 x 0 x 3/5 = 0
1 5 2 3 (19 + 3 = 22)
Test 22 Page 96
6 4 3 3
5. 10 (6 + 7 = 13) Example:
Sum of numbers in (13 - 3 = 10) 20
each column is the
same 6. 17 (19 - 5 = 14)
10
(14 + 3 = 17)
3 + 5 + 1 + 6 = 15
2 + 4 + 5 + 4 = 15 7. 1 (0 - 2 = -2) 40
1 + 9 + 2 + 3 = 15 (-2 + 3 = 1) 20
/2 = 10 x 4 = 40
6 + 3 + 3 + 3 = 15
8. 18 (10 + 11 = 21)
(21 - 3 = 18) 38
1. A = 7 (20 - 13)
2. B = 4 (20 - 16) 9. 5 (11 - 9 = 2) 19
3. C = 4 (20 - 16) (2 + 3 = 5) 38
/2 = 19 x 4 = 76
4. D = 14 (28 - 14)
10. 4 (16 - 15 = 1) 76
5. E = 11 (28 - 17)
6. F = 5 (28 - 23) (1 + 3 = 4 )
12
Test 21 Page 95
Test 20 Page 94 Multiplication 6 12
/2 = 6 x 4 = 24
Example: Example:
4 1 24
2
2 120 3 1. 8
/2 = 4 x 4 = 16
3 2+4=6
6-3=3 54
2. 30 (15 x 2)

7 2 7+2=9 2 x 1 x 3 x 4 x 5 = 120 3. 14
/2 = 7
9-3=6 8 4. 22 (11 x 2)
6 1
/2
6 42
144 5. /2 = 21
1 3 1+3 =4 2 3 6. 28
/2 = 14 x 4 = 56
1
4-3=1 1
6 x 8 x /2 x 2 x 3 = 144 7. 2 (1 x 2)
2 1
1. 6 x /3 x 4 x /3 x 9 = 48 8. 52
/2 = 26 x 4 = 104
1. 22 (10 + 15 = 25) 2. 120 1
(25 - 3 = 22) 1
4X6X10X2 = /4 9. /2 = 1/2
32
3. 1/5 x 1/2 x 1/3 x 1 x 1/4 = 1/120 10. /2 = 16 x 4 = 64
2. 8 (3 + 8 = 11)
(11 - 3 = 8) 4. 500
2X5X2X5 = 5

59
Test 23 Page 97
1 14. 8/15(1/3 + 1/5 )
Example: /3
1 3
5
/9 15. 1/2 (5/6 - 1/3 )
9 139 X 3 =
3 2
/9 16. 3/4 (19/20 - 1/5 )
417
4 7
5
/9 - 2/9 = 3/9 17. 1/3 (14/15 - 3/5 )
1

5-2 3 1 18. 5/8 (3/8 + 1/4 )

5 = 9 = 3
2 9 2
8
19. /9 (5/9 - 1/3 )
1
2 258 x 2 = /6 20. 1/3(11/24 - 1/8 )
6 516
5 5
/6
1 Test 25 Pages 100 &
2
1. 113 x 5 = 565
/3 101
Example:
The missing number is 6 5
/6 - 1/6 = 4/6
2. 996 ÷ 3 = 332 1
/6
The missing number is 3 5-1 4 = 4 =2
=
3. 748 ÷ 187 = 4 9 6 6 3 1
1 /3
4. 224 x 4 = 896 /2
The missing number is 6 7
1
/2 - 1/3 = 3 - 2 = 1/6
1. /10 (1/2 + 1/5 ) 6
5. 856 ÷ 428 = 2
2 3
2. /3 (11/12 - 1/4 ) /9
Test 24 Pages 98 & 99
3
Fractions 3. /5 (2/5 + 1/5 ) 1
7
/8 /2
Example: 4. 1 9 1
/7 ( /14 - /2 ) 7
/8 - 1/2 = 7 - 4 = 3
1 5 1 8 8
1
5. /4 ( /12 - /6 )
/4 1. 1/6 (2/3 - 1/2)
6. 1/3 (13/21 - 2/7 )
1
19
2. 5/12 (3/4 - 1/3)
3 7. /28 (3/7 + 1/4 )
/4 3. 1/10 (1/2 - 2/5)
8. 1/4 (7/12 - 1/3 )
1
/4 + 3/4 = 4/4 4. 3
/20 (3/4 - 3/5)
9
9. /10 (2/5 + 1/2 )
1+3 5. 5
/21 (2/3 - 3/7)
= 1 10. 1/4 (9/20 - 1/5 )
4
6. 3/10 (1/2 - 1/5 )
11. 13/20 (2/5 + 1/4 )
1
7. /20 (1/4 - 1/5 )
12. 1/5 (11/30 - 1/6 )
3
8. /10 (4/5 - 1/2 )
13. 3/4 (11/12 - 1/6 )
7
9. /12 (3/4 - 1/6 )

60
 1-2 7. 4 9. 8
10. 1/12 (5/6 - 3/4 ) 2 =
4 8. 60 10. 9
11. 3/28 (6/7 - 3/4) 5 - 2 = 13
1 4 Test 28 Page 105
4
12. 5/12 (2/3 - 1/4 ) & 106
13
1. 11/4 (31/2 - 21/4) A. Example
13. /24 (2/3 - 1/8 ) C
2. 11/8 (31/4 - 21/8)
14. 1/4 (3/4 - 2/4 )
3. 23/8 (11/8 + 11/4) 1
15. 1
/10 (3/5 - 1/2 ) 2
4. 11/4 (25/8 - 13/8)
16. 1/20 (4/5 - 3/4 ) 2+1=3=c Use the
5. 11/4 (23/4 - 11/2) corresponding number
17. 3/14 (5/7 - 1/2 ) of the alphabet e.g
6. 31/3 (11/6 + 21/6) A=1, B =2
18. 7/30 (5/6 - 3/5 ) C=3 ... Z=26
7. 11/2 (35/8 - 21/8)
19. 9
/28 (3/4 - 3/7 ) I
13
8. 12/3 (35/6 - 21/6)
20. /30 (3/5 - 1/6 )
9. 31/2 (23/8 + 11/8) 5
4
Test 26 Pages 102 & 10. 11/6 (21/3 - 11/6) 4+5 =9=I
103
11. 11/4 (23/4 - 11/2) E
Example:
1 12. 35/6 (11/3 + 21/2)
3 /2
3 2
13. 11/6 (22/3 - 11/2)
7 3 3+2=5=E
7 /8 4 /8 14. 31/3 (51/2 - 21/6)
1. 8 + 6 =14 = N
15. 45/6 (21/3 + 21/2) 2. 10 + 7 = 17 = Q
7
7 /8 - 4 3/8 = 3. 3 + 12 = 15 = O
16. 21/8 (51/4 - 31/8) 4. 18 + 7 = 25 = Y
7-3 4
3 8 = 38 17. 31/10 (51/2 - 22/5) 5.11 + 11 = 22 = V
1 6. 2 + 9 = 11 = K
= 32 18. 43/4 (25/8 + 21/8) 7. 16 + 8 = 24= X
8. 9 + 10 = 19 = S
3
/4 Test 27 Page 104 9. 5 + 15 = 20 = T
1
(Study the pattern and 10 1 + 1 = 2 = B
find out the difference
1 1 B. Example:
3 /4 1 /2 between the members)
1 G H E
3 /4 - 11/2 = 1. 17 4. 45
2. 85 5. 28 M E B
3. 14 6. 21
D F J

61
Using letter codes, A = 1 6 4
5
B = 2 etc.
G + H + E = 20
6 + 4 = 10
10
17 8 5 /2 = 5

M + E + B = 20 1. 11/2 (2+1) ÷ 2
13 5 2
2. 7 (8 x 2) - 9)
D + F + J = 20
4 6 10 3. (3 X 2) - 4)
The numbers of the letter
4. 11 (12 x 2) - 13)
codes when added
horizontally for each row
5. 7 (6 + 8)
gives the same number
2
11. C
12. R
13. I
14. A

Test 29 Page 107

1. 26 (3 x 6) + (4 x 2)
2. 12 (6 x 4) ÷ (2 x 1)
3. 1(3 x 2) ÷ (1 x 6)
4. FISH
5. 60(4 x 3 x 5)
6. 18 (6 x 5) - (4 x 3)
7. 5 (3 x 5) ÷ (3 x 1)
8. 60 (2 x 6) x (5 x 1)
9. 18 (3 x 5) + 3)
10. HIS
Test 30 Page 108
Examples
5 7
6

5+7 =12
12
/2 = 6
8 10
9

8 + 10 =18
18
/2 = 9

62