เฉลยแบบฝึกหัดคณิต ม.1ภาคเรียนที่ 2

‡©≈¬
Àπà«¬°“√‡√’¬π√Ÿâ∑’Ë 1
‡»… à«π·≈–∑»π‘¬¡

°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 1

5 10 15 20 25 19 38 57 76 95
1. = = = = 2. = = = =
7 14 21 28 35 3 6 9 12 15

2 4 6 8 10 17 34 51 68 85
3. = = = = 4. = = = =
13 26 39 52 65 13 26 39 52 65

°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 2

100 100 ÷ 2 100 ÷ 4 100 ÷ 5 100 ÷ 10
1. = = = =
200 200 ÷ 2 200 ÷ 4 200 ÷ 5 200 ÷ 10

50 25 20 10
= = = =
100 50 40 20

400 400 ÷ 2 400 ÷ 4 400 ÷ 8 400 ÷ 10
2. = = = =
240 240 ÷ 2 240 ÷ 4 240 ÷ 8 240 ÷ 10

200 100 50 40
= = = =
120 60 30 24

36 36 ÷ 2 36 ÷ 3 36 ÷ 4 36 ÷ 6
3. = = = =
252 252 ÷ 2 252 ÷ 3 252 ÷ 4 252 ÷ 6

18 12 9 6
= = = =
126 84 63 42

°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 3

18 18 ÷ 18 1 21 21 ÷ 7 3
1. = = 2. = =
36 36 ÷ 18 2 49 49 ÷ 7 7

2 ·ºπ°“√®—¥°“√‡√’¬π√Ÿâ§≥‘μ»“ μ√åæ◊Èπ∞“π ™—Èπ¡—∏¬¡»÷°…“ªï∑’Ë 1 ¿“§‡√’¬π∑’Ë 2

88 88 ÷ 11 8 91 91 ÷ 7 13
3. = = 4. = =
121 121 ÷ 11 11 35 35 ÷ 7 5
153 153 Ϭ 17 9
5. = =
187 187 Ϭ 17 11

·∫∫Ωñ°À—¥ 1

1 1× 2 1× 3 3 3×2 3×3
1. (1) = = (2) = =
4 4×2 4×3 5 5×2 5×3
2 3 6 9
= = = =
8 12 10 15
4 4×2 4×3 5 5×2 5×3
(3) = = (4) = =
7 7×2 7×3 9 9×2 9×3
8 12 10 15
= = = =
14 21 18 27
11 11 × 2 11 × 3 13 13 × 2 13 × 3
(5) = = (6) = =
6 6×2 6×3 9 9×2 9×3
22 33 26 39
= = = =
12 18 18 27

12 12 Ϭ 2 12 Ϭ 3 84 84 ÷ 2 84 ÷ 4
2. (1) = = (2) = =
18 18 Ϭ 2 18 Ϭ 3 96 96 ÷ 2 96 ÷ 4
6 4 42 21
= = = =
9 6 48 24
70 70 Ϭ 5 70 Ϭ 10 32 32 Ϭ 2 32 Ϭ 4
(3) = = (4) = =
30 30 Ϭ 5 30 Ϭ 10 48 48 Ϭ 2 48 Ϭ 4
14 7 16 8
= = = =
6 3 24 12
426 426 Ϭ 2 426 Ϭ 3 1264 1264 ÷ 2 1264 ÷ 4
(5) = = (6) = =
768 768 Ϭ 2 768 Ϭ 3 3216 3216 ÷ 2 3216 ÷ 4
213 124 632 316
= = = =
384 256 1608 804

3. (1) 27 (2) 65 (3) 16 (4) 8 (5) 72

(6) 9 (7) 60 (8) 20 (9) 84 (10) 77

9 4 11 6 3
4. (1) (2) (3) (4) (5)
8 5 7 7 4
11 13 13 19 5
(6) (7) (8) (9) (10)
20 15 23 23 3

·ºπ°“√®—¥°“√‡√’¬π√Ÿâ§≥‘μ»“ μ√åæ◊Èπ∞“π ™—Èπ¡—∏¬¡»÷°…“ªï∑’Ë 1 ¿“§‡√’¬π∑’Ë 2 3

°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 4

9 5 6 8
1. ·≈– 2. Ϫ ·≈– Ϫ 13
11 8 11

9 9×8 72 6 6 × 13 78
«‘∏’∑” = = «‘∏’∑” Ϫ = Ϫ = Ϫ
11 11 × 8 88 11 11 × 13 143

5 5 × 11 55 8 8 × 11 88
= = Ϫ = Ϫ = Ϫ
8 8 × 11 88 13 13 × 11 143

72 55 78 88
‡π◊ËÕß®“° Ͼ ‡π◊ËÕß®“° Ϫ Ͼ Ϫ
88 88 143 143

9 5 6 8
¥—ßπ—Èπ Ͼ μÕ∫ ¥—ßπ—Èπ Ͼ μÕ∫
11 8 11 13

41 36 11
3.
5
·≈– 4
4. Ϫ 8
16
·≈– Ϫ 8 3
7

41 41 × 4 164 11 11 × 7 77
«‘∏’∑” = = «‘∏’∑” Ϫ = Ϫ = Ϫ
5 5×4 20 16 16 × 7 112

36 36 × 5 180 3 3 × 16 48
= = Ϫ = Ϫ = Ϫ
4 4×5 20 7 7 × 16 112

164 180 77 48
‡π◊ËÕß®“° Ͻ ‡π◊ËÕß®“° Ϫ Ͻ Ϫ
20 20 112 112

41 36 11 3
¥—ßπ—Èπ Ͻ μÕ∫ ¥—ßπ—Èπ Ϫ Ͻ Ϫ
5 4 16 7

11 3
π—π§◊Õ
Ë Ϫ8 Ͻ Ϫ8 μÕ∫
16 7

·∫∫Ωñ°À—¥ 2

4 6
1. (1) ,
11 17
«‘∏’∑” ‡π◊ËÕß®“° 4 × 17 = 68

·≈– 6 × 11 = 66

¥—ßπ—Èπ 4 × 17 Ͼ 6 × 11

4 6
®–‰¥â«à“ Ͼ μÕ∫
11 17


9 25
(2) ,
13 29
«‘∏’∑” ‡π◊ËÕß®“° 9 × 29 = 261

·≈– 25 × 13 = 325

¥—ßπ—Èπ 9 × 29 Ͻ 25 × 13

9 25
®–‰¥â«à“ Ͻ μÕ∫
13 29
15 285
(3) ,
17 323
«‘∏’∑” ‡π◊ËÕß®“° 15 × 323 = 4,845

·≈– 17 × 285 = 4,845

¥—ßπ—Èπ 15 × 323 = 17 × 285

15 285
®–‰¥â«à“ = μÕ∫
17 323
7 9
(4) Ϫ , Ϫ
9 13
«‘∏’∑” ‡π◊ËÕß®“° (Ϫ7) × 13 = Ϫ91

·≈– (Ϫ9) × 9 = Ϫ81

¥—ßπ—Èπ (Ϫ7) × 13 Ͻ (Ϫ9) × 9

7 9
®–‰¥â«à“ Ϫ Ͻ Ϫ μÕ∫
9 13
42 53
(5) Ϫ ,Ϫ
51 71
«‘∏’∑” ‡π◊ËÕß®“° (Ϫ42) × 71 = 2,982

·≈– (Ϫ53) × 51 = Ϫ2,703

¥—ßπ—Èπ (Ϫ42) × 71 Ͻ (Ϫ53) ×51

42 53
®–‰¥â«à“ Ϫ Ͻ Ϫ μÕ∫
51 71
5 112
(6) Ϫ 3 , Ϫ 3
8 133
5
«‘∏’∑” æ‘®“√≥“ Ϫ
8
, Ϫ 112
133
‡π◊ËÕß®“° (Ϫ5) × 133 = Ϫ665

·≈– (Ϫ112) × 8 = Ϫ896

¥—ßπ—Èπ (Ϫ5) × 133 Ͼ (Ϫ112) × 8


5 112
®–‰¥â«à“ Ϫ Ͼ Ϫ
8 133
5 112
®–‰¥â«à“ Ϫ3 Ͼ Ϫ3 μÕ∫
8 133

2. (1) = (2) Ͻ (3) Ͼ (4) Ͻ (5) Ͻ (6) =
(7) = (8) = (9) Ͻ (10) Ͼ (11) = (12) Ͻ

3 5 4 7 6
3. (1) , , , ,
5 6 7 8 9
«‘∏’∑” ‡ª≈’Ë¬π‡»… à«π¢â“ßμâπ„Àâ¡’μ—« à«π‡∑à“°—π ‚¥¬À“ §.√.π. ¢Õßμ—« à«π ·μà‡π◊ËÕß®“°
6 2
= ®÷ßÀ“ §.√.π. ¢Õß 5, 6, 7, 8 ·≈– 3
9 3
3 ) 3, 5, 6, 7, 8

2 ) 1, 5, 2, 7, 8

1, 5, 1, 7, 4

§.√.π. ¢Õß 3, 5, 6, 7 ·≈– 8 §◊Õ 3 × 2 × 5 × 7 × 4 = 840
3 3×3×2×7× 4 504
= =
5 5×3×2×7× 4 840
5 5×5×7×4 700
= =
6 6×5×7×4 840
4 4×3×2×5× 4 480
= =
7 7×3×2×5× 4 840
7 7×3×5×7 735
= =
8 8×3×5×7 840
6 2 2×2×5×7×4 560
= = =
9 3 3×2×5×7× 4 840
4 3 6 5 7
¥—ßπ—Èπ ‡√’¬ß≈”¥—∫®”π«π®“°πâÕ¬‰ª¡“°‰¥â¥—ßπ’È , , , ,
7 5 9 6 8
μÕ∫
7 6 11 25 2
(2) Ϫ , Ϫ , Ϫ , Ϫ , Ϫ
9 8 12 28 3
«‘∏’∑” ‡ª≈’Ë¬π‡»… à«π¢â“ßμâπ„Àâ¡’μ—« à«π‡∑à“°—π ‚¥¬À“ §.√.π. ¢Õßμ—« à«π ·μà‡π◊ËÕß®“°
6 3
Ϫ = Ϫ ®÷ßÀ“ §.√.π. ¢Õß 9, 4, 12, 28 ·≈– 3
8 4
3 ) 9, 4, 12, 28, 3

4 ) 3, 4, 14, 28, 1

3, 1, 01, 07, 1

§.√.π. ¢Õß 9, 4, 12, 28 ·≈– 3 §◊Õ 3 × 4 × 3 × 7 = 252
7 7×4×7 196
Ϫ = Ϫ = Ϫ
9 9×4×7 252
6 3 3×9×7 189
Ϫ =Ϫ = Ϫ = Ϫ
8 4 4×9×7 252


11 11 × 3 × 7 231
Ϫ = Ϫ = Ϫ
12 12 × 3 × 7 252
25 25 × 9 225
Ϫ = Ϫ = Ϫ
28 28 × 9 252
2 2×3× 4×7 168
Ϫ = Ϫ = Ϫ
3 3×3× 4×7 252

¥—ßπ—Èπ ‡√’¬ß®”π«π®“°πâÕ¬‰ª¡“°‰¥â¥—ßπ’È Ϫ 12 , Ϫ 25 , Ϫ 9 , Ϫ 6 , Ϫ 2
11
28
7
8 3
μÕ∫

3 7 10 8 12
(3) , , , ,
2 6 9 7 11
«‘∏’∑” ‡ª≈’Ë¬π‡»… à«π¢â“ßμâπ„Àâ¡’μ—« à«π‡∑à“°—π ‚¥¬À“ §.√.π. ¢Õßμ—« à«π
2 ) 2, 6, 9, 7, 11

3 ) 1, 3, 9, 7, 11
1, 1, 3, 7, 11

§.√.π. ¢Õß 2, 6, 9, 7 ·≈– 11 §◊Õ 2 × 3 × 3 × 7 × 11 = 1,386
3 3 ϫ 3 ϫ 3 ϫ 7 ϫ 11 2079
= =
2 2 ϫ 3 ϫ 3 ϫ 7 ϫ 11 1386
7 7 ϫ 3 ϫ 7 ϫ 11 1617
= =
6 6 ϫ 3 ϫ 7 ϫ 11 1386
10 10 ϫ 2 ϫ 7 ϫ 11 1540
= =
9 9 ϫ 2 ϫ 7 ϫ 11 1386
8 8 ϫ 2 ϫ 3 ϫ 3 ϫ 11 1584
= =
7 7 ϫ 2 ϫ 3 ϫ 3 ϫ 11 1386
12 12 ϫ 2 ϫ 3 ϫ 3 ϫ 7 1512
= =
11 11 ϫ 2 ϫ 3 ϫ 3 ϫ 7 1386
12 10 8 7 3
¥—ßπ—Èπ ‡√’¬ß®”π«π®“°πâÕ¬‰ª¡“°‰¥â¥—ßπ’È , , , ,
11 9 7 6 2
μÕ∫

13 15 19 23 18
(4) Ϫ ,Ϫ ,Ϫ ,Ϫ ,Ϫ
8 11 15 17 7
«‘∏’∑” ‡ª≈’Ë¬π‡»… à«π¢â“ßμâπ„Àâ¡’μ—« à«π‡∑à“°—π ‚¥¬À“ §.√.π. ¢Õßμ—« à«π
§.√.π. ¢Õß 8, 11, 15, 17 ·≈– 7 §◊Õ 157,080
13 13 ϫ 11 ϫ 15 ϫ 17 ϫ 7 255255
Ϫ = Ϫ = Ϫ
8 18 ϫ 11 ϫ 15 ϫ 17 ϫ 7 157080
15 15 ϫ 8 ϫ 15 ϫ 17 ϫ 7 214200
Ϫ = Ϫ = Ϫ
11 11 ϫ 8 ϫ 15 ϫ 17 ϫ 7 157080
19 19 ϫ 8 ϫ 11 ϫ 17 ϫ 7 198968
Ϫ = Ϫ = Ϫ
15 15 ϫ 8 ϫ 11 ϫ 17 ϫ 7 157080
23 23 ϫ 8 ϫ 11 ϫ 15 ϫ 7 212520
Ϫ = Ϫ = Ϫ
17 17 ϫ 8 ϫ 11 ϫ 15 ϫ 7 157080
18 18 ϫ 8 ϫ 11 ϫ 15 ϫ 17 403920
Ϫ = Ϫ = Ϫ
7 7 ϫ 8 ϫ 11 ϫ 15 ϫ 17 157080

¥—ßπ—Èπ ‡√’¬ß®”π«π®“°πâÕ¬‰ª¡“°‰¥â¥—ßπ’È Ϫ 18 , Ϫ 13 , Ϫ 15 , Ϫ 17 , Ϫ 19
7 8 11
23
15
μÕ∫


·∫∫Ωñ°À—¥ 3

4 5 7
1. (1) + +
5 6 8

«‘∏’∑” À“ §.√.π. ¢Õß 5, 6 ·≈– 8 ‰¥â 120
4 5 7 4 × 24 5 × 20 7 × 15
+ + = + +
5 6 8 5 × 24 6 × 20 8 × 15

96 100 105
= + +
120 120 120

301
=
120

61
= 2 μÕ∫
120

(2) ⎛ − ⎠ +
13 4⎞ 3
⎝ 15 9 4

«‘∏’∑” À“ §.√.π. ¢Õß 15, 9 ·≈– 4 ‰¥â 180

⎛ 13 − 4⎞ + 3 = ⎛ 13 × 12 − 4 × 20 ⎞ + 3 × 45
⎝ 15 9 ⎠ 4 ⎝ 15 × 12 9 × 20 ⎠ 4 × 45

= ⎛ 156 − 80 ⎞ + 135
⎝ 180 180 ⎠ 180

211
=
180

31
= 1 μÕ∫
180

(3) ⎛ + ⎞ −
2 5 8
⎝ 3 6⎠ 9

«‘∏’∑” À“ §.√.π. ¢Õß 3, 6, 9 ‰¥â 18

⎛ 2 + 5⎞ − 8 = ⎛ 2 × 6 + 5 × 3⎞ − 8 × 2
⎝ 3 6⎠ 9 ⎝ 3 × 6 6 × 3⎠ 9 × 2

= ⎛ 12 + 15⎞ − 16
⎝ 18 18⎠ 18

11
= μÕ∫
18


(10 + 6) + ⎛ + ⎞
3 5 3 5
(4) «‘∏’∑” 10 + 6 = ⎝ 5 6⎠
5 6
3 × 6 5 × 5⎞
= 16 + ⎛
⎝ 5 × 6 + 6 × 5⎠

16 + ⎛ + ⎞
18 25
= ⎝ 30 30 ⎠
43
= 16 +
30
13
= 17 μÕ∫
30
5 26
(5) «‘∏’∑” 10 − 3 = 10 −
7 7
70 26
= −
7 7
44
=
7
2
= 6 μÕ∫
7
3 7 58 97
(6) «‘∏’∑” 11 − 6 = −
5 15 5 15
58 × 3 97
= −
5 × 3 15
174 97
= −
15 15
77
=
15
2
= 5 μÕ∫
15
3 7 43 55
(7) «‘∏’∑” 10 − 6 = −
4 8 4 8
43 × 2 55
= −
4×2 8
86 55
= −
8 8
31
=
8
7
= 3 μÕ∫
8
3 3 78 3
(8) «‘∏’∑” 15 − = −
5 4 5 4
78 × 4 3 × 5
= −
5×4 4×5
312 15
= −
20 20
297
=
20
17
= 14 μÕ∫
20


(9) «‘∏’∑” ⎛12 15 − 10 3⎞ + 5 3 = ⎛ 207 − 43⎞ + 43
⎝ 16 4⎠ 8 ⎝ 16 4⎠ 8

= ⎛ 207 − 172 ⎞ + 86
⎝ 16 16 ⎠ 16

121
=
16

9
= 7 μÕ∫
16

(10) «‘∏’∑” ⎛ 2 1 + 3 1⎞ − 5 = ⎛ 5 + 13⎞ − 5
⎝ 2 4⎠ ⎝2 4 ⎠

= ⎛ 10 + 13⎞ − 20
⎝ 4 4⎠ 4

3
= μÕ∫
4

12 − ⎛1 + ⎞
3 3 5 51 ⎛ 11 5 ⎞
(11) «‘∏’∑” = − +
4 ⎝ 8 12 ⎠ 4 ⎝ 8 12 ⎠

51 × 6 ⎛ 11 × 3 5 × 2 ⎞
= − +
4 × 6 ⎝ 8 × 3 12 × 2 ⎠

306 ⎛ 33 10 ⎞
= − +
24 ⎝ 24 24⎠

306 43
= −
24 24

263
=
24

23
= 10 μÕ∫
24

(12) «‘∏’∑” 5 7 ⎛1 3 ⎞
+ − + = ⎛ 5 × 2 + 7 × 3⎞ − ⎛ 1 + 1 ⎞
12 8 ⎝ 4 12 ⎠ ⎝ 12 × 2 8 × 3⎠ ⎝ 4 4⎠

= ⎛ 10 + 21⎞ − 1
⎝ 24 24⎠ 2

31 12
= −
24 24

19
= μÕ∫
24


⎛ 5⎞ ⎛ 7 ⎞ 5 7
(13) «‘∏’∑” ⎜Ϫ ⎟ ϩ ⎜Ϫ ⎟ = Ϫ Ϫ
⎝ 8⎠ ⎝ 12⎠ 8 12
5ϫ3 7ϫ2
= Ϫ Ϫ
8 ϫ 3 12 ϫ 2
15 14
= Ϫ Ϫ
24 24
29
= Ϫ
24
5
= Ϫ1 μÕ∫
24
⎛ 4⎞ 3 4 ϫ 18 3 ϫ 5
(14) «‘∏’∑” ⎜Ϫ ⎟ ϩ = Ϫ ϩ
⎝ 5⎠ 18 5 ϫ 18 18 ϫ 5

72 15
= Ϫ ϩ
90 90
57
= Ϫ
90
19
= Ϫ μÕ∫
30
12 ⎛ 15⎞ 7 12 ϫ 4 ⎛ 15 ϫ 7⎞ 7 ϫ 28
(15) «‘∏’∑” ϩ ⎜Ϫ ⎟ Ϫ = ϩ ⎜Ϫ ⎟Ϫ
21 ⎝ 12⎠ 3 21 ϫ 4 ⎝ 12 ϫ 7⎠ 3 ϫ 28

48 ⎛ 105⎞ 196
= ϩ ⎜Ϫ ⎟ Ϫ
84 ⎝ 84 ⎠ 84

253
= Ϫ
84
1
= Ϫ3 μÕ∫
84
⎛ 8⎞ 1 3 ⎛ 8 ϫ 40 ⎞ ⎛ 1 ϫ 168 ⎞ ⎛ 3 ϫ 105⎞
(16) «‘∏’∑” ⎜Ϫ ⎟ Ϫ ϩ = ⎜Ϫ ⎟ Ϫ⎜ ⎟ϩ⎜ ⎟
⎝ 21⎠ 5 8 ⎝ 21 ϫ 40 ⎠ ⎝ 5 ϫ 168⎠ ⎝ 8 ϫ 105⎠

320 168 315
= Ϫ Ϫ ϩ
840 840 840
173
= Ϫ μÕ∫
840
1 ⎛ 1 3⎞ 1 ⎛ 6 19⎞
(17) «‘∏’∑” Ϫ ⎜1 ϩ 2 ⎟ = Ϫ⎜ ϩ ⎟
3 ⎝ 5 8⎠ 3 ⎝5 8 ⎠

1 ϫ 40 ⎛ 6 ϫ 24 19 ϫ 15⎞
= Ϫ⎜ ϩ ⎟
3 ϫ 40 ⎝ 5 ϫ 24 8 ϫ 15 ⎠

40 ⎛ 144 285⎞
= Ϫ⎜ ϩ ⎟
120 ⎝ 120 120 ⎠

40 429
= Ϫ
120 120
389
= Ϫ
120
29
= Ϫ3 μÕ∫
120


⎛ 3 8⎞ 7 ⎛ 3 ϫ 117⎞ ⎛ 8 ϫ 65⎞ ⎛ 7 ϫ 45 ⎞
(18) «‘∏’∑” ⎜Ϫ Ϫ ⎟ Ϫ = ⎜Ϫ ⎟ Ϫ⎜ ⎟ Ϫ⎜ ⎟
⎝ 5 9⎠ 13 ⎝ 5 ϫ 117⎠ ⎝ 9 ϫ 65⎠ ⎝ 13 ϫ 45⎠

351 520 315
= Ϫ Ϫ Ϫ
585 585 585

1186
= Ϫ
585

16
= Ϫ2 μÕ∫
585

3
2. μÕπ‡™â“π“¬¥”‡π‘π‡¥‘π∑“ß‰¥â 5
4
°‘‚≈‡¡μ√
5
μÕπ∫à“¬‡¥‘π∑“ß‰¥â 4
6
°‘‚≈‡¡μ√

∂÷ßμ”∫≈‡¢“™—¬ π

(1) «‘∏’∑” μ”∫≈‚§°¡à«ß·≈–μ”∫≈‡¢“™—¬ πÕ¬ŸàÀà“ß°—π
3 5 19
5 +4 = 9+ °‘‚≈‡¡μ√
4 6 12

7
= 10 °‘‚≈‡¡μ√
12

7
¥—ßπ—Èπ μ”∫≈‚§°¡à«ß·≈–μ”∫≈‡¢“™—¬ πÕ¬ŸàÀà“ß°—π 10
12
°‘‚≈‡¡μ√ μÕ∫
2
(2) «‘∏’∑” ¢“°≈—∫‡¥‘π∑“ß‰¥â√–¬–∑“ß 3
5
°‘‚≈‡¡μ√ ®÷ßπ—Ëßæ—°
7 2 11
®ÿ¥∑’Ëπ—Ëßæ—°Àà“ß®“°μ”∫≈‚§°¡à«ß 10 −3 = 7 °‘‚≈‡¡μ√
12 5 60

11
¥—ßπ—Èπ ®ÿ¥∑’Ëπ—Ëßæ—°Àà“ß®“°μ”∫≈‚§°¡à«ß 7
60
°‘‚≈‡¡μ√ μÕ∫
1
3. «‘∏’∑” π“¬·¢Áß·√ßμ—°πÈ”„πμÕπ‡™â“‰¥â 3
3
ªï∫
ö
3
μÕπ∫à“¬μ—°πÈ”‰¥âÕ’° 4
4
ªï∫
ö
1 3 13 1
√«¡μ—°πÈ”‰¥â 3 +4 = 7+ = 8 ªïö∫
3 4 12 12

3
μÕπ§Ë”„™âπÈ”∑’Ëμ—°‰«â‰ª 2
5
ªï∫
ö
1 3 29
¬—ß‡À≈◊ÕπÈ”Õ¬Ÿà 8 −2 = 5 ªï∫
ö
12 5 60

29
¥—ßπ—Èπ ¬—ß‡À≈◊ÕπÈ”Õ¬Ÿà 5
60
ªï∫
ö μÕ∫


3
4. «‘∏’∑” ¡’πÈ”¡—πÕ¬Ÿà 16
4
∂—ß
2
„™âπÈ”¡—π‰ª 5
5
∂—ß
3 2 7
¬—ß‡À≈◊ÕπÈ”¡—π 16 − 5 = 11 ∂—ß
4 5 20

5
π”πÈ”¡—π¡“‡æ‘Ë¡Õ’° 9
6
∂—ß
7 5 11
¥—ßπ—Èπ ®–¡’πÈ”¡—π‡ªìπ 11 + 9 = 21 ∂—ß μÕ∫
20 6 60

5. «‘∏’∑” ©“ß¢â“«¡’¢â“«Õ¬Ÿà 65 ∂—ß
2
«—π·√°μ«ß¢â“«ÕÕ°‰ª 14
3
∂—ß
1
«—π∑’Ë Õßμ«ß¢â“«ÕÕ°‰ªÕ’° 16
2
∂—ß
⎛ 2⎞ 1 5
¥—ßπ—Èπ ®–‡À≈◊Õ¢â“« ⎜ 65−14 ⎟ −16 = 33 ∂—ß
⎝ 3⎠ 2 6

3
«—π∑’Ë “¡π”¢â“«¡“„ à≈ß©“ß 21
4
∂—ß
5 3 7
¥—ßπ—Èπ ®–¡’¢â“«„π©“ß 33 +21 = 55 ∂—ß μÕ∫
6 4 12

6. ‡π◊ËÕß®“°πÈ”Àπ—°°√–‡ªÜ“√«¡°—∫ ‘Ëß¢Õß A, B, C, D, E ·≈– F ¡’πÈ”Àπ—°√«¡
1 7 3 3 4 2 1 19
3 + 4 + 6 + 8 + 3 + 5 + 3 = 35 °‘‚≈°√—¡
2 10 4 5 5 5 5 20

μâÕß°“√πÈ”Àπ—°√«¡°√–‡ªÜ“Àπ—°¡“°∑’Ë ÿ¥ ·μà‰¡à‡°‘ππÈ”Àπ—°∑’Ë°”Àπ¥
(1) 30 °‘‚≈°√—¡
«‘∏’∑” ®–μâÕß‡≈◊Õ° ‘Ëß¢Õß A, C, D, E ·≈– F ´÷Ëß®–¡’πÈ”Àπ—°√«¡°—∫πÈ”Àπ—°°√–‡ªÜ“‡ªìπ
19 3 1
35 − 6 = 29 °‘‚≈°√—¡
20 4 5

¥—ßπ—Èπ ‡≈◊Õ° ‘Ëß¢Õß A, C, D, E ·≈– F μÕ∫
(2) 25 °‘‚≈°√—¡
«‘∏’∑” ®–μâÕß‡≈◊Õ° ‘Ëß¢Õß C, D, E ·≈– F ´÷Ëß®–¡’πÈ”Àπ—°√«¡°—∫πÈ”Àπ—°°√–‡ªÜ“‡ªìπ
19 ⎛ 7
− 4 + 6 ⎞ = 24
3 1
35
20 ⎝ 10 4⎠ 2
°‘‚≈°√—¡
¥—ßπ—Èπ ‡≈◊Õ° ‘Ëß¢Õß C, D, E ·≈– F μÕ∫


(3) 20 °‘‚≈°√—¡
«‘∏’∑” ®–μâÕß‡≈◊Õ° ‘Ëß¢Õß A, C ·≈– F ´÷Ëß®–¡’πÈ”Àπ—°√«¡°—∫πÈ”Àπ—°°√–‡ªÜ“‡ªìπ
1 7 3 1 13
3 + 4 + 8 + 3 = 19 °‘‚≈°√—¡
2 20 5 5 20

¥—ßπ—Èπ ‡≈◊Õ° ‘Ëß¢Õß A, C ·≈– F μÕ∫
(4) 15 °‘‚≈°√—¡
«‘∏’∑” ®–μâÕß‡≈◊Õ° ‘Ëß¢Õß A ·≈– B ´÷Ëß®–¡’πÈ”Àπ—°√«¡°—∫πÈ”Àπ—°°√–‡ªÜ“‡ªìπ
1 7 3 19
3 + 4 + 6 = 14 °‘‚≈°√—¡
2 10 4 20

¥—ßπ—Èπ ‡≈◊Õ° ‘Ëß¢Õß A ·≈– B μÕ∫

°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 5

1
2 1 2 ×1 4 2 4×2
1. × = 2. × =
5 2 5×2 5 7 5×7
1
1 8
= =
5 35
1
⎛ Ϫ 3⎞ ϫ 2 = (Ϫ 3) ϫ 2 2 ⎛ 4⎞ 2 ϫ (Ϫ 4)
3. 4. ϫ ⎜Ϫ ⎟ =
⎝ 5 ⎠ 9 5 ϫ 93 3 ⎝ 7⎠ 3ϫ7
Ϫ2 Ϫ8
= =
15 21
1
8 7 8×7 1 3 1× 3
5. × = 6. × =
9 11 9 × 11 3 5 1
3×5
56 1
= =
99 5
1 1
3 ⎛ Ϫ 7⎞ 3 ϫ (Ϫ 7) ⎛ Ϫ 11⎞ ϫ ⎛ Ϫ 3⎞ = Ϫ 11 ϫ (Ϫ 3)
7. ϫ = 8.
5 ⎝ 9 ⎠ 5ϫ9 ⎝ 12 ⎠ ⎝ 4 ⎠ 12 ϫ 4
3 4
Ϫ7 11
= =
15 16

9. ⎛ Ϫ 2⎞ ϫ ⎛ Ϫ 4⎞ = Ϫ 2 ϫ Ϫ 4 10. ⎛ Ϫ 5⎞ ϫ 5 = (Ϫ 5) ϫ 5
⎝ 5 ⎠ ⎝ 5 ⎠ 5ϫ5 ⎝ 6 ⎠ 8 6ϫ8
8 Ϫ 25
= =
25 48
1
2 4 2×4 3 4 3× 4
11. × = 12. × =
5 5 5×5 5 9 5×9
3
8 4
= =
25 15


°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 6

1
Ϫ 5⎞ 8 ⎛ Ϫ 5⎞
8ϫ⎛
3 5 3
1. 5× = × 2. = ϫ
11 1 11 ⎝ 8 ⎠ 1 ⎝ 8 ⎠
1
15
= = Ϫ5
11
4
= 1
11
6
2 2 18 1 1 9
3. × 18 = × 4. ×9 = ×
3 3 1 2 2 1
1
9
= 12 =
2
1
= 4
2
2 3
Ϫ 3⎞ Ϫ 10 ⎞ ⎛ Ϫ 3⎞ Ϫ 5⎞ 9 ⎛ Ϫ 5⎞
5. (Ϫ 10) ϫ ⎛ = ⎛ ϫ 6. 9ϫ⎛ = ϫ
⎝ 5 ⎠ ⎝ 1 ⎠ ⎝ 5 ⎠ ⎝ 6 ⎠ 1 ⎝ 6 ⎠
1 2
15
= Ϫ6 = Ϫ
2
1
= Ϫ7
2
1
5
7. ⎛ Ϫ 15⎞ ϫ (Ϫ 9) = ⎛ Ϫ 15⎞ ϫ ⎛ Ϫ 9⎞ 8. ⎛ Ϫ 2⎞ ϫ 15 = ⎛ Ϫ 2⎞ ϫ 15
⎝ 18 ⎠ ⎝ 2 18 ⎠ ⎝ 1 ⎠ ⎝ 3 ⎠ ⎝ 3 ⎠ 1
1
15
= = Ϫ10
2
1
= 7
2
3
Ϫ 27⎞ 7
= ⎛
7 5 5 13
9. (Ϫ 27) ϫ ϫ 10. × 13 = ×
9 ⎝ 1 ⎠ 9 8 8 1
1
65
= Ϫ21 =
8
1
= 8
8
4 7
7 7 ⎛ Ϫ 12⎞ 5 5 14
11. ϫ (Ϫ 12) = ϫ 12. × 14 = ×
9 9 ⎝ 1 ⎠ 6 6 1
3 3
28 35
= Ϫ =
3 3
1 2
= Ϫ9 = 11
3 3


°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 7

1 4
1.
2
×4
1
=
2 9
× 2. ⎛Ϫ 1⎞ ϫ 6 2 = ⎛Ϫ 1⎞ ϫ 20
3 2 3 12 ⎝ 5⎠ 3 ⎝ 5⎠ 3
3 1
9 4
= = Ϫ
3 3
1
= 3
3
Ϫ 21⎞
ϫ ⎛Ϫ 10 ⎞ = ϫ⎛ 4. ⎛Ϫ 2 ⎞ ϫ ⎛Ϫ ⎞ = ⎛Ϫ ⎞ ϫ ⎛Ϫ ⎞
9 1 9 1 2 9 2
3.
10 ⎝ 2⎠ 10 ⎝ 2 ⎠ ⎝ 4 ⎠ ⎝ 3⎠ ⎝ 4 ⎠ ⎝ 3⎠
1 1
Ϫ 189 (Ϫ 3) ϫ (Ϫ 2)
= =
20 42
9 3
= Ϫ9 =
20 2
1 5
3 1 3 7 4 1 4 25
5. ×2 = × 6. ×4 = ×
4 3 413 5 6 5 6
1 2
7 4×5
= =
4 63
3 10
= Ϫ1 =
4 3
1
= 3
3

7. ⎛Ϫ 72⎞ ϫ 3 = ⎛ Ϫ 37⎞ ϫ 3 8.
1 1
×3 =
1 7
×
⎝ 5⎠ 4 ⎝ 5 ⎠ 4 3 2 3 2
Ϫ 111 7
= =
20 6
11 1
= Ϫ5 = 1
20 6
1
3 ⎛
ϫ Ϫ2 ⎞ =
⎛Ϫ 1⎞ ϫ 12 = ⎛Ϫ 1⎞ ϫ 7 1 3 ⎛ 7⎞
9. 10. ϫ Ϫ
⎝ 2⎠ 5 ⎝ 2⎠ 2 4 ⎝ 3⎠ 4 ⎝ 3⎠
1
7 7
= Ϫ = Ϫ
4 4
3 3
= Ϫ1 = Ϫ1
4 4
2 1

11.
4
×4
2
=
4 22
× 12. ⎛ Ϫ 6⎞ ϫ ⎛Ϫ 21⎞ = ⎛Ϫ 6⎞ ϫ ⎛Ϫ 7⎞
5 5 5 5 ⎝ 7 ⎠ ⎝ 3⎠ ⎝ 1 7⎠ ⎝ 3 ⎠
1
88
= = 2
25
13
= 3
25


°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 8

15
1 2 13 30 3 3 11
1. 3 ×4 = × 2. 3×2 = ×
4 7 2
4 7 4 1 4
195 33
= =
14 4
13 1
= 13 = 8
14 4
1
1
3 ⎛ 1⎞ 53 ⎛ 5⎞ 5 1 23 3
3. 5 ϫ ⎜Ϫ1 ⎟ = ϫ ⎜Ϫ ⎟ 4. 2 ×1 = ×
10 ⎝ 4⎠ 2 10 ⎝ 4⎠ 9 2
3
9 2
53 23
= Ϫ =
8 6
5 5
= Ϫ6 = 3
8 6
1
1 1 7 13 ⎛ 1⎞ 7 2
5. 2 ×6 = × 6. ⎜Ϫ3 ⎟ × 2 = Ϫ ×
3 2 3 2 ⎝ 2⎠ 1
2 1
91
= = Ϫ7
6
1
= 15
6
1
1 3 2 ⎛ 1⎞ ⎛ 1⎞ ⎛ 5⎞ ⎛ 5⎞
7. 1 ×2 = × 8. ⎜Ϫ1 ⎟ × ⎜Ϫ1 ⎟ = ⎜Ϫ ⎟ × ⎜Ϫ ⎟
2 1
2 1 ⎝ 4⎠ ⎝ 4⎠ ⎝ 4⎠ ⎝ 4⎠
25
= 3 =
16
9
= 1
16

1 2 9 7 ⎛ 5⎞ 30 × ⎛Ϫ 29⎞
5
9. 2 ×1 = × 10. 30 × ⎜Ϫ4 ⎟ = ⎜ ⎟
4 5 4 5 ⎝ 6⎠ 1 ⎝ 6⎠
1
63
= = Ϫ145
20
3
= 3
20
11 6
⎛ 1⎞ × ⎛ 2 ⎞ 73 ⎛ 44⎞ 1 12 17
11. ⎜Ϫ9 ⎟ ⎜Ϫ6 ⎟ = Ϫ × ⎜Ϫ ⎟ 12. 12 × 8 = ×
⎝ 8⎠ ⎝ 7⎠ 2
8 ⎝ 7⎠ 2 1 1 2
803
= = 102
14
5
= 57
14


°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 9

11 4 1
1. 2. Ϫ 3. 15 4. Ϫ
6 13 17
17 5 16 200
5. Ϫ 6. 7. Ϫ 8.
9 23 49 3

°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 10

3 2
5 2 5 9 1 ⎛ 3⎞ 1 ⎛ 4⎞
1. ÷ = × 2. ÷ ⎜Ϫ ⎟ = ×⎜Ϫ ⎟
6 9 2
6 2 2 ⎝ 4⎠ 1
2 ⎝ 3⎠
15 2
= = Ϫ
4 3
3
= 3
4
2 2
3 5 3 16 2 5 2 6
3. ÷ = × 4. ÷ = ×
8 16 1 8 5 3 6 3 5
1
6 4
= =
5 5
1
= 1
5
1 1
⎛ 5⎞ 3 5 2 7 3 7 2
5. ⎜Ϫ ⎟ ÷ = Ϫ × 6. ÷ = ×
⎝ 4⎠ 2 2
4 3 2 2 2 3
1
5 7
= Ϫ =
6 3
1
= 2
3
1 2 1
⎛ 3⎞ ⎛ 3 ⎞ ⎛ 3⎞ ⎛ 10 ⎞ 3 3 3 10
7. ⎜Ϫ ⎟ Ϭ⎜Ϫ ⎟ = ⎜Ϫ ⎟ ϫ⎜Ϫ ⎟ 8. ÷ = ×
⎝ 5⎠ ⎝ 10 ⎠ ⎝ 5⎠ ⎝ 3 ⎠ 5 10 5 13
1 1
2
2 10
= =
1 1
5
= 2 = 2
2 2
2 1 2 6 1 ⎛ 7⎞ 1 ⎛ 8⎞
9. ÷ = × 10. ×⎜Ϫ ⎟ = ×⎜Ϫ ⎟
9 6
3
9 1 4 ⎝ 8⎠ 1
4 ⎝ 7⎠
4 2
= = Ϫ
3 7
1
= 1
3


1
2 5 2 8 ⎛ 5⎞ ⎛ 11⎞ ⎛ 5⎞ ⎛ 3 ⎞
11. ÷ = × 12. ⎜Ϫ ⎟ ÷ ⎜Ϫ ⎟ = ⎜Ϫ ⎟ ϫ ⎜Ϫ ⎟
3 8 3 5 ⎝ 6⎠ ⎝ 3 ⎠ ⎝ 6⎠ ⎝ 11⎠
2
16 5
= =
15 22
1
= 1
15

°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 11

1
9 9 1 ⎛ 10 ⎞ 10 ⎛ 9 ⎞
1. ÷2 = × 2. 10 ÷ ⎜Ϫ ⎟ = × ⎜Ϫ ⎟
10 10 2 ⎝ 9⎠ 1 ⎝ 10 ⎠
1
9
= = Ϫ9
20

3 3 1 1 15 5
3. ÷8 = × 4. 15 ÷ = ×
7 7 8 5 1 1
3
= = 75
56
2
⎛ 1⎞ ⎛ 1⎞ ⎛ 1 ⎞ 3 6 4
5. ⎜Ϫ ⎟ ÷ Ϫ2 = ⎜Ϫ ⎟ ÷ ⎜Ϫ ⎟ 6. 6÷ = ×
⎝ 6⎠ ⎝ 6⎠ ⎝ 2 ⎠ 4 113
1
= = 8
12
2
3 2 4 ⎛ 4⎞ ⎛ 4⎞ 1
7. 2÷ = × 8. ⎜Ϫ ⎟ ÷ 2 = ⎜Ϫ ⎟ ϫ
4 1 3 ⎝ 3⎠ ⎝ 3⎠1 2
8 2
= = Ϫ
3 3
2
= 2
3

2 7 5 ⎛ 3⎞ ⎛ 3⎞ ⎛ 1 ⎞
9. 7÷ = × 10. ⎜Ϫ ⎟ ÷(Ϫ4) = ⎜Ϫ ⎟ ϫ⎜Ϫ ⎟
5 1 2 ⎝ 8⎠ ⎝ 8⎠ ⎝ 4⎠
35 3
= =
2 32
1
= 17
2


°‘®°√√¡μ√«® Õ∫§«“¡‡¢â“„® 12

1 2 85 30 3 ⎛ 2⎞ 23 ⎛ 3⎞
1. 12 ÷ 4 = ÷ 2. 4 ÷⎜Ϫ ⎟ = ×⎜Ϫ ⎟
7 7 7 7 5 ⎝ 3⎠ 5 ⎝ 2⎠
1
85 7 69
= × = Ϫ
1 7 17 30 10
85 9
= = Ϫ6
6 30 10
17
=
6
5
= 2
6
7
5 4 11 5 1 3 21 10
3. 1 ÷ = × 4. 5 ÷ = ×
6 5 6 4 4 10 4 3 1
55 7 × 105
= =
24 42
7 35
= 2 =
24 2
1
= 17
2

⎛ 2⎞ 1 17 16 ⎛ 1 ⎞ ⎛ 3⎞ ⎛ 21⎞ ⎛ 7⎞
5. ⎜Ϫ3 ⎟ ÷3 = Ϫ ÷ 6. ⎜Ϫ10 ⎟ ÷⎜Ϫ1 ⎟ = ⎜Ϫ ⎟ ÷⎜Ϫ ⎟
⎝ 5⎠ 5 5 5 ⎝ 2⎠ ⎝ 4⎠ ⎝ 2 ⎠ ⎝ 4⎠
1 3
17 5 21 ⎛ 4⎞
= Ϫ × = Ϫ ×⎜Ϫ ⎟
1
5 16 2 ⎝ 1 7⎠
2
17 3× 4
= Ϫ =
16 2
1
1
= Ϫ1 = 6
16

·∫∫Ωñ°À—¥ 4
2
4 22 4 × 22 5
1. (1) × = (2) ×0 = 0
11 33 11 × 33 18
1
8
=
33
3 1
42 ⎛ 39 ⎞ 42 × 39 45 68 45 × 68
(3) ×⎜Ϫ ⎟ = Ϫ (4) × =
13 ⎝ 168⎠ 1
13 × 168 17 180 17 × 1804
1 1
42 × 3 68
= Ϫ =
1684 68
1
3
= Ϫ = 1
4


1 7
⎛ 13 ⎞ ⎛ 15⎞ 13 12 12 91
(5) (Ϫ15) × ⎜ ⎟ = ⎜Ϫ ⎟ϫ (6) × 91 = × 5
⎝ 45⎠ ⎝ 1 ⎠ 45 13 131 1
3
13
= Ϫ = 84
3
1
= Ϫ4
3
8 3
⎛ 7⎞ ⎛ 7 ⎞ ⎛ 24⎞ 3 2 3 42
(7) ⎜Ϫ ⎟ ×(Ϫ24) = ⎜Ϫ ⎟ ×⎜Ϫ ⎟ (8) ×8 = ×
⎝ 15⎠ ⎝ 15⎠ ⎝ 1 ⎠ 14 5 141 5
5
56 9
= =
5 5
1 4
= 11 = 1
5 5
4 9
2 7 44 7 4 1 4 81
(9) 14 × = ϫ (10) ×8 = ×
3 11 3 111 9 10 91 10
28 24×9
= =
3 105
1 18
= 9 =
3 5
3
= 3
5
2
⎛ 1⎞ ⎛ 1⎞ ⎛ 13⎞ ⎛ 26⎞ 2 5 58 63
(11) ⎜Ϫ4 ⎟ ×⎜Ϫ5 ⎟ = ⎜Ϫ ⎟ ×⎜Ϫ ⎟ (12) 8 ×2 = ×
⎝ 3⎠ ⎝ 5⎠ ⎝ 3⎠ ⎝ 5⎠ 7 29 7 291
9
338 2 × 63
= =
15 71
8
= 22 = 18
15
17 16 1 1
2. (1) (2) Ϫ (3) (4)
5 15 4 6
5 3 2 6
(5) Ϫ (6) (7) (8) Ϫ
44 29 11 29
1 2
5 15 5 17 8 ⎛ 4⎞ 8 ⎛ 81⎞
3. (1) ÷ = × (2) ÷ ⎜Ϫ ⎟ = × ⎜Ϫ ⎟
6 17 6 153 9 ⎝ 81⎠ 9 ⎝ 4⎠
91
17 2 × 81
= = Ϫ
18 1 9

= Ϫ18
6 4
7 56 7 36 10 40 13
(3) ÷ = × (4) 40 ÷ = ×
6 36 16 56 13 1 10 1
1 7×6
= = 52
568
3
=
4
4
⎛ 12⎞ ⎛ 48⎞ ⎛ 17⎞ 12 7 13
(5) (Ϫ48) ÷ ⎜Ϫ ⎟ = ⎜Ϫ ⎟ × ⎜Ϫ ⎟ (6) 7÷ = ×
⎝ 17⎠ ⎝ 1 ⎠ ⎝ 12⎠ 13 1 12
1
91
= 68 =
12
7
= 7
12

เฉลยแบบฝึกหัดคณิต ม.1ภาคเรียนที่ 2

เฉลยแบบฝึกหัดคณิต ม.1ภาคเรียนที่ 2

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เฉลยแบบฝึกหัดคณิต ม.1ภาคเรียนที่ 2