问题1.简化以下各项，并以p / q的形式写为有理数：
(i)3/4 + 5/6 + -7/8
解决方案：
2 = 2 × 2
6 = 2 × 3
8 = 2 × 2 × 2
LCM is 2 × 2 × 2 × 3 = 24
= (3 × 6 + 5 × 4 + (-7 × 3)) / 24
= (18 + 20 – 21) / 24
= (38 – 21) / 24
= 17 / 24
(ii)2/3 + -5/6 + -7/9
解决方案：
LCM of 3, 6 and 9 is 18
= (2 × 6 + (-5 × 3) + (-7 × 2)) / 18
= (12 – 15 – 14) / 18
= (12 – 29) / 18
= -17 / 18
(iii)-11/2 + 7/6 + -5/8
解决方案：
2 = 2 × 1
6 = 2 × 3
8 = 2 × 2 × 2
LCM is 2 × 2 × 2 × 3 = 24
= (-11 × 12 + 7 × 4 + (-5 × 3)) / 24
= (-132 + 28 – 15) / 24
= (-147 + 28) / 24
= -119 / 24
(iv)-4/5 + -7/10 + -8/15
解决方案：
10 = 5 × 2
15 = 3 × 5
LCM is 5 × 2 × 3 = 30
= (-4 × 6 + (-7 × 3) + (-8 × 2)) / 30
= (-24 – 21 – 16) / 30
= -61 / 30
(v)-9/10 + 22/15 + 13 / -20
解决方案：
This can be written as
-9/10 + 22/15 + -13/20
10 = 2 × 5
15 = 3 × 5
20 = 2 × 2 × 5
LCM is 2 × 2 × 3 × 5 = 60
= (-9 × 6 + 22 × 4 + (-13 × 3)) / 60
= (-54 + 88 – 39) / 60
= (-93 + 88) / 60
= -5 / 60
= -1 / 12
(vi)5/3 + 3 / -2 + -7/3 + 3
解决方案：
This can be written as
5 / 3 + -3 / 2 + -7 / 3 + 3 / 1
LCM is 6
= (5 × 2 + (-3 × 3) + (-7 × 2) + 3 × 6) / 6
= (10 – 9 -14 + 18) / 6
= (28 – 23) / 6
= 5 / 6
问题2.将以下每一项表示为p / q形式的有理数：
(i)-8/3 + -1/4 + -11/6 + 3/8 + -3
解决方案：
4 = 2 × 2
6 = 2 × 3
8 = 2 × 2 × 2
LCM is 2 × 2 × 2 × 3 = 24
= (-8 × 8 + (-1 × 6) + (-11 × 4) + 3 × 3 + (-3 × 24)) / 24
= (-64 – 6 – 44 + 9 – 72) / 24
= (-186 + 9) / 24
= -177 / 24
= -59 / 8
(ii)6/7 +1 + -7/9 + 19/21 + -12/7
解决方案：
(6 / 7 + -12 / 7) + (-7 / 9) + 19 / 21 + 1(Taking numbers with same denominators together)
= (6 – 12) / 7 + (-7 / 9) + 19 / 21+1
= -6 / 7 + -7 / 9 + 19 / 21 + 1 / 1
9 = 3 × 3
21 = 3 × 7
LCM of 7, 1, 9 and 21 is 63
= (-6 × 9 + (-7 × 7) + 19 × 3 + 1 × 63) / 63
= (-54 – 49 + 57 + 63) / 63
= (-103 + 120) / 63
= 17 / 63
(iii)15/2 + 9/8 + -11/3 + 6 + -7/6
解决方案：
15 / 2 + 9/8 + (-11 / 3) + 6 / 1 + (-7 / 6)
LCM of 2, 8, 3, 1 and 6 is 24
= (15 × 12 + 9 × 3 + (-11 × 8) + 6 × 24 + (-7 × 4)) / 24
= (180 + 27 – 88 + 144 – 28) / 24
= (351 – 116) / 24
= (235) / 24
(iv)-7/4 + 0 + -9/5 + 19/10 + 11/14
解决方案：
4 = 2 × 2
5 = 5 × 1
10 = 2 × 5
14 = 2 × 7
LCM is 2 × 2 × 5 × 7 is 140
= (-7 × 35 + (-9 × 28) + 19 × 14 + 11 × 10) / 140
= (-245 – 252 + 266 + 110) / 140
= (-497 + 376) / 140
= (-121) / 140
(v)-7/4 + 5/3 + -1/2 + -5/6 + 2
解决方案：
LCM of 4, 3, 2 and 6 is 12
= (-7 × 3 + 5 × 4 + (-1 × 6) + (-5 × 2) + 2 × 12) / 12
= (-21 + 20 – 6 – 10 + 24) / 12
= (-37 + 44) / 12
= 7 / 12
问题3.简化：
(i)-3/2 + 5/4 + -7/4
解决方案：
Taking numbers with the same denominators together
= -3 / 2 + (5 – 7) / 4
= -3 / 2 – 2 / 4
LCM of 2 and 4 is 4
= (-3 × 2 – 2 × 1) / 4
= (-6 – 2) / 4
= (-8) / 4
= -2
(ii)5/3 + -7/6 + -2/3
解决方案：
Taking numbers with same denominators together
(5 / 3 + -2 / 3) + -7 / 6
= (5 – 2) / 3 + -7 / 6
= 3 / 3 + (-7 / 6)
LCM of 3 and 6 is 6
= (3 × 2 + (-7 × 1)) / 6
= (6 – 7) / 6
= -1 / 6
(iii)5/4 – 7/6 –(-2/3)
解决方案：
This can be written as
5 / 4 – 7 / 6 + 2 / 3
LCM of 4,6 and 3 is 12
= (5 × 3 – 7 × 2 + 2 × 4) / 12
= (15 – 14 + 8) / 12
= (23 – 14) / 12
= 9 / 12
= 3 / 4
(iv)-2/5 –(-3/10)–(-4/7)
解决方案：
This can be written as:
-2 / 5 + 3 / 10 + 4 / 7
LCM of 5,10 and 7 is 70
= (-2 × 14 + 3 × 7 + 4 × 10) / 70
= (-28 + 21 + 40) / 70
= (-28 + 61) / 70
= 33 / 70
(v)5/6 + -2/5 –(-2/15)
解决方案：
This can be written as
5 / 6 + -2 / 5 + 2 / 15
6 = 2 × 3
5 = 5 × 1
15 = 3 × 5
LCM is 2 × 3 × 5 = 30
= (5 × 5 + (-2 × 6) + 2 × 2) / 30
= (25 – 12 + 4) / 30
= (29 – 12) / 30
= 17 / 30
(vi)3/8 –(-2/9)+(-5/36)
解决方案：
This can be written as
3 / 8 + 2 / 9 – 5 / 36
8 = 2 × 2 × 2
9 = 3 × 3
36 = 2 × 2 × 3 × 3
LCM is 2 × 2 × 2 × 3 × 3 = 72
= (3 × 9 + 2 × 8 – 5 × 2) / 72
= (27 + 16 – 10) / 72
= (43 – 10) / 72
= 33 / 72
= 11 / 24