问题1.添加以下有理数：
(i)–5 / 7和3/7
解决方案：
(-5 / 7) + 3 / 7
Since denominators are the same hence numerators will be directly added considering their sign.
Therefore, (-5 + 3) / 7 = (-2) / 7
(ii)-15/4和7/4
解决方案：
Denominators are same so numerators are directly added.
= (-15) / 4 + 7 / 4
= (-15 + 7) / 4
= (-8) / 4
= (4 * (-2)) / 4
= (-2)
(iii)-8/11和-4/11
解决方案：
As denominators are the same numerators are added along with their sign.
= (-8) / 11 + (-4) / 11
= (-8 – 4) / 11 (integers with same sign are added)
= (-12) / 11
(iv)6/13和-9/13
解决方案：
As, denominators are same numerators are added with their sign.
= 6 / 13 + (-9) / 13
= (6 – 9) / 13 (integers with opposite sign)
= (-3) / 13
问题2.添加以下有理数：
(i)3/4和-5/8
解决方案：
Denominators are different, so we need to take the LCM of denominators to make them into like fractions.
LCM of 4 and 8 = 8
= 3 / 4 + (-5) / 8
= (3 × 2 + (-5)) / 8
= (6 – 5) / 8
= 1 / 8
(ii)5 / -9和7/3
解决方案：
Denominators are different, so we need to take the LCM of denominators to make them into like fractions.
LCM of 9 and 3 = 9
= (-5 / 9) + 7 / 3
= (-5 + 7 × 3) / 9
= (-5 + 21) / 9
= 16 / 9
(iii)-3和3/5
解决方案：
Denominators are different, so we need to take the LCM of denominators to make them into like fractions.
= (-3) / 1 + 3 / 5
LCM of 1 and 5 = 5
= ((-3) × 5 + 3) / 5
= (-15 + 3) / 5
= (-12) / 5
(iv)-7/27和11/18
解决方案：
LCM of 27 and 18
27 = 3 × 3 × 3
18 = 2 × 3 × 3
LCM = 3 × 3 × 3 × 2 = 54
Therefore,
= (-7) / 27 + 11 / 18
= ((-7 × 2 + 11 × 3)) / 54
= (-14 + 33) / 54
= 19 / 54
(v)31 / -4和-5 / 8
解决方案：
LCM of 4 and 8 = 8
= ((-31 × 2) + (-5)) / 8
= (-62 – 5) / 8
= (-67) / 8
(vi)5/36和-7/12
解决方案：
LCM of 36 and 12 is 36
= 5 / 36 + (-7) / 12
= (5 + (-7 × 3)) / 36
= (5 + (-21)) / 36
= (-16) / 36
4 is the common factor theta can be canceled
= (-4) / 9
(vii)–5 / 16和7/24
解决方案：
LCM of 16 and 24
16 = 2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
LCM = 2 × 2 × 2 × 2 × 3 = 48
= (-5) / 16 + 7 / 24
= ((-5 × 3) + 7 × 2) / 48
= (-15 + 14) / 48
= (-1) / 48
(viii)7 / -18和8/27
解决方案：
LCM of 18 and 27
18 = 2 × 3 × 3
27 = 3 × 3 × 3
LCM = 3 × 3 × 3 × 2 = 54
= ((-7 × 3) + 8 × 2) / 54
= (-21 + 16) / 54
= (-5) / 54
问题3.简化：
(i)8/9 + -11/6
解决方案：
LCM of 9 and 6
9 = 3 × 3
6 = 2 × 3
LCM = 2 × 3 × 3 = 18
= (8 × 2 + (-11 × 3)) / 18
= (16 – 33) / 18
= (-17) / 18
(ii)3 + 5 / -7
LCM of 1 and 7 is 7
= (3 × 7 + (-5)) / 7
= (21 – 5) / 7
= 16 / 7
(iii)1 / -12 + 2 / -15
解决方案：
LCM of 12 and 15
12 = 2 × 2 × 3
15 = 3 × 5
LCM = 2 × 2 × 3 × 5 = 60
= ((-1 × 5) + (-2 × 4)) / 60
= (-5 – 8) / 60
= (-13) / 60
(iv)-8/19 + -4/57
解决方案：
LCM of 19 and 57 is 57
= ((-8 × 3) + (-4)) / 57
= (-24 – 4) / 57
= (-28) / 57
( v)7/9 + 3 / -4
解决方案：
LCM of 9 and 4 is 36
= (7 × 4 + (-3 × 9)) / 36
= (28 – 27) / 36
= 1 / 36
(六)5/26 + 11 / -39
解决方案：
LCM of 26 and 39
26 = 13×2
39 = 13×3
LCM = 13 × 2 × 3 = 78
= (5 × 3 + (-11 × 2)) / 78
= (15 – 22) / 78
= (-7) / 78
(vii)-16/9 + -5/12
解决方案：
LCM of 16 and 12
9 = 3×3
12 = 2 × 2 × 3
LCM = 3 × 3 × 2 × 2 = 36
= ((-16 × 4) + (-5 × 3)) / 36
= (-64 – 15) / 36
= (-79) / 36
= (-79) / 36
(viii)-13/8 + 5/36
解决方案：
LCM of 8 and 36
8 = 2 × 2 × 2
36 = 2 × 2 × 3 × 3
LCM = 2 × 2 × 2 × 3 × 3 = 72
= ((-13 × 9) + 5 × 2) / 72
= (-117 + 10) / 72
= (-107) / 72
(ix)0 + -3 / 5
解决方案：
0 is the additive identity, if added to any number gives the same number
= (-3) / 5
(x)1 + -4 / 5
解决方案：
LCM of 1 and 5 is 5
= (1 × 5 + (-4)) / 5
= (5 – 4) / 5
= 1 / 5
问题4.将和相加并表示为混合分数：
(i)-12/5和43/10
解决方案：
LCM is 10
= ((-12 × 2 + 43)) / 10
= (-24 + 43) / 10
= 19 / 10
(ii)24/7和-11/4
解决方案：
LCM of 7 and 4 is 28
= (24 × 4 + (-11 × 7)) / 28
= (96 – 77) / 28
= 19 / 28
Proper fraction cannot be converted to mixed fraction
(iii)-31/6和-27/8
解决方案：
LCM of 8 and 6 is 24
= ((-31 × 4) + (-27 × 3)) / 16
= (-124 – 81) / 24
= (-205) / 24
(iv)101/6和7/8
解决方案：
LCM of 8 and 6 is 24
101 / 6 + 7 / 8
= (101 × 4 + 7 × 3) / 24
= (404 + 21) / 24
= 425 / 24
