问题1.在每个以下项中，从第二个减第一个有理数：
(i)3/8和5/8
解决方案：
= 5/8 – 3/8
As denominators are same
= (5 – 3) / 8
= 2/8
= 1/4
(ii)-7/9和4/9
解决方案：
= 4/9 – (-7/9)
= 4/9 + 7/9
As denominators are same
= (4 + 7) / 9
= 11/9
(iii)-2/11和-9/11
解决方案：
= -9/11 – (-2/11)
= -9/11 + 2/11
As denominators are same
= (-9 + 2) / 11
= -7/11
(iv)11/13和-4/13
解决方案：
=-4/13-11/13
As denominators are same
=(-4-11) / 13
=(-15) / 13
(v)1/4和-3/8
解决方案：
=-3/8-1/4
LCM of 4 and 8 is 8
=(-3-1×2) / 8
=(-3-2) / 8
=(-5) / 8
=(-5) / 8
(vi)-2/3和5/6
解决方案：
=5/6- (-2/3)
=5/6+2/3
LCM of 2 and 3 is 6
=(5+(2×2)) / 6
=(5+4) / 6
=9/6
=3/2
(vii)-6/7和-13/14
解决方案：
=-13/14- (-6/7)
=-13/14+6/7
LCM of 14 and 7 is 14
=(-13+6×2) / 14
=(-13+12) / 14
=-1/14
(viii)-8/33和-7/22
解决方案：
=-7/22- (-8/33)
=-7/22+8/33
LCM of 22 and 33
22=11×2
33=11×3
LCM is 66
=(-7×3+8×2) / 66
=(-21+16) / 66
=(-5) / 66
问题2：评估以下各项：
(i)2 / 3-3 / 5
解决方案：
LCM of 3 and 5 is 15
=(2×5-3×3) / 15
=(10-9) / 15
=1/15
(ii)-4 / 7-2 / -3
解决方案：
This can be written as
=-4/7- (-2)/3
=-4/7+2/3
LCM of 7 and 3 is 21
=(-4×3+2×7) / 21
=(-12+14) / 21
=2/21
(iii)4/7 –(-5 / -7)
解决方案：
This can be written as
=4/7-(5)/7
As denominators are same
=(4-5) / 7
=(-1) / 7
(iv)-2 –(5/9)
解决方案：
=-2/1-5/9
LCM of 1 and 9 is 9
=(-2×9-5×1) / 9
=(-18-5) / 9
=(-23) / 9
(v)-3 / -8 –(-2/7)
解决方案：
This can be written as
=3/8+2/7
LCM of 8 and 7 is 56
=(3×7+2×8) / 56
=(21+16) / 56
=37/16
(vi)-4/13 –(-5/26)
解决方案：
This can be written as
=-4/13+5/26
LCM of 13 and 26 is 26
=(-4×2+5×1) / 26
=(-8+5) / 26
=(-3) / 26
(vii)-5/14 –(-2/7)
解决方案：
This can be written as
=-5/14+2/7
LCM of 14 and 7 is 14
=(-5×1+2×2) / 14
=(-5+4) / 14
=(-1) / 14
(viii)13/15 – 12/25
解决方案：
15=3×5
25=5×5
LCM is 5×5×3=75
=(13×5-12×3) / 75
=(65-36) / 75
=(29) / 75
(ix)-6/13 –(-7/13)
解决方案：
This can be written as
=-6/13+7/13
As denominators are same
=(-6+7) / 13
=1/13
(x)7/24 – 19/36
解决方案：
24=2×2×2×3
36=2×2×3×3
LCM is 2×2×2×3×3 =72
=(7×3-19×2) / 72
=(21-38) / 72
=(-17) / 72
(xi)5/63 –(-8/21)
解决方案：
This can be written as
=5/63+8/21
LCM of 21 and 63 is 63
=(5×1+8×3) / 63
=(5+24) / 63
=29/63
问题3.两个数字的和为5/9。如果其中一个数字是1/3，则找到另一个。
解决方案：
Let the other number be x
1/3+x=5/9 (As sum is 5/9)
x=5/9-1/3 (On transposing 1/3)
LCM of 3 and 9 is 9
x=(5×1-1×3) / 9
x=(5-3) / 9
x=2/9
Therefore, other number is 2/9
问题4.两个数字的总和为-1/3。如果其中一个数字是-12/3，请查找另一个。
解决方案：
Let the other number be x
-12/3+x=-1/3 (As -1/3 is the sum)
x=-1/3+12/3(Transposing -12/3)
x=(-1+12) / 3
x=11/3
Therefore, the other number is 11/3
问题5.两个数字的总和为-4/3。如果一个数字是-5，找到另一个。
解决方案：
Sum of two numbers = -4/3
One of the number = -5/1
-5+x=-4/3
x=-4/3+5/1 (Transposing -5)
LCM of 3 and 1 is 3
x= (-4×1+5×3) / 3
= (-4 + 15)/3
= 11/3
The other number is 11/3
问题6.两个有理数之和为-8。如果其中一个数字是-15/7，请找到另一个。
解决方案：
Sum of two rational numbers = -8/1
One of the number = -15/7
Let the other rational number as x
x + -15/7 = -8
7 is the LCM
(7x -15) / 7 = -8
Transposing 7 to the right side
7x -15 = -8×7
7x — 15 = -56
7x = -56+15
x = -41/7
Other number is -41/7
问题7：应将什么添加到-7/8以获得5/9?
解决方案：
Let the number to be added be x
-7/8+x=5/9
x=5/9+7/8 (Transposing -7/8)
LCM of 9 and 8 is 72
x=(5×8+7×9) / 72
x=(40+63) / 72
x=103/72
Therefore, 103/72 should be added
问题8.应该将什么数字加到-5/11以获得26/33?
解决方案：
Let the number to be added be x
-5/11+x=26/33
x=26/33+5/11 (Transposing 5/11)
LCM of 33 and 11 is 33
x=(26×1+5×3) / 33
x=(26+15) / 33
x=41/33
Therefore, 41/33 should be added
问题9.必须将什么数字加到-5/7以获得-2/3?
解决方案：
Let the number be x
-5/7+x=-2/3
x=-2/3+5/7 (Transposing -5/7)
LCM of 3 and 7 is 21
x=(-2×7+5×3) / 21
x=(-14+15) / 21
x=1/21
Therefore, 1/21 should be added
问题10.应该从-5/3中减去多少才能得到5/6?
解决方案：
Let the number be x
-5/3 – x = 5/6
-x = 5/6 + 5/3 (Transposing 5/3)
LCM of 3 and 6 is 6
-x = (5 × 1 + 5 × 2) / 6
-x=(5+10) / 6
-x=15/6
x=-15/6
x=-5/2
Therefore, -5/2 should be subtracted.