问题1.除法：
(i)1乘1/2
解决方案：
= 1 / (1 / 2)
= 1 × (2 / 1)
= 2
ii)5分-5/7
解决方案：
= 5 / (-5 / 7)
= 5 × (-7 / 5)
5 is the common factor
= -7
(iii)-3/4 x 9 / -16
解决方案：
= (-3 / 4) / (-9 / 16)
= -3 / 4 × (-16 / 9)
3 and 4 are the common factor
= (-3 × -16) / (4 × 9)
= 4 / 3
iv)-7/8 x -21/16
解决方案：
= (-7 / 8) / (-21 / 16)
= -7 / 8 × (-16 / 21)
= (-7 × -16) / (8 × 21)
7 and 8 are the common factor
= 2 / 3
v)7 / -4 x 63/64
解决方案：
= 7 / -4 / (63 / 64)
= -7 / 4 × (64 / 63)
= (-7 × 64) / (4 × 63)
4 and 7 are common factor
= -16 / 9
vi)0 x -7/5
解决方案：
= 0 / (-7 / 5)
= 0 × (-5 / 7)
= 0
(vii)-3/4 x -6
解决方案：
= -3 / 4 / (-6 / 1)
= -3 / 4 × (-1 / 6)
= (-3 × -1) / (4 × 6)
3 is the common factor
= 1 / 8
(viii)2/3 by -7/12
解决方案：
= 2 / 3 / (-7 / 12)
= 2 / 3 × (12 / -7)
= (2 × 12) / (3 × -7)
3 is the common factor
= 8 / -7
= -8 / 7
(ix)-4 by -3/5
解决方案：
= -4 / (-3 / 5)
= -4 × (5 / -3)
= (-4 × -5) / 3
= 20 / 3
[x)-3/13 x -4/65
解决方案：
= -3 / 13 / (-4 / 65)
= -3 / 13 × (65 / -4)
= (-3 × -65) / (13 × 4)
13 is the common factor
= (-3 × -5) / 4
= 15 / 4
问题2：找到值并以标准形式表示为有理数：
(i)2/5÷26/15
解决方案：
= 2 / 5 / (26 / 15)
= 2 / 5 × 15 / 26
= (2 × 15) / (5 × 26)
5 and 2 are the common factor
= 3 / 13
(ii)10/3÷-35/12
解决方案：
= 10 / 3 / (-35 / 12)
= 10 / 3 × -12 / 35
= (10 × -12) / (3 × 35)
Common factor is 5 and 3
= (2 × -4) / (7)
= -8 / 7
(iii)-6÷-8/17
解决方案：
= -6 / (-8 / 17)
= -6 × (-17 / 8)
= (-6 × -17) / (8 × 1)
2 is the common factor
= (-3 × -17) / 4
= 51 / 4
(iv)-40/99÷-20
解决方案：
= -40 / 99 / (-20 / 1)
= -40 / 99 × (-1 / 20)
= (-40 × -1) / (99 × 20)
20 is the common factor
= 2 / 99
(v)-22/27÷-110/18
解决方案：
= (-22 / 27) / (-110 / 18)
= (-22 / 27) × (18 / -110)
= (-22 × 18) / (27 × -110)
9 and 22 are the common factor
= 2 / (3 × 5)
= 2 / 15
(vi)-36/125÷-3/75
解决方案：
= (-36 / 125) / (-3 / 75)
= (-36 / 125) × (75 / -3)
= (-12 / 25) × (15 / -1)
= (-12 × 15) / (25 × -1)
= (-12 × -3) / 5
= 36 / 5
问题3。两个有理数的乘积为15。如果一个数字为-10，则找到另一个。
解决方案：
We know that the product of two rational numbers = 15
One of the number = -10
Let the other number be x
-10x = 15
x = 15 / -10
5 is the common factor
= -3 / 2
The other number is -3 / 2
问题4.两个有理数的乘积是-8/9。如果数字之一是-4/15，请找到另一个。
解决方案：
We know that the product of two rational numbers = -8 / 9
One of the number = -4 / 15
Let the other number be x
(-4 / 15) x = -8 / 9
x = (-8 / 9) / (-4 / 15)
= (-8 / 9) × (15 / -4)
3 and 4 are the common factor
= (-2 / 3) × (5 / -1)
= (-2 × 5) / (3 × -1)
= -10 / -3
= 10 / 3
The other number is 10 / 3
问题5.我们应将-1/6乘以多少才能使乘积为-23/9?
解决方案：
Let the number be x
So, x (-1 / 6) = -23 / 9
x = (-23 / 9) / (-1 / 6)
x = (-23 / 9) × (6 / -1)
= (-23 / 3) × (2 × -1)
= (-23 × -2) / (3 × 1)
= 46 / 3
It should be multiplied by 46 / 3
问题6.我们应将-15/28乘以多少才能使乘积为-5/7?
解决方案：
Let the number be x
So, x (-15 / 28) = -5 / 7
x = (-5 / 7) / (-15 / 28)
x = (-5 / 7) × (28 / -15)
= (-5 ×28) / (7 × -15)
5 and 7 are the common factor
= -4 / -3
= 4 / 3
问题7.我们应将-8/13乘以多少才能使乘积为24?
解决方案：
Let the number be x
So, x (-8 / 13) = 24
x = (24) / (-8 / 13)
= (24) × (13 / -8)
= (24 × 13) / (-8)
8 is the common factor
= -3 × 13
= -39
It should be multiplied by -39
问题8.为了产生2/3，应该将-3/4乘以多少?
解决方案：
Let the number be x
x (-3 / 4) = 2 / 3
x = (2 / 3) / (-3 / 4)
= (2 / 3) × (4 / -3)
= -8 / 9
It should be multiplied by -8 / 9
问题9。如果满足，则求(x + y)÷(xy)
(i)x = 2/3，y = 3/2
解决方案：
x + y = 2 / 3 + 3 / 2
LCM is 6
= (2 × 2 + 3 × 3) / 6
= (4 + 9) / 6
= 13 / 6
x – y = 2 / 3 – 3 / 2
LCM is 6
= (2 × 2 – 3 × 3) / 6
= (4 – 9) / 6
= -5 / 6
(x + y) ÷ (x – y) = (13 / 6) / (-5 / 6)
= (13 / 6) × (6 / -5)
= (13 × -6) / (6 × 5)
6 is the common factor
= -13 / 5
(ii)x = 2/5，y = 1/2
解决方案：
x + y = 2 / 5 + 1 / 2
LCM is 10
= (2 × 2 + 1 × 5) / 10
= (4 + 5) / 10
= 9 / 10
x – y = 2 / 5 – 1 / 2
LCM is 10
(2 × 2 – 1 × 5) / 10
= (4 – 5) / 10
= -1 / 10
(x + y) ÷ (x – y) = (9 / 10) / (-1 / 10)
= (9 / 10) × (10 / -1)
= (9 × 10) / (10 × -1)
10 is the common factor
= -9
(iii)x = 5/4，y = -1/3
解决方案：
x + y = 5 / 4 + -1 / 3
LCM is 12
= (5 × 3 – 1 × 4) / 12
= (15 – 4) / 12
= 11 / 12
x – y = 5 / 4 – (-1/3)
= 5 / 4 + 1 / 3
LCM is 12
= (5 × 3 + 1 × 4) / 12
= 19 / 12
(x + y) ÷ (x – y) = (11 / 12) / (19 / 12)
= (11 / 12) × (12 / 19)
= (11 × 12) / (12 × 19)
Common factor is 12
= 11 / 19
(iv)x = 2/7，y = 4/3
解决方案：
x + y = 2 / 7 + 4 / 3
LCM is 21
= (2 × 3 + 4 × 7) / 21
= (6 + 28) / 21
= 34 / 21
x – y = 2 / 7 – 4 / 3
LCM is 21
= (2 × 3 – 4 × 7) / 21
= (6 – 28) / 21
= -22 / 21
(x + y) ÷ (x – y) = (34 / 21) / (-22 / 21)
= (34 / 21) × (21 / -22)
21 is the common factor
= -34 / 22
= -17 / 11
(v)x = 1/4，y = 3/2
解决方案：
x + y = 1 / 4 + 3 / 2
LCM is 4
= (1 + 3 × 2) / 4
= 7 / 4
x – y = 1 / 4 – 3 / 2
LCM is 4
= (1 – 3 × 2) / 4
= -5 / 4
(x + y) ÷ (x – y) = (7 / 4) / (-5 / 4)
= (7 / 4) × (4 / -5)
4 is the common factor
= -7 / 5
问题10：723米的绳索成本为12¾卢比。查找每米的成本。
解决方案：
23 / 3 meters of rope = Rs 51 / 4
Let us consider a number = x
So, x (23 / 3) = 51 / 4
x = (51 / 4) / (23 / 3)
= (51 / 4) × (3 / 23)
= (51 × 3) / (4 × 23)
= 153 / 92
= 1 61 / 92
Cost per meter is Rs 1 61 / 92