问题1.乘以：
(i)7/11 x 5/4
解决方案：
7/11 × 5/4
Multiplying numerator with numerator of other rational number and denominator with denominator
= (7 × 5)/(11 × 4)
= 35/44
(ii)5/7 x -3/4
解决方案：
(5/7) × (-3/4)
Multiplying numerator with numerator of other rational number and denominator with denominator
= (5 × -3)/(7 × 4)
= -15/28
(iii)-2/9 by 5/11
解决方案：
-2/9 × 5/11
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-2 × 5)/(9 × 11)
= -10/99
(iv)-3 // 17除以-5 / -4
解决方案：
-3/17 × 5/4
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-3 × 5)/(17 × 4)
= -15/68
(v)9 / -7至36 / -11
解决方案：
(9/-7) × (36/-11)
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-9 × -36)/(7 × 11)
= 324/77
(vi)-11/13 by -21/7
解决方案：
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-11 × -21)/(13 × 7)
= 231/91
(vii)-3/5 by -4/7
解决方案：
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-3 × -4)/(5 × 7)
= 12/35
(viii)-15/11 by 7
解决方案：
-15/11×7/1
Multiplying numerator with numerator of other rational number and denominator with denominator
=(-15×7)/(11×1)
=-105/11
问题2.相乘
(i)-5/17 x 51 / -60
解决方案：
(-5/17) × (51/-60)
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-5 × -51)/(17 × 60)
Common factor of 5 and 60
= 51/17 × 12
51 and 12 have 3 as common factor
= 17/17 × 4
= 1/4
(ii)-6/11至-55/36
解决方案：
(-6/11) × (-55/36)
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-6 × -55)/(11 × 36)
Common factor of 6 and 36, 55 and 11
= 5/6
(iii)-8/25至-5/16
解决方案：
(-8/25) × (-5/16)
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-8 × -5)/(25 × 16)
Common factor of 8 and 16, 5 and 25
= 1/5 × 2
= 1/10
(iv)6/7至-49/36
解决方案：
(6/7) × (-49/36)
Multiplying numerator with numerator of other rational number and denominator with denominator
= (6 × -49)/(7 × 36)
Common factor of 6 and 36, 49 and 7
= -7/6
(v)8 / -9 x -7 / -16
解决方案：
-8/9 × 7/16
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-8 × 7)/(9 × 16)
Common factor of 8 and 16
= -7/9 × 2
= -7/18
(vi)-8/9 x 3/64
解决方案：
-8/9 × 3/64
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-8 × 3)/(9 × 64)
Common factor of 8 and 64, 3 and 9
= -1/3 × 8
= -1/24
问题3.简化以下各项，并将结果表示为标准格式的有理数：
(i)(-16/21)×(14/5)
解决方案：
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-16 × 14)/(21 × 5)
Common factor of 21 and 14
= (-16 × 2)/(3 × 5)
= -32/15
(ii)(7/6)×(-3/28)
解决方案：
Multiplying numerator with numerator of other rational number and denominator with denominator
= (7 × -3)/(6 × 28)
Common factor of 7, 28, 3 and 6
= -1/2 × 4
= -1/8
(iii)(-19/36)×16
解决方案：
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-19 × 16)/(36 × 1)
Common factor of 16 and 36
= (-19×4)/(9 × 1)
=-76/9
(iv)(-13/9)×(27 / -26)
解决方案：
Multiplying numerator with numerator of other rational number and denominator with denominator
=(-13× -27)/(9×26)
Common factor of 27 and 9 , 13 and 26
=(-1 × -3)/(2)
=3/2
(v)(-9/16)×(-64 / -27)
解决方案：
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-9 × 64) / (16 × 27)
Common factor of 9 and 27, 64 and 16
= (-1 × 4) / (1 × 3)
= -4/3
(六)(-50/7)×(14/3)
解决方案：
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-50 × 14)/(7 × 3)
Common factor of 14 and 7
= (-50 × 2)/(3)
= -100/3
(vii)(-11/9)×(-81 / -88)
解决方案：
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-11 × 81)/(9 × 88)
Common factor of 1, 88, 9 and 81
= (-1 × 9)/(1 × 8)
= -9/8
(viii)(-5/9)×(72 / -25)
解决方案：
Multiplying numerator with numerator of other rational number and denominator with denominator
= (-5 * -72)/(9 × 25)
Common factor of 5 and 25, 9 and 72
= (-1 × -8)/(1 × 5)
= 8/5
4.简化：
(i)((25/8)×(2/5))–((3/5)×(-10/9))
解决方案：
= ((25 × 2)/(8 × 5)) – ((3 × -10)/(5 × 9))
= 50/40 – (-30)/45
= 5/4 + 2/3
LCM of 4 and 3 is 12
= (5 × 3 + 2 × 4)/12
= (15 + 8)/12
= 23/12
(ii)((1/2)×(1/4))+((1/2)×6)
解决方案：
= ((1 × 1)/(2 × 4)) + ((1 × 6)/(1 × 2))
= 1/8 + 3/1
LCM of 8 and 1 is 8
= (1 × 1 + 3 × 8)/8
= (1 + 24)/8
= 25/8
(iii)(-5×(2/15))–(-6×(2/9))
解决方案：
= ((-5 × 2)/(15 × 1)) – ((-6 × 2)/(1 × 9))
= (-10/15) – (-12/9)
Common factor of 10 and 15, 12 and 9
= -2/5 + 4/3
LCM of 5 and 3 is 15
= (-2 × 3 + 4 × 4)/15
= (-6 + 16)/15
= 10/15
Common factor of 10 and 15
= 2/3
(iv)((-9/4)×(5/3))+((13/2)×(5/6))
解决方案：
= (-9 × 5)/(4 × 3) + (13 × 5)/(2 × 6)
Common factor of 9 and 3
= (-45/12) + (65/12)
As denominators are same
= (-45 + 65)/12
= (20)/12
Common factor of 20 and 12
= 5/3
(v)((-4/3)×(12 / -5))+((3/7)×(21/15))
解决方案：
= (-4 * -12)/(3 × 5) + ((3 × 21)/(7 × 15))
= 48/15 + 3/5 (Common factor 3 and 15, 21 and 7)
LCM of 15 and 5 is 15
= (48 + 3 × 3)/15
= (48 + 9)/15
= 57/15
Common factor of 57 and 15
= 19/5
(vi)((13/5)×(8/3))–((-5/2)×(11/3))
解决方案：
= (13 × 8)/(5 × 3) – ((-5 × 11)/(2 × 3))
= 104/15 – 55/6
LCM of 15 and 6 is 3 × 5 × 2 = 30
= (104 × 2 + 55 × 5)/30
= (208 + 275)/30
= 483/30
(vii)((13/7)×(11/26))-((-4/3)×(5/6))
解决方案：
= ((13 × 11)/(7 × 26)) – ((-4 × 5)/(3 × 6))
Common factor of 13 and 26, 4 and 6
= 11/7 × 2 – (-2 × 5/3 × 3)
= 11/14 + 10/9
LCM of 14 and 9 is 126
= (11 × 9 + 10 × 14)/126
= (99 + 140)/126
= 239/126
问题5：简化：
(i)((3/2)×(1/6))+((5/3)×(7/2)–(13/8)×(4/3))
解决方案：
= (3 × 1)/(2 × 6) + (5 × 7)/(3 × 2) – (13 × 4)/(8 × 3)
Common factor of 3 and 6, 4 and 8
= 1/4 + 35/6 – 13/6
LCM of 4 and 6 is 12
= (1 × 3 + 35 × 2 – 13 × 2)/12
= (3 + 70 – 26)/12
= (73 – 26)/12
= 47/12
(ii)((1/4)×(2/7))—(5/14)×(-2/3)+(3/7)×(9/2)
解决方案：
= (1 × 2)/(4 × 7) – (5 × -2)/(14 × 3) + (3 × 9)/(7 × 2)
Common factor of 2 and 4, 2 and 14
= 1/14 – (-5/21) + 27/14
LCM of 21 and 14 is 7 × 2 × 3 = 42
= 1/14 + 5/21 + 27/14
LCM of 14 and 21 is 2 × 7 × 3 = 42
= (1 × 3 + 5 × 2 + 27 × 3)/42
= (3 + 10 + 81)/42
= (94)/42
(iii)((13/9)×(-15/2))+((7/3)×(8/5)+(3/5)×(1/2))
解决方案：
= (13 × -15)/(9 × 2) + ((7 × 8)/(3 × 5) + (3 × 1)/(5 × 2))
Common factor of 9 and 15
= (13 × -5)/(3 × 2) + ((56/15) + 3/10)
= -65/6 + 56/15 + 3/10
6 = 2 × 3
15 = 3 × 5
10 = 2 × 5
LCM is 2 × 3 × 5 = 30
= (-65 × 5 + 56 × 2 + 3 × 3)/30
= (-325 + 112 + 9)/30
= (-325 + 121)/30
= -204/30
(iv)((3/11)×(5/6))–(9/12)×(4/3)+(5/13)×(6/15)
解决方案：
= (3 × 5)/(11 × 6) – ((9 × 4)/(12 × 3) + (5 × 6)/(13 × 15))
Common factor of 3 and 6, 9 and 12, 5 and 15
= 5/22 – 1/1 + 2/13
= 5/22 – 1/1 + 2/13
LCM of 22,1 and 13 is 286
= (5 × 13 – 286 + 2 × 22)/286
= (65 – 286 + 44)/286
= (65 – 330)/286
= -177/286