Please answer the questions
Answers
Step-by-step explanation:
(24)
a) Given numbers are 7/-13 and -8/15
LCM of 13 and 15 = 195
7/-13
= -7/13
= (-7/13)×(15/15)
= (-7×15)/(13×15)
= -105/195
and
-8/15
= (-8/15)×(13/13)
= (-8×13)/(15×13)
=> -104/195
So,
-105/195 < -104/195
-7/13 < -8/15
b) Given numbers are 5/8 and -9/14
We know that
Negative numbers are always less than positive numbers
5/8 > -9/14
c)Given numbers are -11/16 and 13/-16 = -13/16
-11/16 >-13/16
d)Given numbers are -9/-13 = 9/13 and
36/52 = 9/13
Both are same
-9/-13 = 36/52
25)
a) Given numbers are -3/8 , 5/-12, -7/16, -13/18 , 11/-24
The can be written as -3/8, -5/12, -7/16, -13/18, -11/24
The denominators = 8,12,16,18,24
LCM of the denominators = 144
-3/8 = (-3/8)×(18/18) = -54/144
-5/12 = (-5/12)×(12/12) =-60/144
-7/16 = (-7/16)×(9/9) = -63/144
-13/18 = (-13/18)×(8/8) = -104/144
-11/24 = (-11/24)×(6/6) = -66/144
Ascending order of the numbers
= -104/144 , -66/144, -63/144, -60/144, -54/144
-13/8 , -11/24, -7/16, -5/12 , -3/8
b) Given numbers are 9/25 ,2/5, 14/-75, -19/10, 8/15
The denominators = 25 , 5, 75, 10, 15
LCM of the denominators = 150
9/25 = (9/25)×(6/6) = 54/150
2/5 = (2/5)×(30/30) = 60/150
14/-75 =(-14/75)×(2/2) = -28/150
-19/10 = (-19/10)×(15/15) = -285/150
8/15 = (8/15)×(10/10) = 80/150
Ascending order of the numbers
= -285/150, -28/150, 54/150, 60/150, 80/150
-19/10, 14/-75, 9/25, 2/5, 8/15
26)
(a) Given numbers are 7/8, 11/12, 15/-16, 1/4,14/-15
The denominators = 8,12,16,4,15
LCM of the denominators = 240
7/8 = (7/8)×(30/30) = 210/240
11/12 = (11/12)×(20/20) = 220/240
15/-16 = (-15/16)×(15/15) = -225/240
1/4 = (1/4)×(60/60) = 60/240
14/-15 = (-14/15)×(16/16) = -224/240
Descending order of the numbers
= 220/240, 210/240, 60/240, -224/240, -225/240
11/12, 7/8, 1/4, 14/-15, 15/-16
(b) Given numbers are -5/6, 3, -13/-4,17/-6, -11/12, -13/9
The denominators = 6,4,6,12,9
LCM of the denominators = 36
-5/6 = (-5/6)×(6/6) = -30/36
3 =(3)×(36/36) = 108/36
-13/-4 = (13/4)×(9/9) = 117/36
17/-6 = (-17/6)×(6/6) = -102/36
-11/12 = (-11/12)×(3/3) = -33/36
-13/9 = (-13/9)×(4/4) = -42/36
Descending order of the numbers
= 117/36, 108/36, -30/36, -33/36, -42/36,-102/36
-13/-4 , 3, -5/6, -11/12, -13/9, 17/-6
27)
a) Given that
(-5/13)+(12/13)
=> (-5+12)/13
=> 7/13
(-5/13)+(12/13) = 7/13
b)(-8/15)+(-7/15)
=> (-8-7)/15
=> -15/15
=> -1
(-8/15)+(-7/15) = -1
c) (21/25)-(16/25)+(7/25)
=> (21-16+7)/25
=> (28-16)/25
=> 12/25
(21/25)-(16/25)+(7/25) = 12/25
d) (5/12)+(7/36)
LCM of 12 , 36 = 36
=> (15+7)/36
=> 22/36
=> 11/18
(5/12)+(7/36) = 11/18
e)(-8/17)+(-4/51)
LCM of 17 and 51 = 51
=> (-24-4)/51
=> -28/51
(-8/17)+(-4/51) = -28/51
f)(-5/16)+(7/24)+(13/48)
LCM of 16, 24 ,48 = 48
=> (-15+14+13)/48
=> 12/48
=> 1/4
(-5/16)+(7/24)+(13/48) = 1/4
28)
a)(8/-9)×(16/-7)
=> (8×16)/(-9×-7)
=> 128/63
(8/-9)×(16/-7) = 128/63
b) (6/7)×(-49/36)
=> (6×-49)/(7×36)
=> (1×-7)/(1×6)
=> -7/6
(6/7)×(-49/36) = -7/6
c)(-11/9)×(-81/88)
=> (-11×-81)/(9×88)
=> 9/8
(-11/9)×(-81/88) = 9/8
d)(-5/9)×(49/56)×(-72/35)
=> (-5×49×-72)/(9×56×35)
=> (1×7×8)/(1×8×7)
=> 1
(-5/9)×(49/56)×(-72/35) = 1
e)(-13/9)÷(26/27)
=> (-13/9)×(27/26)
=> (-13×27)/(9×26)
=> (1×-3)/(1×2)
=> -3/2
(-13/9)÷(26/27) = -3/2
f) (-25/7)÷(15/14)
=> (-25/7)×(14/15)
=>(-25×14)/(7×15)
=> (-5×2)/(1×3)
=> -10/3
(-25/7)÷(15/14) = -10/3
29)
a)True
b) False
c) True
d)False