Please answer the questions
Answers
Answer:
13. a
14. a
15. a
16. a
Step-by-step explanation:
13)
Given that : (3/7)÷ (7/-4)
=> (3/7)×(-4/7)
=> (3×-4)/(7×7)
=> -12/49
The value of (3/7)÷ (7/-4) is -12/49
14)
Given number = 5/7
Additive inverse of 5/7 is -5/7
15)
Let the rational number be a/b
The inverse of a/b = b/a
Their product = (a/b)×(b/a) = (ab)/(ab) = 1
The product of a rational number and it's inverse is 1.
16)
One of the numbers = -10
Let the other number be X
Their product = -10×X = -10X
According to the given problem
The product of two numbers = 15
=> -10X = 15
=> X = -15/10
=> X = -3/2
The other number = -3/2
17)
a) Distributive Property under multiplication over addition
b) (-11/5×5/6)×3 = (3×5/6)×-11/5
Associative Property
c) Multiplicative Inverse
d)Multiplicative Identity
e) Commutative Property
18)
See the above attachment
19) -3/5 , 25/-29, -15/7 are the left side to the zero.
7/9 , -11/-13, 1/10 are the right side to the zero.
20)
Given numbers are -1 and 1
The Mean method : The ration number between a and b is (a+b)/2
i) (-1+1)/2 = 0/2 = 0
ii) Rational number between -1 and 0 = (-1+0)/2 = -1/2
iii) The rational number between 0 and -1/2
=>[0+(-1/2)]/2
=>(2-1)/2/2
=> 1/4
iv) The rational number between 1/4 and 0
=> [(1/4)+0]/2
=> (1/4)/2
=>1/8
v) The rational number between 0 and 1/8
=> (0+1/8)/2
=> (1/8)/2
=> 1/16
The rational numbers are -1/2,0,1/4,1/8,1/16
21)
Given numbers are 2 and 3
Required rational numbers = 5
On writing the denominator as (5+1) = 6
=> 2×(6/6)=(2×6)/6 = 12/6
=> 3×(6/6)=(3×6)/6 = 18/6
The rational numbers = 13/6 , 14/6, 15/6, 16/6 ,17/6
22)
a) Given numbers are 1/2 and 2/3
required numbers = 10
On writing the denominator as (10+1) = 11 multiple
=> 1/2 = (1/2)×(33/33) = 33/66
=> 2/3 = (2/3)×(22/22) = 44/66
The required numbers are 34/66,35/66,36/66,37/66, 38/66,39/66, 40/66, 41/66,42/66,43/66
b) Given numbers are -3/4 and -4/5
required numbers = 10
On writing the denominator as (10+1) = 11 multiple
=> -3/4 = (-3/4)×(55/55 )= -165/220
=> -4/5 = (-4/5)×(44/44) = -176/220
The required numbers are -166/220, -167/220, -168/220, -169/220, -170/220, -171/220, -172/220,-173/220, -174/220 , -175/220
c)Given numbers are 2/7 and 2
required numbers = 10
=> 2= (2)×(7/7) =14/7
The required numbers are 3/7,4/7,5/7,6/7,7/7,8/7,9/7,10/7,11/7,12/7,13/7
d)Given numbers are -3 and -7/5
required numbers = 10
=> -3 = (-3)×(10/10) = -30/10
=> -7/5 = (-7/5)×(2/2) = -14/10
The required numbers are -15/10,-16/10,
-17/10, -18/10,-19/10,-20/10,-21/10,-22/10,
-23/10,-24/10 -25/10,-26/10,-27/10,-28/10,
-29/10
23)
a) |-7/24 | = 7/24
8/24 , 10/24 15/24 , 25/24, 47/24
b) | 7/13 + (-2/13) |
=> | (7-2)/13 |
=> | -2/13 |
=> 2/13
5/13 , 14/13 ,15/13 , 22/13, 25/13
c) | -16/35 | + |-11/21 |
=> 16/35 + 11/21
LCM of 35 and 21 = 105
=> (48+55)/105
=> 103/105
104/105 , 106/105, 200/105, 205/105, 209/105
d) | -14/27 | +|-3/20|
=> (14/27)+(3/20)
LCM of 27 and 20 = 540
=> (280+81)/540
=> 361/540
390/540, 550/540, 650/540, 1000/540, 1079/540
