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Answer:
Step-by-step explanation:
Question 1.
Additive inverse of any number x is the number which when added to x results in 0.
For [tex]2/-9[/tex]
It can be written as -2/9
Assuming y be the additive inverse of it. So, by definition:
-2/9 + y = 0
y = 2/9 (Answer)
Question 2.
Verify -(-a) = a
Here, a = -19/21
L.H.S would be -[-(-19/21)] = -[19/21] = -19/21
This is equal to R.H.S
Hence proved.
Question 3
The numbers 1 and -1 are their own reciprocals
Question 4
Rational numbers are not closed under Division.
This is because of the possibility of division by zero. Zero is a rational number and division by zero is undefined.
Question 5
To find out rational numbers between 0 and 1, the basic way is to add/subtract a fraction the value of which is between 0 and 1.
Let that fraction be 1/4
so, first rational number will be 0+1/4 = 1/4
Second rational number will be 1-1/4 = 3/4
Question 6
There are infinite number of rational numbers between two numbers.
Question 7
Reciprocal of -2
Reciprocal of any number is calculated by dividing 1 with that number.
So, here reciprocal of -2 will be 1/(-2) which is equal to -1/2
Question 8
Simplify [tex]\frac{7}{6} *\frac{-3}{28}[/tex]
Dividing the 6 in denominator with 3 in numerator. And, dividing 28 in denominator with 7 in numerator.
[tex]\frac{1}{2} *\frac{-1}{4}[/tex]
Multiplying numerator and denominators respectively.
[tex]\frac{1}{2} *\frac{-1}{4} =\frac{-1}{8}[/tex]
Question 9
The denominator of a rational number cannot be Zero.
This is because division by zero is undefined.
Question 10
Zero is the additive identity of a rational number. This is because adding it to them does not change the result.
a+0 = 0+a = a
Question 11
Commutative property states that
a+b = b+a
Two rational numbers can be added in any order.