Students who want to get a grip on the concept Properties of Addition of Rational Numbers can make the most out of the Worksheet on Properties of Addition of Rational Numbers available. Practice the Questions in the Addition of Rational Numbers Properties Worksheet on a regular basis. There are certain properties when it comes to Adding Rational Numbers and to more about them check our Rational Numbers Worksheets.
The Questions covered in the Worksheet for Properties of Addition of Rational Numbers include Closure Property, Commutative Property, Associative, Existence of Additive Identity Property, Existence of Additive Inverse Property, etc.
1. Verify the following:
(i) -12/7 + 2/5 = 2/5 + -12/7
(ii) -5/4 + -9/12 = -9/12 + -5 /4
Solution:
-12/7 + 2/5
Since Denominators are not the same express them as Equivalent Rational Numbers using the LCM.
= (-12*5+2*7)/35
= (-60+14)/35
= -46/35
2/5 + -12/7
Since Denominators are not the same express them as Equivalent Rational Numbers using the LCM.
= (2*7-12*5)/35
= (14-60)/35
= -46/35
Therefore, -12/7 + 2/5 = 2/5 + -12/7
(ii) -5/4 + -9/12
= (-5*3-9*1)/12
= (-15-9)/12
= -24/12
= -2
-9/12 + -5 /4
= (-9*1-5*3)/12
= -24/12 = -2
Therefore, -5/4 + -9/12 = -9/12 + -5 /4
2. Fill in the Blanks
(i) (-3/16) + (-12/7) = (-12/7) + (_____ )
(ii) (-8/11 + 3/7) + (-13/2) = (_____ ) + [3/7 + (-13/2)]
(iii) -11 + (7/13 + -9/10) = (-11 + 7/13) + (_____ )
(iv) -16/3 + _____ = _____ + -16/3 = -16/3
Solution:
(i) (-3/16)
(ii)(-8/11)
(iii)(-9/10)
(iv) 0, 0
3. Find the Additive Inverse for the following Rational Numbers
(i) 1/5
(ii) 24/9
(iii) -15
(iv) -17/3
(v) 15/-2
(vi) 0
Solution:
(i) -1/5
(ii) -24/9
(iii) 15
(iv) 17/3
(v) 15/2
(vi) 0
Additive Inverse of a number is nothing but the number to be added to the given number to make it equal to 0.
4. Which of the following is the sum of 12 1/3 +(-12 1/3)?
a) Positive Number
b) Negative Number
c) Zero
Solution:
c) Zero
Whenever you add a number to its additive inverse the result is 0.
5. State Whether the following statements are True or False?
(i) Which Rational Number has its own Additive Inverse?
(ii) Is the Addition of Rational Numbers Commutative?
(iii) Is the Addition of Rational Numbers Associative?
(iv) Is Subtraction of Rational Numbers Commutative?
(v) Is Subtraction of Rational Numbers Associative?
Solution:
(i) Zero
(ii) True
(iii) True
(iv) False
(v) False
