Practice the questions given in the worksheet on properties of addition of rational numbers. The questions are based on closure property, commutative property, associative property, existence of additive identity property and existence of additive inverse property of addition of rational numbers.
1. Verify the following:
(i) -12/5 + 2/7 = 2/7 + -12/7
(ii) -5/8 + -9/13 = -9/13 + -5 /8
(iii) 3 + -7/12 = -7/12 + 3
(iv) 2/-7 + 12/-35 = 12/-35 + 2/-7
2. Fill in the blanks:
(i) (-3/17) + (-12/5) = (-12/5) + (_____ )
(ii) -9 + (-21/8) = (_____ ) + (-9)
(iii) (-8/13 + 3/7) + (-13/4) = (_____ ) + [3/7 + (-13/4)]
(iv) -12 + (7/12 + -9/11) = (-12 + 7/12) + (_____ )
(v) 19/-5 + (-3/11 + -7/8) = {19/-5 + (_____ )} + -7/8
(vi) -16/7 + _____ = _____ + -16/7 = -16/7
3. Find the additive
inverse of each of the following:
(i) 1/3
(ii) 23/9
(iii) -18
(iv) -17/8
(v) 15/-4
(vi) -16/-5
(vii) -3/11
(viii) 0
(ix) 19/-6
(x) -8/ -7
4. (i) Which rational number is its own additive inverse?
(ii) Is addition commutative on rational numbers?
(iii) Is addition associative on rational numbers?
(iv) Is subtraction commutative on rational numbers?
(v) Is subtraction associative on rational numbers?
Answers for the worksheet on properties of addition of rational numbers are given below to check the exact answers of the above questions on rational numbers.
Answers:
2. (i) -3/17
(ii) -21/8
(iii) -8/13
(iv) -9/11
(v) -3/11
(vi) 0, 0
3. (i) -1/3
(ii) -23/9
(iii) 18
(iv) 17/8
(v) 15/4
(vi) -16/5
(vii) 3/11
(viii) 0
(ix) 19/6
(x) -8/7
4. (i) 0
(ii) Yes
(iii) Yes
(iv) No
(v) No
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Worksheet on Properties of Division of Rational Numbers
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8th Grade Math Practice
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● Rational Numbers
Introduction of Rational Numbers
Is Every Rational Number a Natural Number?
Is Every Rational Number an Integer?
Is Every Rational Number a Fraction?
Equivalent form of Rational Numbers
Rational Number in Different Forms
Properties of Rational Numbers
Lowest form of a Rational Number
Standard form of a Rational Number
Equality of Rational Numbers using Standard Form
Equality of Rational Numbers with Common Denominator
Equality of Rational Numbers using Cross Multiplication
Comparison of Rational Numbers
Rational Numbers in Ascending Order
Rational Numbers in Descending Order
Representation of Rational Numbers on the Number Line
Rational Numbers on the Number Line
Addition of Rational Number with Same Denominator
Addition of Rational Number with Different Denominator
Properties of Addition of Rational Numbers
Subtraction of Rational Number with Same Denominator
Subtraction of Rational Number with Different Denominator
Subtraction of Rational Numbers
Properties of Subtraction of Rational Numbers
Rational Expressions Involving Addition and Subtraction
Simplify Rational Expressions Involving the Sum or Difference
Multiplication of Rational Numbers
Properties of Multiplication of Rational Numbers
Rational Expressions Involving Addition, Subtraction and Multiplication
Reciprocal of a Rational Number
Rational Expressions Involving Division
Properties of Division of Rational Numbers