Worksheet on Properties of Division of Rational Numbers
Practice the questions given in the worksheet on properties of division of rational numbers. The questions are based on verifying the rational numbers using the division properties.
We know, for every rational number a/b, (a/b ÷ 1) = a/b and (a/b ÷ a/b) = 1.
1. Verify whether the given statement is true or false:
(i) 2/9 ÷ 5/11 = 7/9 ÷ 6/13
(ii) 13/5 ÷ 26/10 = 26/10 ÷ 13/5
(iii) -9 ÷ 3/4 = 3/4 ÷ (-9)
(iv) -8/9 ÷ -4/3 = -4/3 ÷ (-8/9)
(v) - 7/24 ÷ 3/-16 = (3/-16) ÷ (-7/24)
2. Verify whether the given statement is true or false:
(i) {-8/9 ÷ 2/7} ÷ 8/5 = -8/9 ÷ {2/7 ÷ 8/5}
(ii) {4/9 ÷ -2/11} ÷ 1/2 = 4/9 ÷ {-2/11 ÷ 1/2}
(iii) {5/9 ÷ 1/3} ÷ 5/2 = 5/9 ÷ {1/3 ÷ 5/2}
(iv) {(-16) ÷ 6/5} ÷ -9/10 = (-16) ÷ {6/5 ÷ (-9/10)}
(v) {-3/5 ÷ (-12/35)} ÷ 1/14 = -3/5 ÷ {-12/35 ÷ 1/14}
3. Answer the following questions:
(i) Are rational numbers always closed under division?
(ii) Are rational numbers always commutative under division?
(iii) Are rational numbers always associative under division?
(iv) Can we divide 1 by 0?
Answers for the worksheet on properties of division of rational numbers are given below to check the exact answers of the above questions.
Answers:
1. (i) False
(ii) False
(iii) False
(iv) False
(v) False
2. (i) False
(ii) False
(iii) False
(iv) False
(v) False
3. (i) No
(ii) No
(iii) No
(iv) No
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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
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