# 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}

(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.

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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Properties of Rational Numbers

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Standard form of a Rational Number

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Equality of Rational Numbers using Cross Multiplication

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Representation of Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

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Properties of Addition of Rational Numbers

Subtraction of Rational Number with Different Denominator

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Properties of Subtraction of Rational Numbers

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