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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