Page 25 - Concepts of Reasoning-8

Worksheet-1.2

Properties of Rational Numbers–Closure, Commutative and Associative Property

1. Fill in the boxes and name the property used. One has been done for you :

1 + 3 = [ ] + 1
[ ] 4 4 7

1 3 3 1
Solution : + = + (Commutative property of rational numbers under addition)
7 4 4 7
9 5 [ ] 9
a. × = ×
[ ] 13 13 7

8 3 [ ] 8
b. + = +
[ ] 5 5 7

2 3 –5 –2 [ ] –5
c. + + = + +
[ ] 5 2 7 5 2

9 5 2 9 × [ ] × 2
×
d. [ ] + 13 3 = 5 13 [ ]
2. Verify whether the following properties of rational numbers hold or not by considering suitable
rational numbers of your choice :
a. Commutative property of rational numbers under subtraction.
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b. Associative property of rational numbers under multiplication.

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3. Match the following :
–3 2 2 –3
a. + = + i. Closed under subtraction
5 7 7 5

–2 3 –8
b. – = ii. Associated under multiplication
14 7 14
2 5 2 5
c. + + 5 = + + 5 iii. Commutative under multiplication
7 12 7 12

–3 12 12 –3
d. × = × iv. Associated under addition
25 17 17 25

e. 2 × –3 × 12 = 2 × –3 × 12 v. Commutative under addition

17 5 17 5

25 Reasoning - 8