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### Exercise 1.2

#### Question 1

**Answer each of the following questions:**

**(i) Does the order in which two integers are added make a difference ?**

**(ii) When you are adding three integers together does it matter which two integers you add first?**

**(ii) Does adding zero to or subtracting zero from a integer change the value of a number?**

Sol :

#### Question 2

**Identify the addition properties used in each of the following questions.**

**(i) 7 + 13 = 13 + 7**

**(ii) 6 + 0 = 6**

**(iii) 8 + ( 1 + 9) = (8 + 1) + 19**

**(iv) 12 + (-12) = 0**

Sol :

#### Question 3

**Put the brackets in each of the following additions to satisfy addition property.**

**(i) 15 + 4 + 1 = (15 + 4) + 1**

**(ii) 18 + (7 + 5) = 18 + 7 + 5**

Sol :

#### Question 4

**(i) Give and example to show that commutative property does not exist for subtraction of integers.**

**(ii) Give an example to show that associative property does not exist for subtraction of integers.**

Sol :

#### Question 5

**Take a = —6 , b = 9 , c = 5 and verify that**

**(i) a + b = b + a**

**(ii) a – b ≠ b – a**

**(iii) a + (b + c) = (a + b) + c**

**(iv) a – ( b – c) ≠ (a – b) – c**

**(v) b + 0 = b**

Sol :

#### Question 6

**Verify a – (b – c) ≠ (a – b) – c for a = 9 , b = 6 , c = 4**

Sol :

#### Question 7

**Match the two columns**

Column 1 | Column 2 |
---|---|

(i) 17 + (-11) = (-11) + 17 | (a) Integers are closed under subtraction |

(ii) 8 + 0 = 8 | (b) Subtraction is not associative for integers |

(iii) 15 – 9 = 6 (an integer) | (c) Commutative property of addition |

(iv) (6 – 7) – 5 ≠ 6 – (7 – 5) | (d) Addition is associative for integers |

(v) (-6) + [(-7)+(-3)] = [(-6)+(-7)]+(-3) | (e) 0 is the additive identity for integers |

Sol :