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**Ques 1:** **Fill in the blanks in the following table**:

Numbers | Closed under | |

Addition | Subtraction | |

Rational numbers | Yes | Yes |

Integers | ..... | Yes |

Whole numbers | ..... | ..... |

Natural numbers | ..... | No |

Numbers | Closed under | |

Multiplication | Division | |

Rational numbers | .... | No |

Integers | ..... | No |

Whole numbers | Yes | ..... |

Natural numbers | ..... | ..... |

**Ans: **Using the closure property over addition, subtraction, multiplication, and division for rational numbers, integers, whole-numbers, and natural numbers, we have:

Numbers | Closed under | |

Addition | Subtraction | |

Rational numbers | Yes | Yes |

Integers | Yes | Yes |

Whole numbers | Yes | No |

Natural numbers | Yes | No |

Numbers | Closed under | |

Multiplication | Division | |

Rational numbers | Yes | No |

Integers | Yes | No |

Whole numbers | Yes | No |

Natural numbers | Yes | No |

**Ques 2: Complete the following table:**

Numbers | Commutative for | |

Addition | Subtraction | |

Rational numbers | Yes | ..... |

Integers | ..... | No |

Whole numbers | ..... | ..... |

Natural numbers | ..... | ..... |

Numbers | Commutative for | |

Multiplication | Division | |

Rational numbers | ..... | ..... |

Integers | ..... | ..... |

Whole numbers | Yes | ..... |

Natural numbers | ..... | No |

**Ans:**

Numbers | Commutative for | |

Addition | Subtraction | |

Rational numbers | Yes | No |

Integers | Yes | No |

Whole numbers | Yes | No |

Natural numbers | Yes | No |

Numbers | Commutative for | |

Multiplication | Division | |

Rational numbers | Yes | No |

Integers | Yes | Yes |

Whole numbers | Yes | Yes |

Natural numbers | Yes | Yes |

**Ques 3:**** Complete the following table:**

Numbers | Associative for | |

Addition | Subtraction | |

Rational numbers | .... | .... |

Integers | .... | .... |

Whole numbers | Yes | .... |

Natural numbers | .... | No |

Numbers | Associative for | |

Multiplication | Division | |

Rational numbers | .... | No |

Integers | .... | .... |

Whole numbers | Yes | .... |

Natural numbers | .... | .... |

**Ans:**

Numbers | Associative for | |

Addition | Subtraction | |

Rational numbers | Yes | No |

Integers | Yes | No |

Whole numbers | Yes | No |

Natural numbers | Yes | No |

Numbers | Associative for | |

Multiplication | Division | |

Rational numbers | Yes | No |

Integers | Yes | No |

Whole numbers | Yes | No |

Natural numbers | Yes | No |

**Ques 4: ****If a property holds for rational numbers, will it also hold for integers? For whole Numbers? Which will? Which will not?****Ans: **

(i) Any property which is true for rational numbers is also true for integers except for any integers â€˜aâ€™ and â€˜bâ€™, (a Ã· b) is not necessarily an integer.

(ii) All properties which are true for rational numbers are also true for whole numbers also except:

(a) For â€˜aâ€™ and â€˜bâ€™ being whole numbers, (a â€“ b) may not be a whole number.

(b) For â€˜aâ€™ and â€˜bâ€™ being whole numbers (b â‰ 0), a Ã· b may not be the whole number.**Ques 5: ****Find using distributive property:**

**Ans: **

(âˆµ LCM of 12 and 9 is 36)

**EXERCISE 1.1 Ques 1. **

(Using distributive property)

(Using commutative property)

(Using distributive property)

**Ques 2.** **Write the additive inverse of each of the following:**

**(i) 2/8(ii) -5/9(iii) -6/-5(iv) 2/-9(v) 19/-6**

Sr. No. | Rational number | Additive inverse |

(i) | ||

(ii) | ||

(iii) | -6/-5 = 6/5 | |

(iv) | ||

(v) |

**Ques 3.** **Verify that â€“(â€“x) = x for:**

**Ans. ****(i) **Given, x = 11/15

â‡’ (-x) = -11/15

â‡’ -(-x) = -(-11/15) = 11/15

Therefore, -(-x) = x

**(ii) **Given, x = -13/17

â‡’ (-x) = -13/17

â‡’ -(-x) = -(-13/17) = 13/17

Therefore, -(-x) = x

**Ques 4. ****Find the multiplicative inverse of the following:**

**Ans:**

Sr. No. | Rational number | Multiplicative inverse |

(i) | â€“13 | -1/13 |

(ii) | -13/19 | -19/13 |

(iii) | 1/5 | 5 |

(iv) | 56/15 | |

(v) | 5/2 | |

(vi) | -1 | -1 |

**Ques 5:** **Name the property under multiplication used in each of the following:**

**Ans:**

Sr. No. | Multiplication | Property used |

(i) | 1 is the multiplicative identity | |

(ii) | Commutative property | |

(iii) | Multiplicative inverse |

**Ques 6**:** Multiply **** by the reciprocal of ****Ans: **As,

Reciprocal of

**Ques 7: ****Tell what property allows you to compute ****Ans:** When rational numbers are rearranged between one or more same operations and still their result does not change then we say that they follow the associative property for that operation. Thus, given equation follows the associative property.

**Ques 8:** **Is 8/9**** the multiplicative inverse of **** Why or why not?****Ans:** Since,

[Which is not equal to 1]

âˆ´ 8/9 is not the multiplicative inverse of

**Ques 9:** **Is 0.3 the multiplicative inverse of ****? Why or why not?****Ans:** Since,

0.3 Ñ… 10/3 = 1

Therefore, 0.3 is the multiplicative inverse of 10/3.

**Ques 10:**** Write: **

(i) The rational number that does not have reciprocal.

(ii) The rational numbers that are equal to their reciprocals. **(iii) The rational number that is equal to its negative.****Ans:**

(i) The rational number zero (0) does not have a reciprocal.

(ii) The rational numbers 1 and (â€“1) are equal to their reciprocals respectively.

(iii) Zero (0) is the rational number that is equal to its negative.

**Ques 11:** **Fill in the blanks:****(i) Zero has ______ reciprocal.(ii) The numbers ______ and ______ are their own reciprocals.(iii) The reciprocal of â€“5 is ______.(iv) Reciprocal of **

(v) The product of two rational numbers is always a ______.

(vi) The reciprocal of a positive rational number is ______.

(i) Zero has no reciprocal.

(ii) The numbers 1 and â€“1 are their own reciprocals.

(iii) The reciprocal of â€“5 is

(iv) The reciprocal of 1/x , where x â‰ 0 is x.

(v) The product of two rational numbers is always a rational number.

(vi) The reciprocal of a positive rational number is positive.

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