The document NCERT Solutions(Part- 1)- Rational Numbers Class 8 Notes | EduRev is a part of the Class 8 Course Class 8 Mathematics by Full Circle.

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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 ‘a’ and ‘b’, (a ÷ 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 ‘a’ and ‘b’ being whole numbers, (a – b) may not be a whole number.

(b) For ‘a’ and ‘b’ being whole numbers (b ≠ 0), a ÷ b may not be the whole number.**Ques 5: ****Find using distributive property:**

**Ans: **

(∵ LCM of 12 and 9 is 36)

**EXERCISE 1.1 Ques 1. **

(Using distributivity)

(Using commutativity)

(Using distributivity)

**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) | ||

(iv) | ||

(v) |

**Ques 3.** **Verify that –(–x) = x for:**

(ii) ∵ x =

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

**Ans:**

Sr. No. | Rational number | Additive inverse |

(i) | –13 | |

(ii) | ||

(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: **∵ Reciprocal of

**Ques 7: ****Tell what property allows you to compute ****Ans:** In computing we use the associativity.

**Ques 8:** **Is 8/9**** the multiplicative inverse of **** Why or why not?****Ans:** Since, [Which is not equal to 1]

∴ 8/9 is not the multiplicative inverse of

[∵ The product of and its multiplicative inverse must be equal to 1]

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

**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 (–1) are equal to their reciprocals respectively.

(iii) ∵ [A rational number] + [Negative of the rational number] = 0

∴ [0] + [0] = 0

So, Negative of 0 is 0.

Hence, 0 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 –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 –1 are their own reciprocals.

(iii) The reciprocal of –5 is

(iv) The reciprocal of 1/x , where x ≠ 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.

REMEMBERThe additive inverse has the same numerator and denominator as the number but has the opposite sign whereas a reciprocal has the same sign as the number but numerator and denominator are interchanged.

**REPRESENTATION OF RATIONAL NUMBERS ON THE NUMBER LINE**

We can also represent a rational number on a number line. In a rational number, the numeral below the bar (denominator), tells the number of equal parts into which the first unit has been divided. The numeral above the bar (numerator) tells ‘how-many’ of these parts are considered.**Ques 1:** To represent 4/7, we divide the distance between 0 and 1 in 7 equal parts such that the 1st marking represents 1/7 , i.e. one out of seven equal parts.

Similarly, 2nd marking represents 2/7

3rd marking represents 3/7

4th marking represents 4/7

5th marking represents 5/7

6th marking represents 6/7

7th marking represents 7/7 (i.e. 1)

Thus, the 4th marking represents the rational number 4/7

**Ques 2:** Let us represent on the number line. In this case we divide the distance between 0 and (–1) into 7 equal parts and then consider 2 parts out them.

Thus, the second marking on the left of 0, represents the rational number

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