Mathematics NCERT Grade 8,
Chapter 1: Rational Numbers- Basic operations on rational numbers are already discussed. Show
The operations for
addition and multiplication are: Operations students will study on rational numbers include:
Section 1.2.6 deals with the
topic- Negative of a number or additive inverse. Further in this chapter reciprocal or multiplicative inverse, distributivity of multiplication over addition for rational numbers are explained.
Solved examples are given in the chapter.
Following those examples students can solve the problems of exercises easily. Page No 14:Question 1:Using appropriate properties find: (i) (ii) Answer:(i) (ii) (By commutativity) Page No 14:Question 2:Write the additive inverse of each of the following: (i) (ii) (iii) (iv) (v)Answer:(i) Additive inverse = (ii) Additive inverse = (iii) Additive inverse = (iv) Additive inverse (v) Additive inverse Page No 14:Question 3:Verify that −(−x) = x for. (i) (ii)Answer:(i) The additive inverse of is asThis equality represents that the additive inverse of is or it can be said that i.e., −(−x) = x.(ii) The additive inverse of is asThis equality represents that the additive inverse of is − i.e., −(−x) = x.Page No 14:Question 4:Find the multiplicative inverse of the following. (i) (ii) (iii)(iv) (v) (vi) −1Answer:(i) −13 Multiplicative inverse = − (ii) Multiplicative inverse = (iii) Multiplicative inverse = 5 (iv) Multiplicative inverse (v) Multiplicative inverse (vi) −1 Multiplicative inverse = −1 Page No 14:Question 5:Name the property under multiplication used in each of the following: (i) (ii) (iii) Answer:(i) i.e., the multiplicative identity.(ii) i.e., Commutativity identity.(iii) i.e., Multiplicative inverse.Page No 14:Question 6:Multiply by the reciprocal of.Answer:Page No 14:Question 7:Tell what property allows you to compute .Page No 14:Question 8:Is the multiplicative inverse of? Why or why not?Answer:If it is the multiplicative inverse, then the product should be 1. However, here, the product is not 1 as Video Solution for rational numbers (Page: 14 , Q.No.: 8)NCERT Solution for Class 8 math - rational numbers 14 , Question 8 Page No 14:Question 9:Is 0.3 the multiplicative inverse of ? Why or why not?Answer:0.3 × = 0.3 ×Here, the product is 1. Hence, 0.3 is the multiplicative inverse of .Page No 15:Question 10:Write: (i) The rational number that does not have a reciprocal. (ii) The rational numbers that are equal to their reciprocals. (iii) The rational number that is equal to its negative. Answer:(i) 0 is a rational number but its reciprocal is not defined. (ii) 1 and −1 are the rational numbers that are equal to their reciprocals. (iii) 0 is the rational number that is equal to its negative. Page No 15:Question 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 , where is __________.(v) The product of two rational numbers is always a __________. (vi) The reciprocal of a positive rational number is __________. Answer:(i) No (ii) 1, −1 (iii) (iv) x (v) Rational number (vi) Positive rational number Page No 20:Question 1:Represent these numbers on the number line. (i) (ii)Answer:(i) can be represented on the number line as follows. (ii) can be represented on the number line as follows.Video Solution for rational numbers (Page: 20 , Q.No.: 1)NCERT Solution for Class 8 math - rational numbers 20 , Question 1 Page No 20:Question 2:Represent on the number line.Answer:can be represented on the number line as follows. Video Solution for rational numbers (Page: 20 , Q.No.: 2)NCERT Solution for Class 8 math - rational numbers 20 , Question 2 Page No 20:Question 3:Write five rational numbers which are smaller than 2. Answer:2 can be represented as .Therefore, five rational numbers smaller than 2 are Video Solution for rational numbers (Page: 20 , Q.No.: 3)NCERT Solution for Class 8 math - rational numbers 20 , Question 3 Page No 20:Question 4:Find ten rational numbers between and.Answer:and can be represented as respectively.Therefore, ten rational numbers between andarePage No 20:Question 5:Find five rational numbers between (i) (ii) (iii) Answer:(i) can be represented as respectively.Therefore, five rational numbers between are
(ii) can be represented as respectively.Therefore, five rational numbers between are
(iii) can be represented as respectively.Therefore, five rational numbers between are
Page No 20:Question 6:Write five rational numbers greater than − 2. Answer:−2 can be represented as − .Therefore, five rational numbers greater than −2 are Page No 20:Question 7:Find ten rational numbers between and.Answer:and can be represented as respectively.Therefore, ten rational numbers between and are Video Solution for rational numbers (Page: 20 , Q.No.: 7)NCERT Solution for Class 8 math - rational numbers 20 , Question 7
View NCERT Solutions for all chapters of Class 8 Why 1 is the multiplicative identity for rational number?Also, 1 is the multiplicative identity for rational numbers because the product of 1 and any rational number is the rational number itself. Thus, 1 is the multiplicative identity for whole numbers, integers and rational numbers.
What is the multiplicative identity of numbers?The multiplicative identity of a real number is 1. When we multiply 1 by any real number then we get the same number.
What are the types of rational numbers Class 8?Positive and Negative Rational Numbers
If both the numerator and denominator are of the same sign. If the numerator and denominator are of opposite signs. Examples of negative rational numbers: -2/17, 9/-11 and -1/5.
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