Tell what property allows you to compute 1 3 × 6 × 4 3 as 1 3 × 6 × 4 3 .

Given, 1 3 × 6 × 4 3 is computed as 1 3 × 6 × 4 3 . By using associative property of rational numbers under multiplication, for any rational numbers a , b and c we have, a × b × c = a × b × c Hence, the required property which allows the given computation is associative property.

Is 8 9 the multiplicative inverse of - 1 1 8 ? Why or why not?

Given numbers are 8 9 and - 1 1 8 . - 1 1 8 is equal to - 9 8 . And, - 9 8 × 8 9 = - 1 A multiplicative inverse or reciprocal for a number x , denoted by 1 x , is a number which when multiplied by x yields the multiplicative identity 1 . But, here we observe that the product is not 1 . Hence, 8 9 is not the multiplicative inverse of - 1 1 8 .

Represent - 2 11 , - 5 11 , - 9 11 on the number line.

- 2 11 , - 5 11 , - 9 11 i.e. - 2 11 , - 5 11 , - 9 11 all are likes between - 1 and 0 . Since we have 11 is the denominator, we divide the part between - 1 and 0 into 11 equal pars starting from 0 , the second, fifth and ninth to its left respectively represent - 2 11 , - 5 11 , - 9 11 Hence, the required number line is shown above.

Find ten rational numbers between - 2 5 and 1 2 .

We need to find ten rational numbers between - 2 5 & 1 2 . Make denominator same, by finding LCM of the denominators. - 2 5 × 2 2 = - 4 10 1 2 × 5 5 = 5 10 Now again, we change the rational numbers to their equivalent rational numbers, Since we need to find 10 rational numbers we multiply and divide by 11 . - 4 10 × 11 11 = - 44 110 5 10 × 11 11 = 55 110 Hence, 10 rational numbers between - 44 110 and 55 110 are: - 43 110 , - 42 110 , - 41 110 , - 39 110 , - 38 110 , - 37 110 , - 36 110 , - 35 110 , - 34 110 .

Find ten rational numbers between 3 5 and 3 4 .

Given, numbers are 3 5 and 3 4 . LCM of 5 and 4 = 20 . So, 3 5 = 3 5 × 4 4 = 12 20 and 3 4 = 3 4 × 5 5 = 15 20 Now again, we change the rational numbers to their equivalent rational numbers, 12 20 = 12 20 × 8 8 = 96 160 and 15 20 = 15 20 × 8 8 = 120 160 Hence, ten rational numbers between 3 5 and 3 4 are 97 160 , 98 160 , 99 160 , 100 160 , 101 160 , 102 160 , 103 160 , 104 160 , 105 160 , 106 160 . There can be numerous rational numbers between 3 5 and 3 4 .

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START UP MATHEMATICS>Chapter 1 - Rational Numbers>SOME NCERT TEXTBOOK QUESTIONS

Monicaa Abhijit Solutions for Chapter: Rational Numbers, Exercise 12: SOME NCERT TEXTBOOK QUESTIONS

Author:Monicaa Abhijit

Monicaa Abhijit Mathematics Solutions for Exercise - Monicaa Abhijit Solutions for Chapter: Rational Numbers, Exercise 12: SOME NCERT TEXTBOOK QUESTIONS

Attempt the practice questions on Chapter 1: Rational Numbers, Exercise 12: SOME NCERT TEXTBOOK QUESTIONS with hints and solutions to strengthen your understanding. START UP MATHEMATICS solutions are prepared by Experienced Embibe Experts.