Q7 of 47 Page 172

Write the following in increasing order:

For arranging rational numbers in increasing or decreasing order, always make sure that the denominator is same.


For given numbers, make the denominator same by taking L.C.M of denominators.


Denominators are – 13, 26, 6, 43, 28, 11


Let us write down the prime factors of numbers


13 = 13 × 1


26 = 13 × 2


6 = 2 × 3


43 = 43 × 1


28 = 2 × 2 × 7


11 = 11 × 1


L.C.M of the given numbers will be = 13 × 2 × 3 × 2 × 11 × 43 × 7


= 516516


Now lets make the denominators equal by multiplying and dividing by terms.



And Similarly all our numbers will become as



Now arranging in increasing order we get,



Hence we have the order as



More from this chapter

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5

Define an operation * on the set of all rational numbers □ as follows:

r*s = r + s –(r × s),


for any two rational numbers r, s. Answer the following with justification:


(i) Is ℚ closed under the operation *?


(ii) Is * an associative operation of ℚ ?


(iii) Is * a commutative operation of ℚ?


(iv) What is a * 1 for any a in ℚ?


(v) Find two integers a ≠ 0 and b ≠ 0 such that a * b = 0.

 6

Find the multiplicative inverses of the following rational numbers.

 8

Write the following in decreasing order:

 9

(a) What is the additive inverse of 0?

(b) What is the multiplicative inverse of 1?


(c) Which integers have multiplicative inverses?