## Rational Number

**Rational Number****Q.1. Write.**

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

**(ii) The rational numbers that is equal to their reciprocals.**

**(iii) The rational number that is equal to its negative.**

**(iv) The additive inverse of a negative number**

**Answer: (i) 0 (ii) 1 and (–1) (iii) 0 (iv) Negative**

**Q. 2. 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 1/x , where x ≠ 0 is ________.**

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

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

**(vii)The number which can be written in the form of p/q , where q≠0, is called _______ number.**

**(A) Rational (B) Irrational (C) Real (D) Natural**

**(viii) All rational numbers have multiplicative inverse except _______ .**

**(A) -1 (B) 1 (C) 0 (D) None**

**(ix) P and q in p/q form of rational number is ----- ------**

**(A) primes (B) Co primes (C) Rational (D) Natural**

**(x) A rational number p/q is said to be in the simplest form if the HCF of p and q is**

**(a) 2 (b) 1 (c) 0 (d) 3**

**(xi) Between any two distinct rational numbers there exist (a) Finite rational numbers (b) Infinite rational numbers (a) No rational number (d) None of the above**

**(xii) A rational number a/b is greater than c/d if**

**(a) ad > bc (b) ad < bc (c) ad = bc (d) ad ≠ bc**

**(xiii) Is zero a rational number (a) Yes (b) No (c) Can‟t say**

**(xiv) Rational numbers are not closed under**

**(a) Addition (b) Multiplication (c) Division (d) Subtraction**

**(xv) If the additive inverse of “b” is “a” then:**

**(A) axb=1 (B) a=b (C) a+b=0 (D) a-b=0**

**Answer: (i) No (ii) 1, –1 (iii) -1/5 (iv) x (v) Rational number (vi) positive (vii) Rational number (viii) C (ix) Co primes (x) (b) (xi) (b) (xii) (a) (xiii) (a) (xiv) (c) (xv) (c) 3**

**. Solve:**

**1. If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. What is the number?**

**2. Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3, and 4 respectively, they add up to 74. Find these numbers.**

**4. Represent the following rational numbers on the number line**

**(a) -1/4 (b) −1 1 5 (c) -3 8 5 (d) -7/10 (e) -5/3**

**5. Find two rational numbers between (i) -2 and 2. (ii) -1 and 0.**

**6. Insert six rational numbers between (i) -1/3 and -2/3 (ii) ¼ and ½**

**7. Arrange the following numbers in ascending order: 4 /− 9 , − 5 /12 ; 7/ − 18 ; − 2/ 3**

**8. Arrange the following numbers in descending order: − 5/6 − 7/12 ; − 13/28 ; 23/−24**

**9 Represent 4 2 3 on the number line.**

**10. What number should be added to −7/8to get 4/9?**

**11. The sum of two rational numbers is −1/2. If one of the numbers is 5/6, find the other.**

**12. What number should be subtracted from −2/3 to get −1/2?**

**13. Verify whether the given statement is true or not: (i) (59÷13) ÷ 52 = 59÷(13÷52)**

**14. Divide the sum of 13/5and−12/7by the product of −31/7and−1/2.**

**15. The product of two rational numbers is −16/9. If one of the numbers is −4/3, find the other.**

**16. Find three rational numbers between 4 and 5.**

**17. Find three rational numbers between 2/3 and 3/4.**

**18. Find the HCF of 9/10, 12/25, 18/35, 21/40 [Hint: HCF of Fraction= (HCF of Numerators/LCM of denominators=3/1400)**

**19. After reading 7/9 of a book, 40 pages are left. How many pages are there in the book?**

**20. A drum full of rice weights 401 6 kg. If the empty drum weights 133 4 kg, find the weight of rice in the drum.**

**21. Raju earns Rs16000/month. He spends ¼ of his income on food; 3/10 of the remainder on house rent and 5/ 21of the remainder on education of children. How much money is still left with him?22.**

**Multiple Choice Questions**

**1. For what value of „a‟ the number -11/a is not a rational number.**

**( a) -1 (b) 1 (c) 0 (d) 10 [(b) 1]**

**3. Find the value of. (-9/5) + -(8 /5) ÷ (5/2) x (- 5/4 )**

**( a) -1 (b) -3 (c) 2 (d) -8**

**4. The additive inverse of -1/3 - ( -1/3 ) is ________.**

**( a) 1/3 (b) 0 (c) -1/3 (d) None of these.**

**5. What is the quotient when a non-zero rational number is divided by its additive inverse?**

**a) 0 b) -1 c) 1 d) None of these**

**Q. Give an example to show that whole numbers are not closed whole number under subtraction Answer: 5 – 7 = – 2, which is not a Whole numbers Hence, whole number are not closed**

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