Rational Numbers

rational numbers class 7

Step by Step solutions of RS Aggarwal ICSE Class-7 Maths chapter 4- Rational Numbers by Goyal Brothers Prakashan is provided.

Table Of Contents
  1. Q1: What are rational numbers? Give four examples of each of positive rationals and negative rationals. Give an example of a rational number which is neither positive nor negative.
  2. Q2: Which of the following are rational numbers?
  3. Q3: Write down the numerator and the denominator of each the following rational numbers:
  4. Q4: Which of the following are positive rational numbers?
  5. Q5: Which of the following are negative rational numbers?
  6. Q6: Find four rational numbers equivalent to each of the following:
  7. Q7: Write each of the following rational numbers with positive denominator:
  8. Q8: Express (frac{4}{9}) as a rational number with numerator:
  9. Q9: Express (frac{3}{8}) as a rational number with denominator
  10. Q10: Express (frac{-6}{11}) as a rational numerator
  11. Q11: Express (frac{2}{-7}) as a rational number with denominator
  12. Q12: Express (frac{-48}{36}) as a rational with numerator
  13. Q13: Express (frac{78}{-117}) as a rational with numerator
  14. Q14: Write each of the following rational numbers in standard form:
  15. Q15: Find the value of x such that:
  16. Q16: State whether the given statement is true or false:
  17. Q1: Which of the two rational numbers is greater in each of the following pairs?
  18. Q2: Fill in the blanks with the correct symbol out of >, = or
  19. Q3: Arrange the following rational numbers in ascending order:
  20. Q4: Arrange the following rational numbers in descending order:
  21. Q1: Add the following rational numbers:
  22. Q2: Add the following rational numbers:
  23. Q3: Evaluate:
  24. Q4: Evaluate:
  25. Q1: Find the additive inverse of:
  26. Q2: Subtract:
  27. Q3: Evaluate:
  28. Q4: The sum of two rational numbers is (frac{-5}{8}). If one of them is (frac{7}{16}), find the other.
  29. Q5: The sum of two rational numbers is -4. If one of them is (frac{-3}{5}), find the other.
  30. Q6: The sum of two rational numbers is (frac{-5}{4}). If one of them is -3, find the other.
  31. Q7: What should be added to (frac{-5}{6}) to get (frac{-2}{3})?
  32. Q8: What should be added to (frac{2}{5}) get -1?
  33. Q9: What should be subtracted from (frac{-3}{4}) to get (frac{-5}{6})?
  34. Q10: What should be subtracted from (frac{-2}{3}) to get 1?
  35. Q1: Multiply:
  36. Q2: Simplify:
  37. Q3: Simplify:
  38. Q4: Simplify:
  39. Q5: Find the cost of (3frac{1}{3}) kg of rice at ₹(40frac{1}{2}) per kg.
  40. Q6: Find the distance covered by a car in (2frac{2}{5}) hours at a speed of (46frac{2}{3}) km per hour.
  41. Q7: Write the multiplicative inverse of:
  42. Q1: Find the multiplicative inverse (or reciprocal) of each of the following rational numbers:
  43. Q2: Evaluate:
  44. Q3: The product of two rational numbers is (frac{2}{5}). If one of them is (frac{-8}{25}), find the other.
  45. Q4: The product of two rational numbers is (frac{-2}{3}). If one of them is (frac{16}{39}), find the other.
  46. Q5: By what rational number should (frac{-9}{35}) be multiplied to get (frac{3}{5})?
  47. Q6: By what rational should (frac{25}{8}) multiplied to get (frac{-20}{7})?
  48. Q7: The cost of 17 pencils is ₹(59frac{1}{2}). Find the cost of each pencil.
  49. Q8: The cost of 20 metres of ribbon is ₹335. Find the cost of each metre of it.
  50. Q9: How many pieces, each of length (2frac{3}{4}) m, can be cut from a rope of length 66 m?
  51. Q10: Fill in the blanks:
  52. Q1: Represent (frac{2}{3}) on the number line
  53. Q2: Represent (-frac{5}{7}) on the number line
  54. Q3: Represent (frac{1}{6}) on the number line
  55. Q4: Represent (-frac{3}{8}) on the number line
  56. Q5: Represent (frac{22}{7}) on the number line
  57. Q6: Represent (frac{23}{-5}) on the number line
  58. Q7: Represent (-frac{3}{4}) on the number line
  59. Q8: Represent (frac{-12}{5}) on the number line
  60. Q9: Represent (frac{13}{6}) on the number line
  61. Q1: Without actual division, show that each of the rational numbers given below is expressible as a terminating decimal:
  62. Q2: By actual division, express each of the following rational numbers as a terminating decimal:
  63. Q3: Without actual division, show that each of the rational numbers given below is expressible as a repeating decimal:
  64. Q4: By actual division, express each of the following as a repeating decimal:
  65. Q5: Fill in the blanks:
  66. Q1: The additive inverse of (frac{5}{9}) is
  67. Q2: The rational number (frac{32}{-40}) expressed in standard form is
  68. Q3: What should be added to (frac{-3}{16}) get (frac{5}{8})?
  69. Q4: The multiplicative inverse of (frac{-3}{7}) is:
  70. Q5: The sum of (-frac{1}{3}) and its multiplicative is
  71. Q6: The product of (-frac{1}{3}) and its additive is
  72. Q7: Which of the rational numbers is equivalent to (frac{-2}{7})?
  73. Q8: If (3frac{3}{4}) m of cloth is required for one suit, then how many suits be prepared from 30 m of cloth?
  74. Q1: Fill in the blanks:
  75. Q2: Write true (T) or false (F):

Exercise: 4-I

Multiple Choice Type

Q1: Fill in the blanks:

i. The multiplicative inverse of a rational number is also called its ______.

Answer:reciprocal

ii. Every negative rational number is ______ than 0.

Answer:less

iii. A rational number \(\frac{p}{q}\) is said to be in standard form, if q is ______ and p and q have no common divisor other than 1.

Answer:positive

iv. \(\frac{-5}{-9}\) is a ______ rational number.

Answer:positive

v. The additive inverse of a rational number \(\frac{a}{b}\) is ______.

Answer:\(-\frac{a}{b}\)

Q2: Write true (T) or false (F):

i. There exists a rational number which is neither positive nor negative.

Answer: True (0 is neither positive nor negative)

ii. Every rational number has a multiplicative inverse.

Answer: False (0 has no multiplicative inverse)

iii. Every rational number when expressed in its standard form has its denominator greater than the numerator.

Answer: False (e.g., \(\frac{5}{3}\), denominator less than numerator)

iv. The sum of a rational and its additive inverse is always.

Answer: 0

v. The product of a rational number and its multiplicative inverse is always.

Answer: 1

vi. Any two equivalent rational numbers have the same standard form.

Answer: True (standard form is unique)

vii. The product of any two rational numbers is also a rational number.

Answer: True

viii. A rational number when divided by another rational number always gives a rational number.

Answer: False (division by zero undefined)

ix. Every rational number can be represented a number line.

Answer: True

x. The rational numbers smaller than a given rational number \(\frac{p}{q}\) lie to the left of \(\frac{p}{q}\).

Answer: True

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