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-C

Q1: Add the following rational numbers:

i. \(\frac{5}{11}\) and \(\frac{4}{11}\)

Step 1: Since denominators are same, add numerators: \[ \frac{5}{11} + \frac{4}{11} = \frac{5 + 4}{11} = \frac{9}{11} \] Answer: \(\frac{9}{11}\)

ii. \(\frac{-3}{8}\) and \(\frac{5}{8}\)

Step 1: Same denominators, add numerators: \[ \frac{-3}{8} + \frac{5}{8} = \frac{-3 + 5}{8} = \frac{2}{8} = \frac{1}{4} \] Answer: \(\frac{1}{4}\)

iii. \(\frac{-6}{13}\) and \(\frac{8}{13}\)

Step 1: Add numerators: \[ \frac{-6}{13} + \frac{8}{13} = \frac{-6 + 8}{13} = \frac{2}{13} \] Answer: \(\frac{2}{13}\)

iv. \(\frac{-8}{15}\) and \(\frac{-7}{15}\)

Step 1: Add numerators: \[ \frac{-8}{15} + \frac{-7}{15} = \frac{-8 – 7}{15} = \frac{-15}{15} = -1 \] Answer: \(-1\)

v. \(\frac{-13}{20}\) and \(\frac{17}{20}\)

Step 1: Add numerators: \[ \frac{-13}{20} + \frac{17}{20} = \frac{-13 + 17}{20} = \frac{4}{20} = \frac{1}{5} \] Answer: \(\frac{1}{5}\)

vi. \(\frac{-3}{8}\) and \(\frac{5}{-8}\)

Step 1: Note \(\frac{5}{-8} = \frac{-5}{8}\). Add numerators: \[ \frac{-3}{8} + \frac{-5}{8} = \frac{-3 – 5}{8} = \frac{-8}{8} = -1 \] Answer: \(-1\)

Q2: Add the following rational numbers:

i. \(\frac{-2}{3}\) and \(\frac{3}{4}\)

Step 1: Find LCM of denominators 3 and 4 = 12
Step 2: Express both fractions with denominator 12: \[ \frac{-2}{3} = \frac{-2 \times 4}{3 \times 4} = \frac{-8}{12}, \quad \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \] Step 3: Add numerators: \[ \frac{-8}{12} + \frac{9}{12} = \frac{-8 + 9}{12} = \frac{1}{12} \] Answer: \(\frac{1}{12}\)

ii. \(\frac{-4}{9}\) and \(\frac{5}{6}\)

Step 1: LCM of 9 and 6 = 18
Step 2: Convert fractions: \[ \frac{-4}{9} = \frac{-4 \times 2}{9 \times 2} = \frac{-8}{18}, \quad \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \] Step 3: Add numerators: \[ \frac{-8}{18} + \frac{15}{18} = \frac{-8 + 15}{18} = \frac{7}{18} \] Answer: \(\frac{7}{18}\)

iii. \(\frac{-5}{18}\) and \(\frac{11}{27}\)

Step 1: LCM of 18 and 27 = 54
Step 2: Convert fractions: \[ \frac{-5}{18} = \frac{-5 \times 3}{18 \times 3} = \frac{-15}{54}, \quad \frac{11}{27} = \frac{11 \times 2}{27 \times 2} = \frac{22}{54} \] Step 3: Add numerators: \[ \frac{-15}{54} + \frac{22}{54} = \frac{-15 + 22}{54} = \frac{7}{54} \] Answer: \(\frac{7}{54}\)

iv. \(\frac{-7}{12}\) and \(\frac{-5}{24}\)

Step 1: LCM of 12 and 24 = 24
Step 2: Convert fractions: \[ \frac{-7}{12} = \frac{-7 \times 2}{12 \times 2} = \frac{-14}{24}, \quad \frac{-5}{24} = \frac{-5}{24} \] Step 3: Add numerators: \[ \frac{-14}{24} + \frac{-5}{24} = \frac{-14 – 5}{24} = \frac{-19}{24} \] Answer: \(\frac{-19}{24}\)

v. \(\frac{-1}{18}\) and \(\frac{-7}{27}\)

Step 1: LCM of 18 and 27 = 54
Step 2: Convert fractions: \[ \frac{-1}{18} = \frac{-1 \times 3}{18 \times 3} = \frac{-3}{54}, \quad \frac{-7}{27} = \frac{-7 \times 2}{27 \times 2} = \frac{-14}{54} \] Step 3: Add numerators: \[ \frac{-3}{54} + \frac{-14}{54} = \frac{-3 – 14}{54} = \frac{-17}{54} \] Answer: \(\frac{-17}{54}\)

vi. \(\frac{21}{-4}\) and \(\frac{-11}{8}\)

Step 1: Write \(\frac{21}{-4} = \frac{-21}{4}\). LCM of 4 and 8 = 8
Step 2: Convert fractions: \[ \frac{-21}{4} = \frac{-21 \times 2}{4 \times 2} = \frac{-42}{8}, \quad \frac{-11}{8} = \frac{-11}{8} \] Step 3: Add numerators: \[ \frac{-42}{8} + \frac{-11}{8} = \frac{-42 – 11}{8} = \frac{-53}{8} \] Answer: \(\frac{-53}{8}\)

Q3: Evaluate:

i. \(\frac{2}{-3} + \frac{-4}{9}\)

Step 1: Rewrite \(\frac{2}{-3} = \frac{-2}{3}\)
Step 2: Find LCM of denominators 3 and 9 = 9
Step 3: Convert fractions: \[ \frac{-2}{3} = \frac{-2 \times 3}{3 \times 3} = \frac{-6}{9}, \quad \frac{-4}{9} = \frac{-4}{9} \] Step 4: Add numerators: \[ \frac{-6}{9} + \frac{-4}{9} = \frac{-6 – 4}{9} = \frac{-10}{9} \] Answer: \(\frac{-10}{9}\)

ii. \(\frac{-1}{2} + \frac{-3}{4}\)

Step 1: LCM of 2 and 4 = 4
Step 2: Convert fractions: \[ \frac{-1}{2} = \frac{-1 \times 2}{2 \times 2} = \frac{-2}{4}, \quad \frac{-3}{4} = \frac{-3}{4} \] Step 3: Add numerators: \[ \frac{-2}{4} + \frac{-3}{4} = \frac{-2 – 3}{4} = \frac{-5}{4} \] Answer: \(\frac{-5}{4}\)

iii. \(\frac{7}{-9} + \frac{-5}{6}\)

Step 1: Rewrite \(\frac{7}{-9} = \frac{-7}{9}\)
Step 2: LCM of 9 and 6 = 18
Step 3: Convert fractions: \[ \frac{-7}{9} = \frac{-7 \times 2}{9 \times 2} = \frac{-14}{18}, \quad \frac{-5}{6} = \frac{-5 \times 3}{6 \times 3} = \frac{-15}{18} \] Step 4: Add numerators: \[ \frac{-14}{18} + \frac{-15}{18} = \frac{-14 – 15}{18} = \frac{-29}{18} \] Answer: \(\frac{-29}{18}\)

iv. \(2 + \frac{-3}{4}\)

Step 1: Write 2 as \(\frac{8}{4}\) (since denominator is 4)
Step 2: Add fractions: \[ \frac{8}{4} + \frac{-3}{4} = \frac{8 – 3}{4} = \frac{5}{4} \] Answer: \(\frac{5}{4}\)

v. \(3 + \frac{-5}{6}\)

Step 1: Write 3 as \(\frac{18}{6}\)
Step 2: Add fractions: \[ \frac{18}{6} + \frac{-5}{6} = \frac{18 – 5}{6} = \frac{13}{6} \] Answer: \(\frac{13}{6}\)

vi. \(-4 + \frac{2}{3}\)

Step 1: Write -4 as \(\frac{-12}{3}\)
Step 2: Add fractions: \[ \frac{-12}{3} + \frac{2}{3} = \frac{-12 + 2}{3} = \frac{-10}{3} \] Answer: \(\frac{-10}{3}\)

Q4: Evaluate:

i. \(\frac{-3}{8} + \frac{5}{8} + \frac{7}{8}\)

Step 1: All denominators are same (8), so add numerators: \[ \frac{-3 + 5 + 7}{8} = \frac{9}{8} \] Answer: \(\frac{9}{8}\)

ii. \(\frac{11}{3} + \frac{-5}{3} + \frac{-2}{3}\)

Step 1: All denominators are same (3), so add numerators: \[ \frac{11 – 5 – 2}{3} = \frac{4}{3} \] Answer: \(\frac{4}{3}\)

iii. \(-1 + \frac{2}{-3} + \frac{5}{6}\)

Step 1: Rewrite \(\frac{2}{-3} = \frac{-2}{3}\)
Step 2: Express -1 as fraction with denominator 6: \[ -1 = \frac{-6}{6} \] Step 3: Find LCM of denominators 3 and 6 = 6
Step 4: Convert all to denominator 6: \[ \frac{-2}{3} = \frac{-4}{6}, \quad \frac{5}{6} = \frac{5}{6}, \quad -1 = \frac{-6}{6} \] Step 5: Add numerators: \[ \frac{-6}{6} + \frac{-4}{6} + \frac{5}{6} = \frac{-6 – 4 + 5}{6} = \frac{-5}{6} \] Answer: \(\frac{-5}{6}\)

iv. \(\frac{7}{26} + \frac{-11}{13} + 2\)

Step 1: Express 2 as fraction with denominator 26: \[ 2 = \frac{52}{26} \] Step 2: Convert \(\frac{-11}{13}\) to denominator 26: \[ \frac{-11}{13} = \frac{-22}{26} \] Step 3: Add all fractions: \[ \frac{7}{26} + \frac{-22}{26} + \frac{52}{26} = \frac{7 – 22 + 52}{26} = \frac{37}{26} \] Answer: \(\frac{37}{26}\)

v. \(3 + \frac{-7}{8} + \frac{-3}{4}\)

Step 1: Express 3 as fraction with denominator 8: \[ 3 = \frac{24}{8} \] Step 2: Convert \(\frac{-3}{4}\) to denominator 8: \[ \frac{-3}{4} = \frac{-6}{8} \] Step 3: Add all fractions: \[ \frac{24}{8} + \frac{-7}{8} + \frac{-6}{8} = \frac{24 – 7 – 6}{8} = \frac{11}{8} \] Answer: \(\frac{11}{8}\)

vi. \(\frac{-13}{8} + \frac{7}{16} + \frac{-3}{4}\)

Step 1: Find LCM of denominators 8, 16, and 4 = 16
Step 2: Convert all fractions to denominator 16: \[ \frac{-13}{8} = \frac{-26}{16}, \quad \frac{7}{16} = \frac{7}{16}, \quad \frac{-3}{4} = \frac{-12}{16} \] Step 3: Add numerators: \[ \frac{-26}{16} + \frac{7}{16} + \frac{-12}{16} = \frac{-26 + 7 – 12}{16} = \frac{-31}{16} \] Answer: \(\frac{-31}{16}\)

previous
next

Pages: 1 2 3 4 5 6 7 8 9 10

Share the Post:

Leave a Comment

Your email address will not be published. Required fields are marked *

Related Posts​

Join Our Newsletter

Name
Email
The form has been submitted successfully!
There has been some error while submitting the form. Please verify all form fields again.

Start typing and press enter to search

Scroll to Top