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: The additive inverse of \(\frac{5}{9}\) is

Step 1: Understand the definition of additive inverse.
The **additive inverse** of a number is the number that when **added** to the original gives **zero**.

Step 2: Find the number which when added to \(\frac{5}{9}\) gives 0.
Let the additive inverse be \(x\). So,
\[ \frac{5}{9} + x = 0 \] Solving for \(x\), \[ x = -\frac{5}{9} \]Answer: b. \(-\frac{5}{9}\)

Q2: The rational number \(\frac{32}{-40}\) expressed in standard form is

Step 1: Recall that the standard form of a rational number has the negative sign (if any) only in the numerator.

Step 2: Simplify \(\frac{32}{-40}\) by dividing numerator and denominator by their greatest common divisor (GCD).
GCD of 32 and 40 is 8.
\[ \frac{32}{-40} = \frac{32 \div 8}{-40 \div 8} = \frac{4}{-5} \]Step 3: Rewrite \(\frac{4}{-5}\) as \(\frac{-4}{5}\) to put the negative sign in numerator (standard form).
\[ \frac{4}{-5} = \frac{-4}{5} \]Answer: d. \(\frac{-4}{5}\)

Q3: What should be added to \(\frac{-3}{16}\) get \(\frac{5}{8}\)?

Step 1: Let the required number be \(x\). Then,
\[ \frac{-3}{16} + x = \frac{5}{8} \]Step 2: Solve for \(x\):
\[ x = \frac{5}{8} – \frac{-3}{16} = \frac{5}{8} + \frac{3}{16} \]Step 3: Find common denominator (LCM of 8 and 16 is 16) and add:
\[ \frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \] \[ x = \frac{10}{16} + \frac{3}{16} = \frac{13}{16} \]Answer: d. \(\frac{13}{16}\)

Q4: The multiplicative inverse of \(\frac{-3}{7}\) is:

Step 1: Recall that the multiplicative inverse (or reciprocal) of a rational number \(\frac{a}{b}\) is \(\frac{b}{a}\), such that
\[ \frac{a}{b} \times \frac{b}{a} = 1 \]Step 2: For \(\frac{-3}{7}\), the reciprocal is
\[ \frac{7}{-3} = \frac{-7}{3} \]Step 3: Check the product:
\[ \frac{-3}{7} \times \frac{-7}{3} = \frac{21}{21} = 1 \]Answer: a. \(\frac{-7}{3}\)

Q5: The sum of \(-\frac{1}{3}\) and its multiplicative is

Step 1: Find the multiplicative inverse (reciprocal) of \(-\frac{1}{3}\).
\[ \text{Multiplicative inverse of } -\frac{1}{3} = -3 \]Step 2: Now, add the number and its reciprocal:
\[ -\frac{1}{3} + (-3) = -\frac{1}{3} – 3 \]Step 3: Convert \(-3\) to fraction with denominator 3:
\[ -3 = -\frac{9}{3} \]Step 4: Add the fractions:
\[ -\frac{1}{3} – \frac{9}{3} = -\frac{10}{3} \]Step 5: Convert \(-\frac{10}{3}\) into a mixed fraction:
\[ -\frac{10}{3} = -3\frac{1}{3} \]Answer: d. \(-3\frac{1}{3}\)

Q6: The product of \(-\frac{1}{3}\) and its additive is

Step 1: Find the additive inverse of \(-\frac{1}{3}\).
\[ \text{Additive inverse of } -\frac{1}{3} = \frac{1}{3} \]Step 2: Now, find the product of \(-\frac{1}{3}\) and \(\frac{1}{3}\):
\[ -\frac{1}{3} \times \frac{1}{3} = -\frac{1 \times 1}{3 \times 3} = -\frac{1}{9} \]Answer: c. \(-\frac{1}{9}\)

Q7: Which of the rational numbers is equivalent to \(\frac{-2}{7}\)?

Step 1: Understand that two rational numbers \(\frac{a}{b}\) and \(\frac{c}{d}\) are equivalent if:
\[ a \times d = b \times c \]Step 2: Check each option one by one:a. \(\frac{-14}{21}\): Check if \(-2 \times 21 = 7 \times -14\) \[ -2 \times 21 = -42, \quad 7 \times (-14) = -98 \quad \Rightarrow \text{Not equal} \]b. \(\frac{-8}{14}\): Check if \(-2 \times 14 = 7 \times -8\) \[ -2 \times 14 = -28, \quad 7 \times (-8) = -56 \quad \Rightarrow \text{Not equal} \]c. \(\frac{-14}{49}\): Check if \(-2 \times 49 = 7 \times -14\) \[ -2 \times 49 = -98, \quad 7 \times (-14) = -98 \quad \Rightarrow \text{Equal!} \]d. \(\frac{-6}{28}\): Check if \(-2 \times 28 = 7 \times -6\) \[ -2 \times 28 = -56, \quad 7 \times (-6) = -42 \quad \Rightarrow \text{Not equal} \]Answer: c. \(\frac{-14}{49}\)

Q8: If \(3\frac{3}{4}\) m of cloth is required for one suit, then how many suits be prepared from 30 m of cloth?

Step 1: Convert the mixed fraction \(3\frac{3}{4}\) to an improper fraction:
\[ 3\frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \]Step 2: Let the number of suits be \(x\). Then,
\[ x \times \frac{15}{4} = 30 \]Step 3: Solve for \(x\):
\[ x = \frac{30}{\frac{15}{4}} = 30 \times \frac{4}{15} = \frac{30 \times 4}{15} = \frac{120}{15} = 8 \]Answer: c. 8 suits

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