CBSE Class 8 Mathematics Rational Numbers MCQs Set 36

Download CBSE MCQs for Class 8 Mathematics: Rational Numbers

Explore reliable objective questions for Rational Numbers tailored for Class 8 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Chapter-wise Objective Questions: Rational Numbers

Access the complete set of multiple-choice questions for Rational Numbers below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official CBSE textbooks.

Multiple Choice Questions

Question 1: Using the properties of rational numbers, find \( -\frac{2}{3}\times\frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times\frac{1}{6} \).
(a) \( 2 \)
(b) \( -2 \)
(c) \( \frac{1}{2} \)
(d) \( \frac{5}{2} \)
Show Answer & Explanation

Answer: (a) \( 2 \)

Explanation:
1. Multiply first: -2/5 and 3/30 = 1/10.
2. Value = -2/5 + 5/2 - 1/10 = (-4 + 25 - 1)/10 = 20/10 = 2.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 2: Evaluate \( \frac{2}{5}\times\left(-\frac{3}{7}\right)-\frac{1}{6}\times\frac{3}{2}+\frac{1}{14}\times\frac{2}{5} \).
(a) \( -\frac{39}{28} \)
(b) \( \frac{11}{28} \)
(c) \( -\frac{11}{28} \)
(d) \( \frac{17}{28} \)
Show Answer & Explanation

Answer: (c) \( -\frac{11}{28} \)

Explanation:
1. Products: -6/35, 3/12 = 1/4 and 2/70 = 1/35.
2. Value = -6/35 - 1/4 + 1/35 = -5/35 - 1/4 = -1/7 - 1/4 = \( -\frac{11}{28} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 3: Find the value of \( \frac{5}{7}+\frac{1}{3}+\frac{8}{9}+\frac{1}{14} \).
(a) \( \frac{379}{126} \)
(b) \( \frac{127}{126} \)
(c) \( \frac{253}{126} \)
(d) \( -\frac{253}{126} \)
Show Answer & Explanation

Answer: (c) \( \frac{253}{126} \)

Explanation:
1. Rearrange: 5/7 + 1/14 = 11/14 and 1/3 + 8/9 = 11/9.
2. Total = 11/14 + 11/9 = (99 + 154)/126 = 253/126.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 4: Subtract \( -\frac{7}{9} \) from \( \frac{4}{9} \).
(a) \( \frac{2}{9} \)
(b) \( \frac{11}{9} \)
(c) \( -\frac{11}{9} \)
(d) \( \frac{20}{9} \)
Show Answer & Explanation

Answer: (b) \( \frac{11}{9} \)

Explanation:
1. Required value = \( \frac{4}{9} \) - (\( -\frac{7}{9} \)).
2. Using the common denominator the result is \( \frac{11}{9} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 5: Subtract \( -\frac{2}{11} \) from \( -\frac{9}{11} \).
(a) \( \frac{4}{11} \)
(b) \( -\frac{7}{11} \)
(c) \( -\frac{18}{11} \)
(d) \( \frac{7}{11} \)
Show Answer & Explanation

Answer: (b) \( -\frac{7}{11} \)

Explanation:
1. Required value = \( -\frac{9}{11} \) - (\( -\frac{2}{11} \)).
2. Using the common denominator the result is \( -\frac{7}{11} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 6: Subtract \( \frac{1}{4} \) from \( -\frac{3}{8} \).
(a) \( -\frac{5}{8} \)
(b) \( \frac{3}{8} \)
(c) \( \frac{5}{8} \)
(d) \( -\frac{13}{8} \)
Show Answer & Explanation

Answer: (a) \( -\frac{5}{8} \)

Explanation:
1. Required value = \( -\frac{3}{8} \) - (\( \frac{1}{4} \)).
2. Using the common denominator the result is \( -\frac{5}{8} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 7: Subtract \( -\frac{6}{7} \) from \( -\frac{13}{14} \).
(a) \( \frac{13}{14} \)
(b) \( -\frac{15}{14} \)
(c) \( -\frac{1}{14} \)
(d) \( \frac{1}{14} \)
Show Answer & Explanation

Answer: (c) \( -\frac{1}{14} \)

Explanation:
1. Required value = \( -\frac{13}{14} \) - (\( -\frac{6}{7} \)).
2. Using the common denominator the result is \( -\frac{1}{14} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 8: Subtract \( -\frac{8}{33} \) from \( -\frac{7}{22} \).
(a) \( -\frac{71}{66} \)
(b) \( \frac{5}{66} \)
(c) \( \frac{61}{66} \)
(d) \( -\frac{5}{66} \)
Show Answer & Explanation

Answer: (d) \( -\frac{5}{66} \)

Explanation:
1. Required value = \( -\frac{7}{22} \) - (\( -\frac{8}{33} \)).
2. Using the common denominator the result is \( -\frac{5}{66} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 9: The sum of two rational numbers is \( \frac{5}{9} \). If one of them is \( \frac{1}{3} \), the other number is:
(a) \( -\frac{7}{9} \)
(b) \( \frac{2}{9} \)
(c) \( -\frac{2}{9} \)
(d) \( \frac{11}{9} \)
Show Answer & Explanation

Answer: (b) \( \frac{2}{9} \)

Explanation:
1. Other number = sum - given number = \( \frac{5}{9} \) - (\( \frac{1}{3} \)).
2. = \( \frac{2}{9} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 10: The sum of two rational numbers is \( -\frac{4}{3} \). If one of them is \( -5 \), the other number is:
(a) \( -\frac{11}{3} \)
(b) \( \frac{8}{3} \)
(c) \( \frac{14}{3} \)
(d) \( \frac{11}{3} \)
Show Answer & Explanation

Answer: (d) \( \frac{11}{3} \)

Explanation:
1. Other number = sum - given number = \( -\frac{4}{3} \) - (\( -5 \)).
2. = \( \frac{11}{3} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 11: The sum of two rational numbers is \( -8 \). If one of them is \( -\frac{15}{7} \), the other number is:
(a) \( \frac{41}{7} \)
(b) \( -\frac{48}{7} \)
(c) \( -\frac{41}{7} \)
(d) \( -\frac{34}{7} \)
Show Answer & Explanation

Answer: (c) \( -\frac{41}{7} \)

Explanation:
1. Other number = sum - given number = \( -8 \) - (\( -\frac{15}{7} \)).
2. = \( -\frac{41}{7} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 12: What should be added to \( -\frac{7}{8} \) so as to get \( \frac{5}{9} \)?
(a) \( -\frac{103}{72} \)
(b) \( \frac{31}{72} \)
(c) \( \frac{175}{72} \)
(d) \( \frac{103}{72} \)
Show Answer & Explanation

Answer: (d) \( \frac{103}{72} \)

Explanation:
1. Required number = 5/9 - (-7/8) = 5/9 + 7/8.
2. = (40 + 63)/72 = 103/72.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 13: What number should be added to \( -\frac{5}{11} \) so as to get \( \frac{26}{33} \)?
(a) \( \frac{8}{33} \)
(b) \( \frac{41}{33} \)
(c) \( -\frac{41}{33} \)
(d) \( \frac{74}{33} \)
Show Answer & Explanation

Answer: (b) \( \frac{41}{33} \)

Explanation:
1. Required number = 26/33 + 5/11 = 26/33 + 15/33.
2. = 41/33.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 14: What number should be added to \( -\frac{5}{7} \) to get \( -\frac{2}{3} \)?
(a) \( -\frac{1}{21} \)
(b) \( \frac{1}{21} \)
(c) \( \frac{22}{21} \)
(d) \( -\frac{20}{21} \)
Show Answer & Explanation

Answer: (b) \( \frac{1}{21} \)

Explanation:
1. Required number = -2/3 + 5/7 = (-14 + 15)/21 = 1/21.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 15: What number should be subtracted from \( -\frac{5}{3} \) to get \( \frac{5}{6} \)?
(a) \( -\frac{3}{2} \)
(b) \( -\frac{5}{2} \)
(c) \( \frac{5}{2} \)
(d) \( -\frac{7}{2} \)
Show Answer & Explanation

Answer: (b) \( -\frac{5}{2} \)

Explanation:
1. Let the number be x: -5/3 - x = 5/6, so x = -5/3 - 5/6.
2. x = (-10 - 5)/6 = -5/2.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 16: What should be added to \( \left(\frac{2}{3}+\frac{3}{5}\right) \) to get \( -\frac{2}{15} \)?
(a) \( -\frac{2}{5} \)
(b) \( -\frac{7}{5} \)
(c) \( -\frac{12}{5} \)
(d) \( \frac{7}{5} \)
Show Answer & Explanation

Answer: (b) \( -\frac{7}{5} \)

Explanation:
1. 2/3 + 3/5 = 19/15.
2. Required number = -2/15 - 19/15 = -21/15 = -7/5.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 17: What should be added to \( \left(\frac{1}{2}+\frac{1}{3}+\frac{1}{5}\right) \) to get 3?
(a) \( \frac{59}{30} \)
(b) \( -\frac{59}{30} \)
(c) \( \frac{29}{30} \)
(d) \( \frac{89}{30} \)
Show Answer & Explanation

Answer: (a) \( \frac{59}{30} \)

Explanation:
1. 1/2 + 1/3 + 1/5 = 31/30.
2. Required number = 3 - 31/30 = 59/30.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 18: What should be subtracted from \( \left(\frac{3}{4}-\frac{2}{3}\right) \) to get \( -\frac{1}{6} \)?
(a) \( \frac{5}{4} \)
(b) \( -\frac{3}{4} \)
(c) \( -\frac{1}{4} \)
(d) \( \frac{1}{4} \)
Show Answer & Explanation

Answer: (d) \( \frac{1}{4} \)

Explanation:
1. 3/4 - 2/3 = 1/12.
2. x = 1/12 - (-1/6) = 1/12 + 2/12 = 3/12 = 1/4.

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 19: Simplify \( \frac{3}{4}+\frac{5}{6}+\frac{-7}{8} \) and write the result in the form p/q.
(a) \( -\frac{17}{24} \)
(b) \( -\frac{7}{24} \)
(c) \( \frac{41}{24} \)
(d) \( \frac{17}{24} \)
Show Answer & Explanation

Answer: (d) \( \frac{17}{24} \)

Explanation:
1. LCM of the denominators gives the common denominator.
2. The sum is \( \frac{17}{24} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

Question 20: Simplify \( \frac{2}{3}+\frac{-5}{6}+\frac{-7}{9} \) and write the result in the form p/q.
(a) \( \frac{1}{18} \)
(b) \( -\frac{17}{18} \)
(c) \( -\frac{35}{18} \)
(d) \( \frac{17}{18} \)
Show Answer & Explanation

Answer: (b) \( -\frac{17}{18} \)

Explanation:
1. LCM of the denominators gives the common denominator.
2. The sum is \( -\frac{17}{18} \).

Teacher's Note:
1. Bring all fractions to a common denominator before adding or subtracting.
2. Check the sign of each term carefully; most mistakes come from dropping a minus sign.

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Rational Numbers Objective Questions & Solutions for Class 8 Mathematics

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FAQs

Where can I access latest CBSE Class 8 Mathematics Rational Numbers MCQs Set 36?

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Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 8 material?

Yes, our CBSE Class 8 Mathematics Rational Numbers MCQs Set 36 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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