CBSE Class 8 Mathematics Rational Numbers MCQs Set 23

Multiple Choice Questions (MCQs) for Class 8 Mathematics: Rational Numbers

Access targeted multiple-choice questions for Rational Numbers designed to align with the latest CBSE academic syllabus for Class 8 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Practice Rational Numbers MCQs for Class 8 Mathematics

Navigate directly to the 50 objective questions for Rational Numbers using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question 1: Simplify: \( -\frac{2}{3}\times\frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times\frac{1}{6} \)
(a) 2
(b) \( \frac{5}{2} \)
(c) −2
(d) 3
Show Answer & Explanation

Answer: (a) 2

Explanation:
1. \( -\frac{2}{3}\times\frac{3}{5} = -\frac{2}{5} \) and \( \frac{3}{5}\times\frac{1}{6} = \frac{1}{10} \).
2. Expression = \( -\frac{2}{5}+\frac{5}{2}-\frac{1}{10} = \frac{-4+25-1}{10} = \frac{20}{10} = 2 \).

Teacher's Note:
1. Do the multiplications first, then add and subtract with a common denominator.
2. Here the LCM of the denominators is 10.

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

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

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

Teacher's Note:
1. Reduce each product before combining.
2. Use LCM 28 for the last step.

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. LCM of 7, 3, 9 and 14 is 126.
2. \( \frac{90}{126}+\frac{42}{126}+\frac{112}{126}+\frac{9}{126} = \frac{253}{126} \).

Teacher's Note:
1. Convert every fraction to the denominator 126.
2. Add the numerators only after the denominators match.

Question 4: Subtract the first rational number from the second: \( \frac{3}{8},\ \frac{5}{8} \)
(a) \( -\frac{3}{4} \)
(b) \( \frac{1}{4} \)
(c) \( -\frac{1}{4} \)
(d) \( \frac{5}{4} \)
Show Answer & Explanation

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

Explanation:
1. Required value = second − first = \( \frac{5}{8}-\left(\frac{3}{8}\right) \).
2. Using a common denominator this equals \( \frac{1}{4} \).

Teacher's Note:
1. Subtracting a number means adding its additive inverse.
2. Mind the order: second minus first.

Question 5: Subtract the first rational number from the second: \( \frac{11}{13},\ -\frac{4}{13} \)
(a) \( -\frac{15}{13} \)
(b) \( \frac{15}{13} \)
(c) \( -\frac{2}{13} \)
(d) \( -\frac{28}{13} \)
Show Answer & Explanation

Answer: (a) \( -\frac{15}{13} \)

Explanation:
1. Required value = second − first = \( -\frac{4}{13}-\left(\frac{11}{13}\right) \).
2. Using a common denominator this equals \( -\frac{15}{13} \).

Teacher's Note:
1. Subtracting a number means adding its additive inverse.
2. Mind the order: second minus first.

Question 6: Subtract the first rational number from the second: \( -\frac{2}{3},\ \frac{5}{6} \)
(a) \( -\frac{3}{2} \)
(b) \( \frac{5}{2} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{3}{2} \)
Show Answer & Explanation

Answer: (d) \( \frac{3}{2} \)

Explanation:
1. Required value = second − first = \( \frac{5}{6}-\left(-\frac{2}{3}\right) \).
2. Using a common denominator this equals \( \frac{3}{2} \).

Teacher's Note:
1. Subtracting a number means adding its additive inverse.
2. Mind the order: second minus first.

Question 7: Subtract the first rational number from the second: \( -\frac{8}{33},\ -\frac{7}{22} \)
(a) \( \frac{61}{66} \)
(b) \( -\frac{71}{66} \)
(c) \( -\frac{5}{66} \)
(d) \( \frac{5}{66} \)
Show Answer & Explanation

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

Explanation:
1. Required value = second − first = \( -\frac{7}{22}-\left(-\frac{8}{33}\right) \).
2. Using a common denominator this equals \( -\frac{5}{66} \).

Teacher's Note:
1. Subtracting a number means adding its additive inverse.
2. Mind the order: second minus first.

Question 8: The sum of two numbers is \( \frac{5}{9} \). If one of the numbers is \( \frac{1}{3} \), the other 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 = \( \frac{5}{9}-\frac{1}{3} = \frac{5-3}{9} = \frac{2}{9} \).

Teacher's Note:
1. Other number = sum − given number.

Question 9: The sum of two numbers is \( -\frac{1}{3} \). If one of the numbers is \( \frac{-12}{3} \), the other is
(a) \( \frac{11}{3} \)
(b) \( -\frac{11}{3} \)
(c) \( \frac{14}{3} \)
(d) \( \frac{8}{3} \)
Show Answer & Explanation

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

Explanation:
1. Other number = \( -\frac{1}{3}-\left(-4\right) = -\frac{1}{3}+4 = \frac{11}{3} \).

Teacher's Note:
1. Subtracting −4 means adding 4.

Question 10: The sum of two rational numbers is −8. If one of them is \( \frac{-15}{7} \), the other is
(a) \( \frac{41}{7} \)
(b) \( -\frac{34}{7} \)
(c) \( -\frac{48}{7} \)
(d) \( -\frac{41}{7} \)
Show Answer & Explanation

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

Explanation:
1. Other number = \( -8-\left(-\frac{15}{7}\right) = -8+\frac{15}{7} = \frac{-56+15}{7} = -\frac{41}{7} \).

Teacher's Note:
1. Convert −8 to sevenths before adding.

Question 11: What should be added to \( -\frac{7}{8} \) so as to get \( \frac{5}{9} \)?
(a) \( \frac{175}{72} \)
(b) \( \frac{31}{72} \)
(c) \( \frac{103}{72} \)
(d) \( -\frac{103}{72} \)
Show Answer & Explanation

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

Explanation:
1. Required number = \( \frac{5}{9}-\left(-\frac{7}{8}\right) = \frac{5}{9}+\frac{7}{8} = \frac{40+63}{72} = \frac{103}{72} \).

Teacher's Note:
1. Number to add = target − given number.

Question 12: 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 = \( \frac{26}{33}+\frac{5}{11} = \frac{26+15}{33} = \frac{41}{33} \).

Teacher's Note:
1. Number to add = target − given number.

Question 13: What 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: (a) \( \frac{1}{21} \)

Explanation:
1. Required number = \( -\frac{2}{3}+\frac{5}{7} = \frac{-14+15}{21} = \frac{1}{21} \).

Teacher's Note:
1. Target minus the given number.

Question 14: What number should be subtracted from \( \frac{-5}{3} \) to get \( \frac{5}{6} \)?
(a) \( \frac{5}{2} \)
(b) \( -\frac{3}{2} \)
(c) \( -\frac{7}{2} \)
(d) \( -\frac{5}{2} \)
Show Answer & Explanation

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

Explanation:
1. Let the number be x. Then \( -\frac{5}{3}-x = \frac{5}{6} \).
2. \( x = -\frac{5}{3}-\frac{5}{6} = \frac{-10-5}{6} = -\frac{5}{2} \).

Teacher's Note:
1. Form the equation, then isolate x.

Question 15: What number should be subtracted from \( \frac{3}{7} \) to get \( \frac{5}{4} \)?
(a) \( \frac{5}{28} \)
(b) \( -\frac{51}{28} \)
(c) \( -\frac{23}{28} \)
(d) \( \frac{23}{28} \)
Show Answer & Explanation

Answer: (c) \( -\frac{23}{28} \)

Explanation:
1. \( x = \frac{3}{7}-\frac{5}{4} = \frac{12-35}{28} = -\frac{23}{28} \).

Teacher's Note:
1. Number to subtract = given number − result.

Question 16: What should be added to \( \frac{1}{2}+\frac{1}{3}+\frac{1}{5} \) to get 3?
(a) \( \frac{29}{30} \)
(b) \( \frac{59}{30} \)
(c) \( -\frac{59}{30} \)
(d) \( \frac{89}{30} \)
Show Answer & Explanation

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

Explanation:
1. The sum is \( \frac{15+10+6}{30} = \frac{31}{30} \).
2. Required number = \( 3-\frac{31}{30} = \frac{59}{30} \).

Teacher's Note:
1. First find the sum, then subtract it from the target.

Question 17: What should be subtracted from \( \frac{3}{4}-\frac{2}{3} \) to get \( \frac{-1}{6} \)?
(a) \( \frac{1}{4} \)
(b) \( -\frac{1}{4} \)
(c) \( \frac{5}{4} \)
(d) \( -\frac{3}{4} \)
Show Answer & Explanation

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

Explanation:
1. \( \frac{3}{4}-\frac{2}{3} = \frac{1}{12} \).
2. Required number = \( \frac{1}{12}-\left(-\frac{1}{6}\right) = \frac{1}{12}+\frac{2}{12} = \frac{1}{4} \).

Teacher's Note:
1. Evaluate the bracket first.
2. Subtracting a negative number adds it.

Question 18: Simplify: \( \frac{3}{4}+\frac{5}{6}+\frac{-7}{8} \)
(a) \( -\frac{17}{24} \)
(b) \( \frac{41}{24} \)
(c) \( -\frac{7}{24} \)
(d) \( \frac{17}{24} \)
Show Answer & Explanation

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

Explanation:
1. LCM of 4, 6 and 8 is 24.
2. \( \frac{18}{24}+\frac{20}{24}-\frac{21}{24} = \frac{17}{24} \).

Teacher's Note:
1. Convert each fraction to 24ths.

Question 19: Simplify: \( \frac{-3}{2}+\frac{5}{4}-\frac{7}{4} \)
(a) −1
(b) −3
(c) −2
(d) 2
Show Answer & Explanation

Answer: (c) −2

Explanation:
1. \( \frac{-6}{4}+\frac{5}{4}-\frac{7}{4} = \frac{-8}{4} = -2 \).

Teacher's Note:
1. Same denominators: add the numerators.

Question 20: Multiply: \( \frac{7}{11}\times\frac{5}{4} \)
(a) \( -\frac{9}{44} \)
(b) \( \frac{35}{44} \)
(c) \( -\frac{35}{44} \)
(d) \( \frac{79}{44} \)
Show Answer & Explanation

Answer: (b) \( \frac{35}{44} \)

Explanation:
1. Multiply numerators and denominators: \( \frac{35}{44} \).

Teacher's Note:
1. Numerator times numerator, denominator times denominator.

Question 21: Simplify: \( \frac{-16}{21}\times\frac{14}{5} \)
(a) \( -\frac{32}{15} \)
(b) \( \frac{32}{15} \)
(c) \( -\frac{17}{15} \)
(d) \( -\frac{47}{15} \)
Show Answer & Explanation

Answer: (a) \( -\frac{32}{15} \)

Explanation:
1. Cancel 7: \( \frac{-16}{3}\times\frac{2}{5} = \frac{-32}{15} \).

Teacher's Note:
1. Cancel common factors before multiplying.

Question 22: Multiply: \( \frac{-11}{13}\times\frac{-21}{7} \)
(a) \( -\frac{33}{13} \)
(b) \( \frac{46}{13} \)
(c) \( \frac{20}{13} \)
(d) \( \frac{33}{13} \)
Show Answer & Explanation

Answer: (d) \( \frac{33}{13} \)

Explanation:
1. The product of two negatives is positive: \( \frac{11\times 21}{13\times 7} = \frac{33}{13} \).

Teacher's Note:
1. Negative times negative is positive.

Question 23: Simplify: \( \left(\frac{25}{8}\times\frac{2}{5}\right)-\left(\frac{3}{5}\times\frac{-10}{9}\right) \)
(a) \( \frac{35}{12} \)
(b) \( \frac{11}{12} \)
(c) \( \frac{23}{12} \)
(d) \( -\frac{23}{12} \)
Show Answer & Explanation

Answer: (c) \( \frac{23}{12} \)

Explanation:
1. \( \frac{25}{8}\times\frac{2}{5} = \frac{5}{4} \) and \( \frac{3}{5}\times\frac{-10}{9} = -\frac{2}{3} \).
2. \( \frac{5}{4}+\frac{2}{3} = \frac{15+8}{12} = \frac{23}{12} \).

Teacher's Note:
1. Evaluate each bracket separately, then subtract.

Question 24: Simplify: \( \left(-5\times\frac{2}{15}\right)-\left(-6\times\frac{2}{9}\right) \)
(a) \( -\frac{1}{3} \)
(b) \( \frac{2}{3} \)
(c) \( -\frac{2}{3} \)
(d) \( \frac{5}{3} \)
Show Answer & Explanation

Answer: (b) \( \frac{2}{3} \)

Explanation:
1. \( -5\times\frac{2}{15} = -\frac{2}{3} \) and \( -6\times\frac{2}{9} = -\frac{4}{3} \).
2. \( -\frac{2}{3}+\frac{4}{3} = \frac{2}{3} \).

Teacher's Note:
1. Subtracting a negative number adds its positive value.

Question 25: Simplify: \( \left(\frac{8}{5}\times\frac{-3}{2}\right)+\left(\frac{-3}{10}\times\frac{11}{16}\right) \)
(a) \( -\frac{417}{160} \)
(b) \( \frac{417}{160} \)
(c) \( -\frac{257}{160} \)
(d) \( -\frac{577}{160} \)
Show Answer & Explanation

Answer: (a) \( -\frac{417}{160} \)

Explanation:
1. \( \frac{8}{5}\times\frac{-3}{2} = -\frac{12}{5} \) and \( \frac{-3}{10}\times\frac{11}{16} = -\frac{33}{160} \).
2. \( -\frac{384}{160}-\frac{33}{160} = -\frac{417}{160} \).

Teacher's Note:
1. Use the common denominator 160 for the final addition.

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Multiple Choice Questions (MCQs) for Class 8 Mathematics Rational Numbers

About Rational Numbers MCQs for Class 8 Mathematics

Test your conceptual understanding of Rational Numbers with these targeted multiple-choice questions. Designed in alignment with the latest CBSE curriculum for Class 8 Mathematics, these problem sets build accuracy and prepare students for objective exams.

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FAQs

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