CBSE Class 8 Mathematics Rational Numbers MCQs Set 46

Practice 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.

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View or download the dedicated Rational Numbers MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: The rational numbers that are equal to their own reciprocals are:
(a) 0 and 1
(b) 0 and -1
(c) 1 and -1
(d) 2 and 1/2
Show Answer & Explanation

Answer: (c) 1 and -1

Explanation:
1. a = 1/a gives a x a = 1, so a = 1 or a = -1.

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: The only rational number that is equal to its own negative is:
(a) 1/2
(b) -1
(c) 1
(d) 0
Show Answer & Explanation

Answer: (d) 0

Explanation:
1. a = -a gives 2a = 0, so a = 0.

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: The reciprocal of \( -5 \) is:
(a) \( \frac{1}{5} \)
(b) \( 5 \)
(c) \( -\frac{1}{5} \)
(d) \( \frac{4}{5} \)
Show Answer & Explanation

Answer: (c) \( -\frac{1}{5} \)

Explanation:
1. Reciprocal of -5 is 1/(-5) = -1/5.

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 4: The product of two rational numbers is always a:
(a) whole number
(b) rational number
(c) natural number
(d) integer
Show Answer & Explanation

Answer: (b) rational number

Explanation:
1. The product of p/q and r/s is pr/qs, with qs not zero, which is again a rational number.

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: What must be added to \( 5x^2-7x+2 \) to produce \( 7x^2-1 \)?
(a) \( 2x^2+7x-3 \)
(b) \( 2x^2+7x+3 \)
(c) \( 2x^2-3 \)
(d) \( 12x^2-7x+1 \)
Show Answer & Explanation

Answer: (a) \( 2x^2+7x-3 \)

Explanation:
1. Required expression = (7x^2 - 1) - (5x^2 - 7x + 2).
2. = 2x^2 + 7x - 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 6: What must be added to \( 1-x+x^2-2x^3 \) to obtain \( x^3 \)?
(a) \( 3x^3+x^2-x+1 \)
(b) \( -1+x+x^2-3x^3 \)
(c) \( 3x^3-x^2+x-1 \)
(d) \( x^3-x^2+x-1 \)
Show Answer & Explanation

Answer: (c) \( 3x^3-x^2+x-1 \)

Explanation:
1. Required = x^3 - (1 - x + x^2 - 2x^3).
2. = x^3 - 1 + x - x^2 + 2x^3 = 3x^3 - x^2 + x - 1.

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: What must be added to the sum of \( 4x^2+3x-7 \) and \( 3x^2+6x+5 \) to get 1?
(a) \( 7x^2+9x-2 \)
(b) \( -7x^2+9x+3 \)
(c) \( -7x^2-9x+3 \)
(d) \( 7x^2+9x-3 \)
Show Answer & Explanation

Answer: (c) \( -7x^2-9x+3 \)

Explanation:
1. Sum = 7x^2 + 9x - 2.
2. Required = 1 - (7x^2 + 9x - 2) = -7x^2 - 9x + 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 8: By what number should \( \frac{1}{-15} \) be divided so that the quotient is \( \frac{1}{-5} \)?
(a) \( \frac{1}{3} \)
(b) \( -\frac{1}{3} \)
(c) \( 3 \)
(d) \( \frac{4}{3} \)
Show Answer & Explanation

Answer: (a) \( \frac{1}{3} \)

Explanation:
1. Let the number be x: (-1/15) / x = -1/5.
2. x = (-1/15) / (-1/5) = (1/15) x 5 = 1/3.

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 9: Simplify \( \left(\frac{5}{8}\right)^{-7}\times\left(\frac{8}{5}\right)^{-5} \).
(a) \( \frac{89}{25} \)
(b) \( \frac{64}{25} \)
(c) \( \frac{39}{25} \)
(d) \( -\frac{64}{25} \)
Show Answer & Explanation

Answer: (b) \( \frac{64}{25} \)

Explanation:
1. (8/5)^-5 = (5/8)^5.
2. Product = (5/8)^(-7+5) = (5/8)^-2 = (8/5)^2 = 64/25.

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: Simplify \( \left(\frac{-2}{3}\right)^{-2}\times\left(\frac{4}{5}\right)^{-3} \).
(a) \( \frac{1381}{256} \)
(b) \( \frac{1125}{256} \)
(c) \( \frac{869}{256} \)
(d) \( -\frac{1125}{256} \)
Show Answer & Explanation

Answer: (b) \( \frac{1125}{256} \)

Explanation:
1. (-2/3)^-2 = 9/4 and (4/5)^-3 = 125/64.
2. Product = 1125/256.

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: Simplify \( \left(\frac{3}{7}\right)^{-2}\times\left(\frac{7}{6}\right)^{-3} \).
(a) \( -\frac{24}{7} \)
(b) \( \frac{17}{7} \)
(c) \( \frac{31}{7} \)
(d) \( \frac{24}{7} \)
Show Answer & Explanation

Answer: (d) \( \frac{24}{7} \)

Explanation:
1. (3/7)^-2 = 49/9 and (7/6)^-3 = 216/343.
2. Product = (49 x 216)/(9 x 343) = 24/7.

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: The value of \( \frac{8^{-1}\times5^{3}}{2^{-4}} \) is:
(a) 125
(b) 25
(c) 250
(d) 500
Show Answer & Explanation

Answer: (c) 250

Explanation:
1. 8^-1 = 1/8, 5^3 = 125 and 1/2^-4 = 16.
2. Value = (1/8) x 125 x 16 = 250.

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: By what number should \( (-4)^{-2} \) be multiplied so that the product is \( 10^{-2} \)?
(a) \( \frac{25}{4} \)
(b) \( \frac{1}{100} \)
(c) \( \frac{4}{25} \)
(d) \( -\frac{4}{25} \)
Show Answer & Explanation

Answer: (c) \( \frac{4}{25} \)

Explanation:
1. (-4)^-2 = 1/16 and 10^-2 = 1/100.
2. Number = (1/100) / (1/16) = 16/100 = 4/25.

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: By what number should \( (-12)^{-1} \) be divided so that the quotient is \( \left(\frac{2}{3}\right)^{-1} \)?
(a) \( -\frac{19}{18} \)
(b) \( \frac{1}{18} \)
(c) \( -\frac{1}{18} \)
(d) \( \frac{17}{18} \)
Show Answer & Explanation

Answer: (c) \( -\frac{1}{18} \)

Explanation:
1. (-12)^-1 = -1/12 and (2/3)^-1 = 3/2.
2. Number = (-1/12) / (3/2) = -1/18.

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.

Question 15: Find m if \( \left(\frac{2}{9}\right)^{3}\times\left(\frac{2}{9}\right)^{-6}=\left(\frac{2}{9}\right)^{2m-1} \).
(a) m = 1
(b) m = 2
(c) m = -1
(d) m = -2
Show Answer & Explanation

Answer: (c) m = -1

Explanation:
1. Left side = (2/9)^(3-6) = (2/9)^-3.
2. So 2m - 1 = -3, giving m = -1.

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: Which of the following is a rational number between \( \frac{3}{5} \) and \( \frac{3}{4} \)?
(a) \( \frac{3}{5} \)
(b) \( \frac{4}{5} \)
(c) \( \frac{1}{2} \)
(d) \( \frac{27}{40} \)
Show Answer & Explanation

Answer: (d) \( \frac{27}{40} \)

Explanation:
1. 3/5 = 0.6 and 3/4 = 0.75.
2. 27/40 = 0.675 lies between them.

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: Which of the following is smaller than 2?
(a) \( \frac{9}{4} \)
(b) \( \frac{5}{2} \)
(c) \( \frac{7}{4} \)
(d) \( \frac{13}{6} \)
Show Answer & Explanation

Answer: (c) \( \frac{7}{4} \)

Explanation:
1. 7/4 = 1.75 < 2.
2. 9/4 = 2.25, 5/2 = 2.5 and 13/6 = 2.17 are greater than 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 18: Which of the following is greater than -2?
(a) \( -\frac{9}{4} \)
(b) \( -\frac{5}{2} \)
(c) \( -\frac{7}{3} \)
(d) \( -\frac{3}{2} \)
Show Answer & Explanation

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

Explanation:
1. -3/2 = -1.5 > -2.
2. The others are -2.5, -2.33 and -2.25, all less than -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 19: How many rational numbers lie between any two different rational numbers?
(a) none
(b) infinitely many
(c) exactly one
(d) exactly two
Show Answer & Explanation

Answer: (b) infinitely many

Explanation:
1. The mean of two rational numbers is rational and lies between them; repeating this gives infinitely many.

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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Practice MCQs for Class 8 Mathematics Rational Numbers

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FAQs

Where can I access latest CBSE Class 8 Mathematics Rational Numbers MCQs Set 46?

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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 46 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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