CBSE Class 8 Mathematics Number System MCQs Set 20

Multiple Choice Questions (MCQs) for Class 8 Mathematics: Number System

Review structured MCQ sets for Class 8 Mathematics Number System. Built according to official CBSE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Practice Number System MCQs for Class 8 Mathematics

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Multiple Choice Questions

Question 1: Evaluate \( (-3)\times(-9)\times(-6)\times(12) \).
(a) -324
(b) 324
(c) -1944
(d) 1944
Show Answer & Explanation

Answer: (c) -1944

Explanation:
1. Three of the four factors are negative, so the product is negative.
2. 27 × 6 = 162 and 162 × 12 = 1944, so the product is -1944.

Teacher's Note:
1. An odd number of negative factors gives a negative product.
2. Multiply the absolute values first, then fix the sign.

Question 2: Evaluate \( (-1)\times(-5)\times(-7)\times(-3)\times 4 \).
(a) -84
(b) -420
(c) 420
(d) 84
Show Answer & Explanation

Answer: (c) 420

Explanation:
1. Four factors are negative (an even number), so the product is positive.
2. 1 × 5 × 7 × 3 × 4 = 420.

Teacher's Note:
1. Count the negative signs: even gives positive, odd gives negative.
2. Multiply the absolute values in any order.

Question 3: Find the value of \( (-2)\times 15625+(-98)\times 15625 \).
(a) 1562500
(b) -1562500
(c) -156250
(d) -1500000
Show Answer & Explanation

Answer: (b) -1562500

Explanation:
1. Take 15625 common: 15625 × (-2 - 98) = 15625 × (-100).
2. = -1562500.

Teacher's Note:
1. Use the distributive property to avoid two big multiplications.
2. The sum inside the bracket is -100.

Question 4: Find the value of \( 1487\times 327+(-487)\times 327 \).
(a) 32700
(b) 327000
(c) -327000
(d) 1000
Show Answer & Explanation

Answer: (b) 327000

Explanation:
1. Take 327 common: 327 × (1487 - 487) = 327 × 1000.
2. = 327000.

Teacher's Note:
1. Distributive property: a × b + c × b = (a + c) × b.
2. 1487 - 487 = 1000.

Question 5: Which is greater: \( (8-9)\times 10 \) or \( 8-9\times 10 \)?
(a) \( 8-9\times10 \) (it equals -82)
(b) \( (8-9)\times10 \) (it equals -10)
(c) both are equal
(d) cannot be compared
Show Answer & Explanation

Answer: (b) \( (8-9)\times10 \) (it equals -10)

Explanation:
1. (8 - 9) × 10 = -1 × 10 = -10.
2. 8 - 9 × 10 = 8 - 90 = -82.
3. -10 > -82, so the first is greater.

Teacher's Note:
1. Compare the two values on the number line.
2. Of two negative numbers, the one nearer to zero is greater.

Question 6: The additive inverse of \( -(x+2) \) is:
(a) \( x+2 \)
(b) \( \frac{1}{x+2} \)
(c) \( -(x+2) \)
(d) \( -\frac{1}{x+2} \)
Show Answer & Explanation

Answer: (a) \( x+2 \)

Explanation:
1. The additive inverse of a is -a.
2. So the additive inverse of -(x + 2) is -(-(x + 2)) = x + 2.

Teacher's Note:
1. Sum of a number and its additive inverse is 0.
2. Check: -(x + 2) + (x + 2) = 0.

Question 7: The sum of two rational numbers is \( -\frac{3}{5} \). If one of the numbers is \( -\frac{9}{20} \), the other number is:
(a) \( -\frac{3}{20} \)
(b) \( -\frac{3}{5} \)
(c) \( \frac{3}{20} \)
(d) \( -\frac{21}{20} \)
Show Answer & Explanation

Answer: (a) \( -\frac{3}{20} \)

Explanation:
1. Other number = sum - given number = \( -\frac{3}{5} \) - \( -\frac{9}{20} \).
2. = \( -\frac{3}{5} \) + \( \frac{9}{20} \) = \( -\frac{3}{20} \).

Teacher's Note:
1. Subtracting a negative number means adding its positive.
2. Use the LCM 20 for the common denominator.

Question 8: What number should be added to \( -\frac{5}{8} \) to get \( \frac{5}{9} \)?
(a) \( \frac{5}{72} \)
(b) \( \frac{25}{72} \)
(c) \( -\frac{85}{72} \)
(d) \( \frac{85}{72} \)
Show Answer & Explanation

Answer: (d) \( \frac{85}{72} \)

Explanation:
1. Required number = \( \frac{5}{9} \) - (\( -\frac{5}{8} \)) = \( \frac{5}{9} \) + \( \frac{5}{8} \).
2. LCM of 9 and 8 is 72: \( \frac{5}{9} \) + \( \frac{5}{8} \) = \( \frac{85}{72} \).

Teacher's Note:
1. Number to add = target - given number.
2. Check: -5/8 + 85/72 = (-45 + 85)/72 = 40/72 = 5/9.

Question 9: Subtract \( \left(\frac{-2}{3}+\frac{4}{6}\right) \) from the sum of \( \frac{5}{12} \) and \( \frac{4}{3} \). The result is:
(a) \( -\frac{7}{4} \)
(b) \( \frac{15}{4} \)
(c) \( \frac{1}{12} \)
(d) \( \frac{7}{4} \)
Show Answer & Explanation

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

Explanation:
1. Sum of 5/12 and 4/3 = 5/12 + 16/12 = 21/12 = 7/4.
2. (-2/3 + 4/6) = -2/3 + 2/3 = 0.
3. 7/4 - 0 = 7/4.

Teacher's Note:
1. Simplify each bracket first.
2. 4/6 reduces to 2/3, which cancels -2/3.

Question 10: What should be subtracted from \( -\frac{3}{4} \) so as to get \( \frac{5}{6} \)?
(a) \( \frac{19}{12} \)
(b) \( -\frac{19}{12} \)
(c) \( -\frac{1}{12} \)
(d) \( \frac{1}{12} \)
Show Answer & Explanation

Answer: (b) \( -\frac{19}{12} \)

Explanation:
1. Required number = \( -\frac{3}{4} \) - \( \frac{5}{6} \).
2. LCM of 4 and 6 is 12: \( -\frac{3}{4} \) - \( \frac{5}{6} \) = \( -\frac{19}{12} \).

Teacher's Note:
1. Number to subtract = given number - result.
2. Check: -3/4 - (-19/12) = -9/12 + 19/12 = 10/12 = 5/6.

Question 11: What should be added to \( \left(\frac{2}{3}+\frac{3}{5}\right) \) to get \( -\frac{2}{15} \)?
(a) \( -\frac{7}{5} \)
(b) \( -\frac{4}{15} \)
(c) \( -\frac{19}{15} \)
(d) \( \frac{7}{5} \)
Show Answer & Explanation

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

Explanation:
1. 2/3 + 3/5 = 10/15 + 9/15 = 19/15.
2. Required number = -2/15 - 19/15 = -21/15 = -7/5.

Teacher's Note:
1. Number to add = target - sum already present.
2. Reduce -21/15 by dividing by 3.

Question 12: What should be subtracted from \( \left(\frac{3}{4}-\frac{2}{3}\right) \) to get \( -\frac{1}{6} \)?
(a) \( \frac{1}{12} \)
(b) \( -\frac{1}{12} \)
(c) \( \frac{1}{4} \)
(d) \( -\frac{1}{4} \)
Show Answer & Explanation

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

Explanation:
1. 3/4 - 2/3 = 9/12 - 8/12 = 1/12.
2. Required number = 1/12 - (-1/6) = 1/12 + 2/12 = 3/12 = 1/4.

Teacher's Note:
1. Number to subtract = given number - result.
2. Check: 1/12 - 1/4 = -2/12 = -1/6.

Question 13: Evaluate \( \frac{-12}{5}+\frac{-7}{20}+\frac{3}{14}+\frac{1}{7}+\frac{-1}{10} \).
(a) \( -\frac{303}{40} \)
(b) \( \frac{349}{140} \)
(c) \( -\frac{339}{140} \)
(d) \( -\frac{349}{140} \)
Show Answer & Explanation

Answer: (d) \( -\frac{349}{140} \)

Explanation:
1. LCM of 5, 20, 14, 7, 10 is 140.
2. Numerators: -336 - 49 + 30 + 20 - 14 = -349.
3. Sum = \( -\frac{349}{140} \).

Teacher's Note:
1. Convert every term to the common denominator 140.
2. Add all numerators with their signs.

Question 14: Evaluate \( \frac{-6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7} \).
(a) \( -\frac{67}{18} \)
(b) \( -\frac{77}{18} \)
(c) \( \frac{77}{18} \)
(d) \( -\frac{77}{9} \)
Show Answer & Explanation

Answer: (b) \( -\frac{77}{18} \)

Explanation:
1. Group the terms with denominator 7: -6/7 - 15/7 = -21/7 = -3.
2. -5/6 - 4/9 = -15/18 - 8/18 = -23/18.
3. -3 - 23/18 = -54/18 - 23/18 = -77/18.

Teacher's Note:
1. Combine like denominators first to save effort.
2. The answer is negative because every term is negative.

Question 15: Simplify \( \left(\frac{4}{5}\times\frac{-3}{2}\right)+\left(\frac{9}{5}\times\frac{-10}{3}\right)-\left(\frac{1}{2}\times\frac{3}{4}\right) \).
(a) \( \frac{303}{40} \)
(b) \( -\frac{249}{40} \)
(c) \( -\frac{303}{40} \)
(d) \( -\frac{343}{40} \)
Show Answer & Explanation

Answer: (c) \( -\frac{303}{40} \)

Explanation:
1. First product = -12/10 = -6/5; second product = -90/15 = -6; third product = 3/8.
2. -6/5 - 6 - 3/8 = (-48 - 240 - 15)/40.
3. = \( -\frac{303}{40} \).

Teacher's Note:
1. Do each product first, then add and subtract.
2. LCM of 5, 1 and 8 is 40.

Question 16: The product of two rational numbers is \( -\frac{28}{81} \). If one of the numbers is \( \frac{14}{27} \), the other number is:
(a) \( -\frac{3}{2} \)
(b) \( \frac{2}{3} \)
(c) \( -\frac{2}{3} \)
(d) \( -\frac{14}{27} \)
Show Answer & Explanation

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

Explanation:
1. Other number = product / given number = \( -\frac{28}{81} \) × \( \frac{27}{14} \).
2. = \( -\frac{2}{3} \) = \( -\frac{2}{3} \).

Teacher's Note:
1. Division by a rational number means multiplying by its reciprocal.
2. Cancel common factors before multiplying.

Question 17: By what number should \( \frac{3}{-14} \) be multiplied so that the product is \( \frac{5}{12} \)?
(a) \( -\frac{5}{18} \)
(b) \( \frac{35}{18} \)
(c) \( -\frac{35}{18} \)
(d) \( -\frac{18}{35} \)
Show Answer & Explanation

Answer: (c) \( -\frac{35}{18} \)

Explanation:
1. Required number = (5/12) ÷ (3/(-14)) = (5/12) × (-14/3).
2. = -70/36 = -35/18.

Teacher's Note:
1. Number to multiply by = product ÷ given number.
2. Check: (3/(-14)) × (-35/18) = 105/252 = 5/12.

Question 18: Divide the sum of \( \frac{65}{12} \) and \( \frac{12}{7} \) by their difference.
(a) \( \frac{599}{311} \)
(b) \( \frac{599}{144} \)
(c) \( \frac{311}{599} \)
(d) \( -\frac{599}{311} \)
Show Answer & Explanation

Answer: (a) \( \frac{599}{311} \)

Explanation:
1. Sum = 65/12 + 12/7 = (455 + 144)/84 = 599/84.
2. Difference = 65/12 - 12/7 = (455 - 144)/84 = 311/84.
3. Quotient = 599/311.

Teacher's Note:
1. Use the common denominator 84 for both sum and difference.
2. The denominators 84 cancel in the division.

Question 19: By what number should \( -\frac{33}{16} \) be divided to get \( -\frac{11}{4} \)?
(a) \( \frac{4}{3} \)
(b) \( -\frac{3}{4} \)
(c) \( \frac{3}{4} \)
(d) \( \frac{3}{4} \)
Show Answer & Explanation

Answer: (c) \( \frac{3}{4} \)

Explanation:
1. Required number = dividend ÷ quotient = (-33/16) ÷ (-11/4).
2. = (-33/16) × (4/-11) = 132/176 = 3/4.

Teacher's Note:
1. Divisor = dividend ÷ quotient.
2. Check: (-33/16) ÷ (3/4) = -33/12 = -11/4.

Question 20: The product of two rational numbers is 15. If one of the numbers is -10, the other number is:
(a) 150
(b) \( -\frac{3}{2} \)
(c) -150
(d) \( \frac{3}{2} \)
Show Answer & Explanation

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

Explanation:
1. Other number = 15 ÷ (-10) = -15/10 = -3/2.

Teacher's Note:
1. Product ÷ one number gives the other number.
2. A positive product with a negative factor needs a negative other factor.

Question 21: The product of two rational numbers is \( -\frac{7}{15} \). If one of them is -1, the other number is:
(a) \( \frac{7}{15} \)
(b) \( -\frac{7}{15} \)
(c) \( \frac{15}{7} \)
(d) 7
Show Answer & Explanation

Answer: (a) \( \frac{7}{15} \)

Explanation:
1. Other number = (-7/15) ÷ (-1) = 7/15.

Teacher's Note:
1. Dividing by -1 only changes the sign.
2. Check: (-1) × (7/15) = -7/15.

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FAQs

Where can I access latest CBSE Class 8 Mathematics Number System MCQs Set 20?

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

Yes, our CBSE Class 8 Mathematics Number System MCQs Set 20 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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