CBSE Class 8 Mathematics Rational Numbers MCQ Assignment Set 02

Question. If \( \frac{0}{15} \) is a rational number, can you say that its reciprocal is also a rational number ?
(a) yes
(b) No
(c) Sometime
(d) never
Answer: (b) No
In simple words: The value of \( \frac{0}{15} \) is equal to 0. Flipping 0 gives \( \frac{1}{0} \), which is not a rational number because we cannot divide by 0.
Exam Tip: Always remember that the number 0 is the only rational number that does not have a reciprocal.

Question. The multiplicative identity for rational numbers is
(a) 0
(b) -1
(c) 1
(d) \( \frac{1}{\text{rational no.}} \)
Answer: (c) 1
In simple words: When we multiply any rational number by 1, the value does not change.
Exam Tip: Do not confuse multiplicative identity (which is 1) with additive identity (which is 0).

Question. Rational numbers are not closed under
(a) Addition
(b) Subtraction
(c) Multiplication
(d) Division
Answer: (d) Division
In simple words: If you divide any rational number by 0, the answer is not a rational number.
Exam Tip: Rational numbers are closed under addition, subtraction, and multiplication, but division is the exception due to division by zero.

Question. Commutative property in rational numbers are valid under all the four operations (+, -, x, /)
(a) yes
(b) No
(c) Sometime
(d) None of the options
Answer: (b) No
In simple words: Changing the order of numbers during subtraction or division changes the answer.
Exam Tip: Commutativity only holds for addition and multiplication of rational numbers.

Question. The additive identity for rational numbers is
(a) 1
(b) -1
(c) 0
(d) None of the options
Answer: (c) 0
In simple words: If you add 0 to any rational number, the number stays exactly the same.
Exam Tip: Keep in mind that 0 is the additive identity because adding it to any number leaves the identity of that number unchanged.

Question. Between two rational numbers, how many rational numbers one can find.
(a) 5
(b) 4
(c) 3
(d) Infinite
Answer: (d) Infinite
In simple words: There are endless rational numbers packed between any two rational numbers.
Exam Tip: This property of rational numbers is called the density property.

Question. The additive inverse of \( \left(-\frac{5}{12}\right) \) is
(a) \( \frac{12}{5} \)
(b) \( \frac{12}{-5} \)
(c) \( \frac{5}{12} \)
(d) \( -\frac{5}{12} \)
Answer: (c) \( \frac{5}{12} \)
In simple words: Just change the minus sign to a plus sign to find the additive inverse.
Exam Tip: The sum of any number and its additive inverse must always be equal to 0.

Question. The multiplicative inverse of \( \left(\frac{3}{4}\right) \) is
(a) \( \frac{3}{4} \)
(b) \( -\frac{3}{4} \)
(c) \( -\frac{4}{3} \)
(d) \( \frac{4}{3} \)
Answer: (d) \( \frac{4}{3} \)
In simple words: To find the multiplicative inverse, turn the fraction upside down.
Exam Tip: The product of a rational number and its multiplicative inverse is always 1.

Question. The reciprocal of 1 is
(a) 0
(b) -1
(c) 1
(d) does not Exist
Answer: (c) 1
In simple words: Flipping 1 upside down as a fraction still gives you 1.
Exam Tip: Only 1 and -1 are rational numbers that are equal to their own reciprocals.

Question. Distributive property for any three rational numbers a, b, c is
(a) \( a+b+c = b+a+c \)
(b) \( a.b.c = b.a.c \)
(c) \( a+(b+c) = (a+b)+c \)
(d) \( ax(b+c) = axb + axc \)
Answer: (d) \( ax(b+c) = axb + axc \)
In simple words: This property shows how multiplying a number by a sum is the same as multiplying each part first.
Exam Tip: This is the distributive property of multiplication over addition, which helps to simplify complex equations.

Question. Can you represent any rational number on the number line ?
(a) yes
(b) not every
(c) only few
(d) None of the options
Answer: (a) yes
In simple words: We can mark a spot for every single rational number on the number line.
Exam Tip: Every rational number corresponds to a unique point on the number line.

Question. Find one rational between \( \frac{1}{2} \) and \( \frac{1}{4} \) using the idea of mean
(a) \( \frac{3}{8} \)
(b) \( \frac{4}{8} \)
(c) \( \frac{5}{8} \)
(d) \( \frac{6}{8} \)
Answer: (a) \( \frac{3}{8} \)
In simple words: Add \( \frac{1}{2} \) and \( \frac{1}{4} \) together to get \( \frac{3}{4} \), then divide by 2 to get \( \frac{3}{8} \).
Exam Tip: To find a number exactly in the middle of two numbers, find their average by adding them and dividing by 2.

Question. Find a number whose reciprocal is same as the number
(a) 0
(b) -1
(c) 1
(d) None of the options
Answer: (c) 1
In simple words: The reciprocal of 1 is 1, and the reciprocal of -1 is -1. Both options are correct.
Exam Tip: Both 1 and -1 are equal to their reciprocals, so look carefully at the options provided.

Question. Multiply \( \frac{6}{13} \) by the reciprocal of \( -\frac{7}{15} \)
(a) \( \frac{90}{91} \)
(b) \( \frac{91}{90} \)
(c) \( -\frac{90}{91} \)
(d) \( -\frac{91}{90} \)
Answer: (c) \( -\frac{90}{91} \)
In simple words: The reciprocal of \( -\frac{7}{15} \) is \( -\frac{15}{7} \). Multiplying \( \frac{6}{13} \) by \( -\frac{15}{7} \) gives \( -\frac{90}{91} \).
Exam Tip: Be sure to find the reciprocal of the second fraction first before multiplying the numerators and denominators.

Question. If \( -\frac{6}{13} \times x = 1 \), the value of x is
(a) \( \frac{13}{6} \)
(b) \( -\frac{13}{6} \)
(c) \( \frac{6}{13} \)
(d) \( \frac{13}{-6} \)
Answer: (b) \( -\frac{13}{6} \)
In simple words: Since the product is 1, \( x \) must be the reciprocal of \( -\frac{6}{13} \), which is \( -\frac{13}{6} \).
Exam Tip: When the product of two numbers is 1, they are reciprocals of each other.

Question. Is 0.3 the multiplicative inverse of \( 3\frac{1}{3} \) ?
(a) yes
(b) No
(c) Sometime
(d) None of the options
Answer: (a) yes
In simple words: \( 3\frac{1}{3} \) equals \( \frac{10}{3} \), and \( 0.3 \) equals \( \frac{3}{10} \). Since \( \frac{10}{3} \times \frac{3}{10} = 1 \), they are multiplicative inverses.
Exam Tip: Convert decimals and mixed fractions into improper fractions first to make calculations simple.

Question. If x, y are two rational numbers then \( |x \times y| \) is
(a) \( < |x| \times |y| \)
(b) \( \le |x| \times |y| \)
(c) \( = |x| \times |y| \)
(d) None of the options
Answer: (c) \( = |x| \times |y| \)
In simple words: Multiplying two numbers and then taking the absolute value is the same as taking their absolute values first and then multiplying.
Exam Tip: The absolute value of a product is always exactly equal to the product of the individual absolute values.

Question. If a, b, c are any three rational numbers and a \(\neq\) 0, what can you say about \( (b+c)\div a = b\div a + c\div a \) ?
(a) True
(b) False
(c) not always true
(d) None of the options
Answer: (a) True
In simple words: Dividing a sum by a number is equal to dividing each part first and then adding them.
Exam Tip: Remember that division is right-distributive over addition, so \( (b+c)\div a = \frac{b}{a} + \frac{c}{a} \) is always true.

Question. Which of the following statements is true ?
(a) \( \frac{7}{9} < \frac{9}{11} < \frac{11}{13} \)
(b) \( \frac{9}{11} < \frac{11}{13} < \frac{7}{9} \)
(c) \( \frac{9}{11} < \frac{7}{9} < \frac{11}{13} \)
(d) \( \frac{7}{9} > \frac{9}{11} < \frac{11}{13} \)
Answer: (a) \( \frac{7}{9} < \frac{9}{11} < \frac{11}{13} \)
In simple words: Converting these to decimals gives \( 0.77 \), \( 0.81 \), and \( 0.84 \), which shows \( \frac{7}{9} \) is indeed the smallest.
Exam Tip: When the difference between the numerator and denominator is the same for proper fractions, the one with larger numbers is always greater.

Question. After arranging \( \frac{1}{2} \), \( \frac{7}{-8} \) and \( -\frac{4}{5} \) in descending order, the middle number is
(a) \( \frac{1}{2} \)
(b) \( -\frac{4}{5} \)
(c) \( \frac{7}{-8} \)
(d) \( -\frac{3}{8} \)
Answer: (b) \( -\frac{4}{5} \)
In simple words: The decimal values are \( 0.5 \), \( -0.875 \), and \( -0.8 \). In order from largest to smallest, they are \( 0.5 \), then \( -0.8 \), then \( -0.875 \). The middle number is \( -0.8 \).
Exam Tip: For negative numbers, the one with the smaller absolute value is actually larger (e.g., \( -0.8 > -0.875 \)).

Question. The difference between the greatest and the least of \( -\frac{5}{9} \), \( \frac{2}{9} \), \( \frac{1}{9} \)
(a) \( -\frac{7}{9} \)
(b) \( \frac{9}{-7} \)
(c) \( \frac{7}{9} \)
(d) \( \frac{3}{9} \)
Answer: (c) \( \frac{7}{9} \)
In simple words: Subtract the smallest number \( -\frac{5}{9} \) from the largest number \( \frac{2}{9} \) to get \( \frac{7}{9} \).
Exam Tip: Be careful with signs. Subtracting a negative number becomes addition: \( \frac{2}{9} - \left(-\frac{5}{9}\right) = \frac{2}{9} + \frac{5}{9} \).

Question. Divide the sum of \( -\frac{5}{6} \) and \( -\frac{7}{12} \) by their product
(a) \( \frac{35}{69} \)
(b) \( \frac{35}{-72} \)
(c) \( -\frac{102}{35} \)
(d) \( \frac{102}{35} \)
Answer: (c) \( -\frac{102}{35} \)
In simple words: The sum of the numbers is \( -\frac{17}{12} \) and the product is \( \frac{35}{72} \). Dividing the sum by the product gives \( -\frac{102}{35} \).
Exam Tip: Find the sum and the product separately first before trying to perform the final division.

Question. The perimeter of a rectangle if its length is \( 5\frac{2}{3} \) m and width is \( 1\frac{1}{3} \) m.
(a) 14
(b) \( \frac{14}{3} \)
(c) 7
(d) \( \frac{21}{5} \)
Answer: (a) 14
In simple words: Add the length and width to get 7 m, then multiply by 2 to find the total perimeter of 14 m.
Exam Tip: Always state the formula \( \text{Perimeter} = 2(\text{length} + \text{width}) \) before substituting values.

Question. Subtract the sum of \( -1\frac{1}{3} \) and \( 2\frac{5}{6} \) from \( -5\frac{2}{6} \)
(a) \( 6\frac{5}{6} \)
(b) \( -6\frac{5}{6} \)
(c) \( 5\frac{6}{5} \)
(d) \( 7\frac{5}{6} \)
Answer: (b) \( -6\frac{5}{6} \)
In simple words: The sum of the first two numbers is \( \frac{3}{2} \). Subtracting this from \( -5\frac{2}{6} \) gives \( -6\frac{5}{6} \).
Exam Tip: Remember that "subtract A from B" means the operation is \( B - A \), not \( A - B \).

Question. The simplified form of \( \frac{5}{16} \times \frac{8}{25} \times \frac{-4}{3} \times \frac{15}{2} \) is
(a) 1
(b) 0
(c) -1
(d) 5
Answer: (c) -1
In simple words: Simplify the numbers by dividing common factors in the top and bottom before multiplying. This easily gives -1.
Exam Tip: Simplify the calculation by cross-cancelling numerators and denominators first to work with smaller numbers.