Important MCQs on Rational Numbers With Explanation

Ans. (b) 1

Explanation: Any integer multiplied by one equals the original number.

For example, 5 x 1 = 5

We multiply the denominators and numerators of any two rational integers independently before simplifying the fraction that is a resultant.

We have (a/b x 1) = (1 x a/b) = a/b for every rational integer a/b.

For rationals, 1 is known as the multiplicative identity. The multiplicative inverse of every nonzero rational integer a/b is b/a. As a result, (a/b x b/a) = (b/a x a/b) = 1

Read More: Additive Identity Vs Multiplicative Identity

Ans. (c) Multiplication and Addition

Explanation: As per associative property,

A+B = B+A

A*B = B*A

Where A and B are two integers.

Ans. (a) 0

Explanation: Any integer added by zero equals the original number.

For example, 5+0 = 5

If we consider a/b as a number that is rational,

then, a/b + 0 = 0 + a/b = a/b, then

For rational numbers, zero is the additive identity. To add or subtract two rational numbers, first, equalise their denominators, then add their numerators.

Ans. (a) p/q

Explanation: A rational number may be written as p/q, where p and q are both integers and q is not zero. Rational numbers are one of the most common forms of numbers we study in arithmetic, second only to integers. 

Ans. (c) Both positive and negative 

Explanation: An integer can be positive or negative, and it can also be zero. An integer is a number that has no decimal or fractional element from the set of positive and negative numbers, including zero. If an integer is bigger than zero, it is considered positive such as 1,2, 3, etc. If an integer is less than zero, it is considered negative, such as -1, -2, etc. 

Ans. (c) 157/84

Explanation: Given,3/4 + 5/6 + 2/7

LCM of 4, 6, 7 = 84

The least common multiple of two numbers a and b, generally represented as lcm(a, b), is the smallest positive integer divisible by both a and b in arithmetic and number theory.

When the denominators are the same and the rational numbers are added, we obtain;

⇒ 63/84 + 70/84 + 24/84

⇒ 157/84

Read More: Multiplication and Division of Integers

Ans. (d) Countless

Explanation: The numbers 3/4 and 1 may be expressed as 30/40 and 40/40, respectively. As a result, the rational numbers between them are as follows:

31/40, 32/40, 33/40, 34/40,35/40,36/40, 37/40, 38/40, 39/40.

Between any two rational numbers, there are innumerable rational numbers.

In arithmetic, a rational number can be defined as a number that can be expressed as the quotient p/q of two numbers with q is not equal to 0.

Ans. (a) 7/12

Explanation: We know that the average of any two numbers is in the middle of the two. The average value in a collection of numbers is the average value, which is obtained by dividing the sum of all the values by the number of values.

Let's calculate the average of the two rational integers we've been provided.

= (1/2+2/3)/2

= (7/6)/ (2/1)

= 7/6 × 1/2

= 7/12

Therefore, the rational number is 7/12.

Read More: Decimal To Fraction Formula

Ans. (a) √4 and -4/5

Explanation: When simplified, a rational number should be either a terminating decimal or a non-terminating decimal with recurring decimal patterns. As a result, among the specified integers, the rational numbers are √4 and -4/5. Numbers that may be written as a ratio of two integers are known as rational numbers. It consists entirely of integers and can be written as fractions or decimals. 

Ans. (d) When it comes to division, rational numbers are not associative.

Explanation: In Math, the associative property asserts that the order in which numbers are grouped by brackets (parentheses) has no effect on their total or product when adding or multiplying them. Addition and multiplication are both affected by the associative property.

Read More: Decimal Expansion of Rational Numbers

Ans. (a) 1

Explanation: In a given mathematical system, multiplicative identity is an identity element, such as 1 in the group of rational numbers without 0 that remains intact any element by which it is multiplied. Multiplication's associative property asserts that the product of three or more integers remains the same regardless of how the numbers are arranged, i.e, (P × Q) × R = P × (Q × R)