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Which of the following statements is always true? (a) (x – y)/2 is a rational number between x and y. (b) (x + y)/2 is a rational number between x and y. (c) (x × y)/2 is a rational number between x and y. (d) (x ÷ y)/2 is a rational number between x and y.

The correct answer is (b) (x + y)/2 is a rational number between x and y. Explanation Let us assume the value of x and y is 2 and... View Article

(x + y)/2 is a rational number (a) Between x and y (b) Less than x and y both. (c) Greater than x and y both. (d) Less than x but greater than y

The correct answer is (a) Between x and y Explanation Let us assume the value of x and y is 3 and 7 respectively Then, = (3 + 7)/ 2 = 10/2... View Article

Between two given rational numbers, we can find (a) one and only one rational number. (b) only two rational numbers. (c) only ten rational numbers. (d) infinitely many rational numbers.

The correct answer is (d) infinitely many rational numbers. Explanation There are unlimited rational numbers between two rational... View Article

Which of the following is an example of distributive property of multiplication over addition for rational numbers. (a) – (1/4) × {(2/3) + (-4/7)} = [-(1/4) × (2/3)] + [(-1/4) × (-4/7)] (b) – (1/4) × {(2/3) + (-4/7)} = [(1/4) × (2/3)] – (-4/7) (c) – (1/4) × {(2/3) + (-4/7)} = (2/3) + (-1/4) × (-4/7) (d) – (1/4) × {(2/3) + (-4/7)} = {(2/3) + (-4/7)} – (1/4)

The correct answer is (a) – (1/4) × {(2/3) + (-4/7)} = [-(1/4) × (2/3)] + [(-1/4) × (-4/7)] Explanation The... View Article

The reciprocal of (-3/8) × (-7/13) is

The correct answer is (a) 104/21 Explanation The reciprocal is defined as the multiplicative inverse of a number. A Reciprocal is... View Article

If y be the reciprocal of rational number x, then the reciprocal of y will be (a) x (b) y (c) x/y (d) y/x

The correct answer is (a) x Explanation The reciprocal is defined as the multiplicative inverse of a number. A Reciprocal is described as the... View Article

The reciprocal of any rational number p/q, where p and q are integers and q ≠ 0, is (a) p/q (b) 1 (c) 0 (d) q/p

The correct answer is (d) q/p Explanation The reciprocal is defined as the multiplicative inverse of a number. A Reciprocal is described as the... View Article

The reciprocal of 0 is (a) 1 (b) -1 (c) 0 (d) Not defined

The correct answer is (d) Not defined Explanation The reciprocal is defined as the multiplicative inverse of a number. A Reciprocal is... View Article

The reciprocal of -1 is (a) 1 (b) -1 (c) 0 (d) Not defined

The correct answer is (b) -1 Explanation The reciprocal is defined as the multiplicative inverse of a number. A Reciprocal is described as the... View Article

If x be any rational number then x + 0 is equal to (a) x (b) 0 (c) -x (d) Not defined

The correct answer is (a) x Explanation The rational number 0 is the additive identity for rational numbers. If x is a rational... View Article

The multiplicative inverse of [latex]-1tfrac{1}{7}[/latex] is (a) 8/7 (b) -8/7 (c) 7/8 (d) 7/-8

The correct answer is (d) 7/-8 Explanation The multiplicative inverse also known as reciprocal implies is something which is opposite. The... View Article

– (-x) is same as (a) -x (b) x (c) 1/x (d) -1/x

The correct answer is (b) x Explanation In the case of multiplication of integers, two signs are multiplied together. ... View Article

To get the product 1, we should multiply (8/21) by (a) 8/21 (b) -8/21 (c) 21/8 (d) -21/8

The correct answer is (c) 21/8 Explanation = (8/21) × (21/8) = (8 × 21) / (21 × 8) = 168/168 = 1... View Article

If x + 0 = 0 + x = x, which is rational number, then 0 is called (a) identity for addition of rational numbers. (b) additive inverse of x. (c) multiplicative inverse of x. (d) reciprocal of x.

The correct answer is (a) identity for addition of rational numbers. Explanation Additive identity states that when a number is added to... View Article

Multiplicative inverse of a negative rational number is (a) a positive rational number. (b) a negative rational number. (c) 0 (d) 1

The correct answer is (b) a negative rational number. Explanation The multiplicative inverse also known as reciprocal implies is something that... View Article

The additive inverse of -7/19 is (a) -7/19 (b) 7/19 (c) 19/7 (d) -19/7

The correct answer is (b) 7/19 Explanation An additive inverse of a number is the value, which on adding with the original number... View Article

One (1) is (a) the identity for addition of rational numbers. (b) the identity for subtraction of rational numbers. (c) the identity for multiplication of rational numbers. (d) the identity for division of rational numbers.

The correct answer is (c) the identity for multiplication of rational numbers. Explanation The rational number 1 is the multiplicative... View Article

Zero (0) is (a) the identity for addition of rational numbers. (b) the identity for subtraction of rational numbers. (c) the identity for multiplication of rational numbers. (d) the identity for division of rational numbers.

The correct answer is (a) the identity for the addition of rational numbers. Explanation The rational number 0 is the additive identity for... View Article

Which of the following expressions shows that rational numbers are associative under multiplication. (a) [(2/3) × ((-6/7) × (3/5))] = [((2/3) × (-6/7)) × (3/5)] (b) [(2/3) × ((-6/7) × (3/5))] = [(2/3) × ((3/5) × (-6/7))] (c) [(2/3) × ((-6/7) × (3/5))] = [((3/5) × (2/3)) × (-6/7)] (d) [((2/3) × (-6/7)) × (3/5)] = [((-6/7) × (2/3)) × (3/5)]

The correct answer is (a) [(2/3) × ((-6/7) × (3/5))] = [((2/3) × (-6/7)) × (3/5)] Explanation Rational numbers follow... View Article

(-3/8) + (1/7) = (1/7) + (-3/8) is an example to show that (a) addition of rational numbers is commutative. (b) rational numbers are closed under addition. (c) addition of rational number is associative. (d) rational numbers are distributive under addition.

The correct answer is (a) addition of rational numbers is commutative. Explanation For rational numbers, addition and multiplication are... View Article

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