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For every rational numbers x, y and z, x + (y × z) = (x + y) × (x + z). State whether the statement is true (T) or false (F).

The given statement is False Explanation For every rational numbers a, b and c, [a × (b + c) = (a × b) + (a × c)] Hence... View Article

For every rational number x, x × 0 = x. State whether the statement is true (T) or false (F).

The given statement is False Explanation Zero Property of multiplication states that any number multiplied by 0 is equal to zero only. A... View Article

For all rational numbers x and y, (x) × (y) = (y) × (x) State whether the statement is true (T) or false (F).

The given statement is True Explanation Let us assume that x = 7, y = 8 Then, LHS = 7 × 8 = 56 RHS = 8 × 7 = 56 By... View Article

The negative of 1 is 1 itself. State whether the statement is true (T) or false (F).

The given statement is False Explanation A number is said to be negative if it posses a negative sign in the number. The negative... View Article

The negative of 0 does not exist. State whether the statement is true (T) or false (F).

The given statement is True Explanation In regular arithmetic, the number 0 does not possess any sign, so that −0, +0 and 0 are identical. The... View Article

The negative of the negative of any rational number is the number itself. State whether the statement is true (T) or false (F).

The given statement is True Explanation Let y be a positive rational number. Then, The negative of y is = – (- y) = y NOTE: As per the... View Article

If x + y = 0, then -y is known as the negative of x, where x and y are rational numbers. State whether the statement is true (T) or false (F).

The given statement is False Explanation If x and y are rational numbers, then y is known as the negative of x. Hence the given statement... View Article

The reciprocal of a non-zero rational number q/p is the rational number q/p. State whether the statement is true (T) or false (F).

The given statement is False Explanation Reciprocal is the inverse of a value or a number. If n is a real number, then its reciprocal will... View Article

If x/y is the additive inverse of c/d, then, (x/y) – (c/d) = 0 State whether the statement is true (T) or false (F).

The given statement is False Explanation An additive inverse of a number is the value, which on adding with the original number results in... View Article

For every rational number x, x + 1 = x. State whether the statement is true (T) or false (F).

The given statement is True Explanation Let x = 7 Then, 7 + 1 = 8 7 ≠ 8 So, we observe that x + 1 ≠ x Hence the given statement... View Article

The additive inverse of 1/2 is -2. State whether the statement is true (T) or false (F).

The given statement is False Explanation An additive inverse of a number is the value, which on adding with the original number results in... View Article

The multiplicative inverse of -3/5 is 5/3 State whether the statement is true (T) or false (F).

The given statement is False Explanation The multiplicative inverse of a number x is given by x-1, such that when it is multiplied by its... View Article

If a ≠ 0, the multiplicative inverse of a/b is b/a. State whether the statement is true (T) or false (F).

The given statement is True Explanation The multiplicative inverse of a number x is given byx-1, such that when it is multiplied by its... View Article

9/6 lies between 1 and 2. State whether the statement is true (T) or false (F).

The given statement is True Explanation Let us express the given rational numbers with a common denominator. 1 and 2 can... View Article

-7/2 lies between -3 and -4. State whether the statement is true (T) or false (F).

The given statement is True Explanation Let us express the given rational numbers with a common denominator. -3 and -4 can be... View Article

5/10 lies between 1/2 and 1. State whether the statement is true (T) or false (F).

The given statement is False Explanation Let us express the given rational numbers with a common denominator. and 1. On... View Article

5/6 lies between 2/3 and 1. State whether the statement is true (T) or false (F).

The given statement is True Explanation Let us express the given rational numbers with a common denominator. 2/3 and 1 On... View Article

If r/s is a rational number, then s cannot be equal to zero. State whether the statement is true (T) or false (F).

The given statement is True Explanation If r/s is a rational number, then s cannot be equal to zero. And r can be equal to zero (0) or any... View Article

If p/q is a rational number, then p cannot be equal to zero. State whether the statement is true (T) or false (F).

The given statement is False Explanation If p/q is a rational number, p can be equal to zero (0) or any integer. So the given... View Article

If x/y is a rational number, then y is always a whole number. State whether the statement is true (T) or false (F).

The given statement is False Explanation If x/y is a rational number, then y is not equal to 0. But 0 is a whole number. From the... View Article

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