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0 is a rational number. State whether the statement is true (T) or false (F).

The given statement is True Explanation A rational number, can be defined as any number which can be represented in the form of p/q where q... View Article

-3/4 is smaller than -2. 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 -2. On... View Article

Subtraction of rational number is commutative. State whether the statement is true (T) or false (F).

The given statement is False Explanation Subtraction of rational number is not commutative. Let x and y are any two rational number, Then, x... View Article

Rational numbers are closed under addition and multiplication but not under subtraction. State whether the statement is true (T) or false (F).

The given statement is False Explanation According to the properties of rational numbers: Rational numbers are closed under addition,... View Article

Between any two rational numbers there are exactly ten rational numbers. State whether the statement is true (T) or false (F).

The given statement is False Explanation There are unlimited rational numbers between two rational numbers. We can find unlimited... View Article

If x and y are negative rational numbers, then so is x + y. State whether the statement is true (T) or false (F).

The given statement is True Explanation For rational numbers x and y, if x < y then x – y is a negative rational number. Let us... View Article

For rational numbers x and y, if x < y then x - y is a positive rational number. State whether the statement is true (T) or false (F).

The given statement is False Explanation For rational numbers x and y, if x < y then x – y is a negative rational number.... View Article

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

The given statement is False Explanation The appropriate form is for any rational number x, (x) × (-1) = – x. Hence the given... View Article

-1 is not the reciprocal of any rational number. State whether the statement is true (T) or false (F).

The given statement is False Explanation The reciprocal is defined as the multiplicative inverse of a number. In other words, the... View Article

1 is the only number which is its own reciprocal. State whether the statement is true (T) or false (F).

The given statement is False Explanation The reciprocal is defined as the multiplicative inverse of a number. In other words, the reciprocal... View Article

For all rational numbers a, b and c, a (b + c) = ab + bc. State whether the statement is true (T) or false (F).

The given statement is False Explanation The distributive Property States that when a factor is multiplied by the sum/addition of two... View Article

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

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