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The number tt is rational. Which statement about 5+t5 + t is true?\newlineChoices:\newline(A) 5+t5 + t is rational.\newline(B) 5+t5 + t is irrational.\newline(C) 5+t5 + t can be rational or irrational, depending on the value of tt.

Full solution

Q. The number tt is rational. Which statement about 5+t5 + t is true?\newlineChoices:\newline(A) 5+t5 + t is rational.\newline(B) 5+t5 + t is irrational.\newline(C) 5+t5 + t can be rational or irrational, depending on the value of tt.
  1. Identify Number Nature: Identify the nature of the number 55.55 is a whole number, which is also a rational number because it can be expressed as the fraction 51\frac{5}{1}.
  2. Properties of Rational Numbers: Understand the properties of rational numbers. The sum of two rational numbers is always a rational number. This is because if you have two fractions ab\frac{a}{b} and cd\frac{c}{d}, their sum ad+bcbd\frac{ad + bc}{bd} is also a fraction, which means it is a rational number.
  3. Apply Property to Problem: Apply the property to the given problem.\newlineSince tt is a rational number and 55 is a rational number, their sum 5+t5 + t must also be a rational number according to the property of rational numbers.
  4. Choose Correct Statement: Choose the correct statement from the given choices.\newlineBased on the previous step, the statement (A) "5+t5 + t is rational" is the correct choice.

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