The number y is irrational. Which statement about y - 4 is true? Choices: (A)y - 4 is rational. (B)y - 4 is irrational. (C)y - 4 can be rational or irrational, depending on the value of y.

Question

The number y is irrational. Which statement about y - 4 is true?   Choices: (A)y - 4 is rational. (B)y - 4 is irrational. (C)y - 4 can be rational or irrational, depending on the value of y.

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Nature of Number 4: Understand the nature of the number 4. 4 is a whole number, and therefore it is a rational number.Subtraction of Rational and Irrational Numbers: Consider the subtraction of a rational number from an irrational number. Subtracting a rational number from an irrational number will result in an irrational number. This is because the difference between a rational and an irrational number cannot be expressed as a ratio of two integers.Application to Given Problem: Apply this understanding to the given problem. Since y is irrational and 4 is rational, y - 4 will be irrational.Checking for Exceptions: Check for any exceptions that could make y - 4 rational. There are no values of y that are irrational where subtracting 4 would result in a rational number. Unlike addition where two irrationals could potentially sum to a rational (as in the case of r + √10), subtraction of a rational from an irrational will always yield an irrational number.

The number $y$ is irrational. Which statement about $y - 4$ is true? $\newline$ Choices: $\newline$ (A) $y - 4$ is rational. $\newline$ (B) $y - 4$ is irrational. $\newline$ (C) $y - 4$ can be rational or irrational, depending on the value of $y$ .

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More problems from Properties of operations on rational and irrational numbers

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The number y y y is irrational. Which statement about y−4 y - 4 y−4 is true?\newlineChoices:\newline(A)y−4 y - 4 y−4 is rational.\newline(B)y−4 y - 4 y−4 is irrational.\newline(C)y−4 y - 4 y−4 can be rational or irrational, depending on the value of y y y.

The number $y$ is irrational. Which statement about $y - 4$ is true? $\newline$ Choices: $\newline$ (A) $y - 4$ is rational. $\newline$ (B) $y - 4$ is irrational. $\newline$ (C) $y - 4$ can be rational or irrational, depending on the value of $y$ .