The number y is rational. Which statement about y + 7 is true? Choices: (A)y + 7 is rational. (B)y + 7 is irrational. (C)y + 7 can be rational or irrational, depending on the value of y.

Identify Number 7: Identify the nature of the number 7. 7 is an integer, and all integers are rational numbers because they can be expressed as a ratio of integers (7/1 in this case).Combine with y: Combine the rational number y with the rational number 7. The sum of two rational numbers is always rational. This is because the sum of two ratios of integers is another ratio of integers, which by definition is a rational number.Determine Truth: Determine the truth of the given statements based on the previous step. Since y is rational and 7 is rational, their sum y + 7 must also be rational. This means that statement (A) is true, while statements (B) and (C) are false.

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The number $y$ is rational. Which statement about $y + 7$ is true? $\newline$ Choices: $\newline$ (A) $y + 7$ is rational. $\newline$ (B) $y + 7$ is irrational. $\newline$ (C) $y + 7$ can be rational or irrational, depending on the value of $y$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

y

is rational. Which statement about

y + 7

is true?

\newline

Choices:

\newline

(A)

y + 7

is rational.

\newline

(B)

y + 7

is irrational.

\newline

(C)

y + 7

can be rational or irrational, depending on the value of

y

Identify Number $7$ : Identify the nature of the number $7$ . $7$ is an integer, and all integers are rational numbers because they can be expressed as a ratio of integers ( $\frac{7}{1}$ in this case).
Combine with $y$ : Combine the rational number $y$ with the rational number $7$ . $\newline$ The sum of two rational numbers is always rational. This is because the sum of two ratios of integers is another ratio of integers, which by definition is a rational number.
Determine Truth: Determine the truth of the given statements based on the previous step. $\newline$ Since $y$ is rational and $7$ is rational, their sum $y + 7$ must also be rational. This means that statement (A) is true, while statements (B) and (C) are false.