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The number $w$ is rational. Which statement about $9 + w$ is true? $\newline$ Choices: $\newline$ (A) $9 + w$ is rational. $\newline$ (B) $9 + w$ is irrational. $\newline$ (C) $9 + w$ can be rational or irrational, depending on the value of $w$ .

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

w

is rational. Which statement about

9 + w

is true?

\newline

Choices:

\newline

(A)

9 + w

is rational.

\newline

(B)

9 + w

is irrational.

\newline

(C)

9 + w

can be rational or irrational, depending on the value of

w

.

Identify Number $9$ : Identify the nature of the number $9$ . $9$ is a whole number, which is also a rational number because it can be expressed as the fraction $\frac{9}{1}$ .
Sum of Rational Numbers: Understand the property of the sum of two rational numbers. The sum of two rational numbers is always a rational number. This is because if you have two fractions $\frac{a}{b}$ and $\frac{c}{d}$ , their sum $\frac{ad + bc}{bd}$ is also a fraction, which means it is a rational number.
Apply Property: Apply the property to the given numbers. $\newline$ Since $w$ is a rational number and $9$ is a rational number, their sum $9 + w$ must also be a rational number according to the property of rational numbers.
Conclude Statement: Conclude the correct statement from the given choices. $\newline$ Based on the property that the sum of two rational numbers is rational, the statement about $9 + w$ being rational is true.

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