The number z is rational. Which statement about 5 + z is true? Choices: (A)5 + z is rational. (B)5 + z is irrational. (C)5 + z can be rational or irrational, depending on the value of z.

Identify Number Nature: Identify the nature of the number 5. 5 is a whole number, which is also a rational number because it can be expressed as the fraction 5/1.Sum Property 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 a/b and c/d, their sum (ad + bc) / (bd) is also a fraction, which means it is a rational number.Apply Property to Given Numbers: Apply the property to the given numbers. Since z is a rational number and 5 is a rational number, their sum 5 + z is also a rational number.

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

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

z

is rational. Which statement about

5 + z

is true?

\newline

Choices:

\newline

(A)

5 + z

is rational.

\newline

(B)

5 + z

is irrational.

\newline

(C)

5 + z

can be rational or irrational, depending on the value of

z

Identify Number Nature: Identify the nature of the number $5$ . $5$ is a whole number, which is also a rational number because it can be expressed as the fraction $\frac{5}{1}$ .
Sum Property 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 to Given Numbers: Apply the property to the given numbers. $\newline$ Since $z$ is a rational number and $5$ is a rational number, their sum $5 + z$ is also a rational number.