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

Identify Number Type: Identify whether 7 is a rational or irrational number. 7 is an integer, and all integers are rational numbers because they can be expressed as a fraction where the denominator is 1 (7/1).Rational Number Definition: We know: b is a rational number. 7 is a rational number. Determine the nature of the sum b + 7. The sum of two rational numbers is always rational. This is because if b can be expressed as a fraction a/c and 7 as 7/1, their sum (a/c) + (7/1) can be expressed as a common fraction, which is the definition of a rational number.

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

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

b

is rational. Which statement about

b + 7

is true?

\newline

Choices:

\newline

(A)

b + 7

is rational.

\newline

(B)

b + 7

is irrational.

\newline

(C)

b + 7

can be rational or irrational, depending on the value of

b

Identify Number Type: Identify whether $7$ is a rational or irrational number. $\newline$ $7$ is an integer, and all integers are rational numbers because they can be expressed as a fraction where the denominator is $1$ ( $\frac{7}{1}$ ).
Rational Number Definition: We know: $b$ is a rational number. $7$ is a rational number. Determine the nature of the sum $b + 7$ . The sum of two rational numbers is always rational. This is because if $b$ can be expressed as a fraction $\frac{a}{c}$ and $7$ as $\frac{7}{1}$ , their sum $\left(\frac{a}{c}\right) + \left(\frac{7}{1}\right)$ can be expressed as a common fraction, which is the definition of a rational number.