The number c is rational. Which statement about 6 + c is true? Choices: (A)6 + c is rational. (B)6 + c is irrational. (C)6 + c can be rational or irrational, depending on the value of c.

Identify Nature of 6: Identify the nature of the number 6. 6 is an integer, and all integers are rational numbers because they can be expressed as a fraction where the denominator is 1 (6/1).Property of Sum: Understand the property of the sum of two rational numbers. The sum of two rational numbers is always rational. 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: Apply the property to the given numbers. Since c is given to be a rational number and 6 is also a rational number, their sum 6 + c must also be a rational number according to the property stated in the previous step.

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The number $c$ is rational. Which statement about $6 + c$ is true? $\newline$ Choices: $\newline$ (A) $6 + c$ is rational. $\newline$ (B) $6 + c$ is irrational. $\newline$ (C) $6 + c$ can be rational or irrational, depending on the value of $c$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

c

is rational. Which statement about

6 + c

is true?

\newline

Choices:

\newline

(A)

6 + c

is rational.

\newline

(B)

6 + c

is irrational.

\newline

(C)

6 + c

can be rational or irrational, depending on the value of

c

Identify Nature of $6$ : Identify the nature of the number $6$ . $6$ is an integer, and all integers are rational numbers because they can be expressed as a fraction where the denominator is $1$ ( $\frac{6}{1}$ ).
Property of Sum: Understand the property of the sum of two rational numbers. $\newline$ The sum of two rational numbers is always rational. 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 $c$ is given to be a rational number and $6$ is also a rational number, their sum $6 + c$ must also be a rational number according to the property stated in the previous step.