The number b is rational. Which statement about b + 10 is true? Choices: (A)b + 10 is rational. (B)b + 10 is irrational. (C)b + 10 can be rational or irrational, depending on the value of b.

Identify Number Nature: Identify the nature of the number 10. 10 is an integer, which is also a rational number because it can be expressed as the ratio of two integers (10/1).Rational Number Properties: Understand the properties of rational numbers. The sum of two rational numbers is always a rational number. This is because if you have two rational numbers, a/b and c/d, their sum (ad + bc) / bd is also a rational number since integers are closed under addition and multiplication.Apply Property to Problem: Apply the property to the given problem. Since b is a rational number and 10 is a rational number, their sum b + 10 must also be a rational number according to the property of rational numbers.

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The number $b$ is rational. Which statement about $b + 10$ is true? $\newline$ Choices: $\newline$ (A) $b + 10$ is rational. $\newline$ (B) $b + 10$ is irrational. $\newline$ (C) $b + 10$ 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 + 10

is true?

\newline

Choices:

\newline

(A)

b + 10

is rational.

\newline

(B)

b + 10

is irrational.

\newline

(C)

b + 10

can be rational or irrational, depending on the value of

b

Identify Number Nature: Identify the nature of the number $10$ . $10$ is an integer, which is also a rational number because it can be expressed as the ratio of two integers ( $\frac{10}{1}$ ).
Rational Number Properties: Understand the properties of rational numbers. The sum of two rational numbers is always a rational number. This is because if you have two rational numbers, $\frac{a}{b}$ and $\frac{c}{d}$ , their sum $\frac{ad + bc}{bd}$ is also a rational number since integers are closed under addition and multiplication.
Apply Property to Problem: Apply the property to the given problem. $\newline$ Since $b$ is a rational number and $10$ is a rational number, their sum $b + 10$ must also be a rational number according to the property of rational numbers.