Let a and b be rational numbers. Is a-b rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (C) It can be either rational or irrational

Evaluate Rational Numbers: Evaluate the properties of rational numbers. Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. The set of rational numbers is closed under addition, subtraction, and multiplication. This means that the sum, difference, or product of any two rational numbers is also a rational number.Apply Closure Property: Apply the closure property to the subtraction of two rational numbers. If a and b are both rational numbers, then their difference a - b is also a rational number. This is because the set of rational numbers is closed under the operation of subtraction.Conclude Based on Closure: Conclude the answer based on the closure property. Since a and b are rational, and rational numbers are closed under subtraction, a - b must also be a rational number. Therefore, the correct answer is (A) Rational.

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Let
a and
b be rational numbers. Is
a-b rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(C) It can be either rational or irrational

Let $a$ and $b$ be rational numbers. Is $a-b$ rational or irrational? $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational $\newline$ (C) It can be either rational or irrational

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Math Problems

Algebra 2

Classify rational and irrational numbers

Full solution

Q. Let

a

and

b

be rational numbers. Is

a-b

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Evaluate Rational Numbers: Evaluate the properties of rational numbers. Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. The set of rational numbers is closed under addition, subtraction, and multiplication. This means that the sum, difference, or product of any two rational numbers is also a rational number.
Apply Closure Property: Apply the closure property to the subtraction of two rational numbers. If $a$ and $b$ are both rational numbers, then their difference $a - b$ is also a rational number. This is because the set of rational numbers is closed under the operation of subtraction.
Conclude Based on Closure: Conclude the answer based on the closure property. $\newline$ Since $a$ and $b$ are rational, and rational numbers are closed under subtraction, $a - b$ must also be a rational number. Therefore, the correct answer is ( $A$ ) Rational.