Operations on Rational and Irrational Numbers Answers

Determine whether each of the following problems will have a rational or an irrational answer. Your answer should be either the word “rational” or “irrational.”

The sum of a rational number and an irrational number is alwayssometimes✔ never rational.

The product of a rational number and an irrational number is ✔ alwayssometimesnever irrational.

The product of two rational numbers is alwayssometimes✔ never irrational.

A repeating decimal + A fraction

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Add. Express your answer as a fraction. Do not include spaces in your answer.

What type of answer would you expect from the problem below? Explain why you expect that type of answer. ✔ Rational; Both numbers can be written as fractions, so the answer will be a fraction, which is a rational number.Irrational; Both numbers can be written as fractions, so the answer will be a fraction, which is an irrational number.Rational; One number is a fraction and the other is a decimal, so they are not like terms and cannot be combined.

Multiply. Express your answer in simplest form.

What type of answer would you expect from the problem below? Explain why you expect that type of answer. Rational; Both numbers can be written as fractions, so the answer will be a fraction, which is a rational number.✔ Irrational; When these numbers are multiplied, the answer still has an irrational number in it, so the answer is irrational.Irrational; When these numbers are multiplied, the answer is not possible because there is a negative sign in the radical, so the answer is irrational.