Question

Pls check if these are correct. 1) If the following statement true or false? Explain your reasoning. All integers are rational numbers. (1 pt.) - The statement is false because 0 is an integer but cannot be written as the ratio of two integers - The statement is true because all numbers are rational numbers ✅ The statement is true because any integer x can be written in the for x/1, which is the ratio of two integers - The statement is false because 1/2 is a rational number but not an integer 2) Which of the following must describe an irrational number?(1 point) ✅ A number with a non repeating and non terminating decimal expansion - A number with a non terminating decimal expansion - A number with a non repeating decimal expansion - A number with a repeating or terminating decimal expansion 3)Which axiom is used to prove that the product of two rational numbers is rational?(1 point) - Natural numbers are closed under multiplication - Whole numbers are closed under division ✅ Integers are closed under multiplication - Integers are closed under division 4) Without calculating, how do you know the product 2/21 x 3/31 is rational? (1 point) - The product of any two positive numbers is rational. - When multiplying fractions, the product of two fractions is rational so long as both fractions are less than 1. ✅ Rational numbers are closed under multiplication, meaning that the product of rational numbers is rational. - When multiplying fractions. the product of two fractions is rational so long as both fractions are fully reduced 5) What rational number, when multiplied by an irrational number, has a product that is a rational number? (1 point) ✅ 1/2 - 1/10 - 0 - 1 Thx if you help

Answer 1

Answer: please find the answer in the explanation

Step-by-step explanation:

1.) All integers are rational numbers. 

The statement is false because 1/2 is a rational number but not an integer

2.) Which of the following must describe an irrational number?

- A number with a repeating or terminating decimal expansion.

3.) Which axiom is used to prove that the product of two rational numbers is rational?

Integers are closed under division

4.) Without calculating, how do you know the product 2/21 x 3/31 is rational?

When multiplying fractions, the product of two fractions is rational so long as both fractions are less than 1. 

5.) What rational number, when multiplied by an irrational number, has a product that is a rational number? 1/10