MN 1-5 Operations on Real NUmbers

Consider the follwoing statements. Select all that are always true.

• The sum of a rational number and a rational number is rational.

• The sum of a rational number and an irrational number is irraional.

• The sum of an irrational number and an irrational number is irrational.

Consider the follwoing statements. Select all that are always true.

• The product of a rational number and a rational number is rational.

• The product of a rational number and an irrational number is irraional.

• The product of a irational number and an irrational number is irrational.

Tags

Rational numbers

If the product of p * q * r is irrational, and p is a rational number, which of the following statements can be said about q and r.

• Only q can be irrational.

• Both q and r must be irrational

• Both q and r may be irrational.

• r may be rational if q is irrational

• Both q and r must be rational.

Let m and n be non-zero rational numbers.

Select the answer that makes this statement true.

The result of m + n can be

• rational

• irrational

• both rational and irrational

Let m and n be non-zero rational numbers.

Select the answer that makes this statement true.

The result of m / n can be

• rational

• irrational

• both rational and irrational

Let m be a non-zero rational number and x be an irrational number.

Select the answer that makes this statement true.

The result of m * x can be

• rational

• irrational

• both rational and irrational

Let x and y both be irrational numbers.

Select the answer that makes this statement true.

The result of x - y can be

• rational

• irrational

• both rational and irrational

Let x and y both be irrational numbers.
Select the answer that makes this statement true.
The result of x / y can be 

• rational

• irrational

• both rational and irrational

Let x be an  irrational number and n be a non-zero rational number.
Select the answer that makes this statement true.
The result of x / n can be 

• rational

• irrational

• both rational and irrational

Let x and y be irrational numbers and m be a non-zero rational number.
Select the answer that makes this statement true.
The result of x * y * m can be 

• rational

• irrational

• both rational and irrational