# If a is a rational number and b is an irrational number, then the sum a + b is

A) rational.

B) imaginary.

C) irrational.

D) an integer.

**Solution:**

Consider two rational numbers

a = 1/6 and b = 2/3

A rational number is a type of real numbers, which is in the form of p/q where q is not equal to zero. Any fraction with non-zero denominators is a rational number.

Irrational numbers are the real numbers that cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio, such as p/q, where p and q are integers, q≠0.

Sum of two numbers is

a + b = 1/6+ 2/3

By further calculation

a + b = (1 + 4)/6

a + b = 5/6 (rational number)

Therefore, the sum a + b is a rational number.

## If a is a rational number and b is an irrational number, then the sum a + b is

A) rational.

B) imaginary.

C) irrational.

D) an integer.

**Summary:**

If a is a rational number and b is an irrational number, then the sum a + b is rational.