State true or false:

Every rational number is a whole number.

• (a) True
• (b) False

The statement "Every rational number is a whole number" is False. To understand why, let’s break down the concepts of rational numbers and whole numbers.

Defining Rational Numbers

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the numerator is an integer and the denominator is a non-zero integer. For example, numbers like 1/2, -3, and 4.75 can all be classified as rational numbers because they can be represented in fraction form:

• 1/2 is already a fraction.
• -3 can be expressed as -3/1.
• 4.75 can be expressed as 19/4.

Understanding Whole Numbers

Whole numbers, on the other hand, are a specific subset of rational numbers. They include all non-negative integers starting from zero: 0, 1, 2, 3, and so forth. Whole numbers do not include fractions or negative numbers.

Examples to Illustrate the Difference

Let’s look at some examples to clarify:

• The number 0 is a whole number and also a rational number (0/1).
• The number 5 is a whole number and can be expressed as 5/1, making it rational.
• However, the number 1/2 is a rational number but not a whole number.
• Similarly, -3 is a rational number (as -3/1) but not a whole number.

Conclusion

From this, we can see that while all whole numbers are indeed rational numbers (since they can be expressed as a fraction), not all rational numbers qualify as whole numbers. Therefore, the statement is false. Rational numbers encompass a broader range, including fractions and negative numbers, which do not fit into the whole number category.