FTCE General Knowledge Math Practice Test

Which of the following best describes a rational number?

1. A number that cannot be expressed as a fraction

2. A number that can be expressed as the ratio of two integers

3. A number that can only be a whole number

4. A number that is always positive

The correct answer is: A number that can be expressed as the ratio of two integers

A rational number is defined as any number that can be expressed as the quotient or ratio of two integers, where the denominator is not zero. This means that for a number to be rational, it must be able to be written in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers, and \( b \) is not equal to zero. Examples of rational numbers include whole numbers (since they can be expressed with a denominator of 1, such as \( \frac{3}{1} \)), fractions (such as \( \frac{1}{2} \)), and negative numbers (like \( -\frac{5}{3} \)). This broad definition ensures that rational numbers encompass a wide variety of numerical forms, not limited to positive or whole numbers. The other choices present misunderstandings about rational numbers. The first choice incorrectly claims that rational numbers cannot be expressed as fractions, directly contradicting the definition. The third option stating that rational numbers can only be whole numbers overlooks fractions and negative integers, both of which are also rational. Finally, the idea that rational numbers are always positive excludes negative fractions and integers, which are very much part of the rational number set.