Question 34

A whole number can be written as an equivalent fraction by multiplying by a form of 1.

A whole number can indeed be expressed as an equivalent fraction by multiplying it by a form of 1, such as \( \frac{n}{n} \) where \( n \) is any non-zero integer. This concept is visually reinforced through the use of a number line, which shows the relationship between whole numbers and their fractional representations.

A) There are two equivalent fractions between any two whole numbers.

This statement is incorrect because, while there can be multiple fractions between any two whole numbers, the number of equivalent fractions is not limited to two. There can be infinitely many fractions between two whole numbers, depending on how finely one chooses to divide the interval.

B) There are exactly two proper fractions between any two whole numbers.

This option is also incorrect. Similar to Option A, there is no fixed quantity of proper fractions that exist between any two whole numbers. In fact, an infinite number of proper fractions can be found between any two whole numbers, making this statement misleading.

C) A whole number can be written as an equivalent fraction by multiplying by a form of 1.

This option is correct, as it accurately describes how whole numbers can be represented as fractions. For example, the whole number 2 can be expressed as \( \frac{2}{1} \) or \( \frac{4}{2} \), both of which are valid equivalent fractions formed by multiplying by different forms of 1.

D) Two equivalent fractions can be written as a whole number by dividing by a form of 1.

This statement is incorrect because dividing equivalent fractions by a form of 1 does not necessarily yield a whole number. Instead, it often results in another fraction. For instance, \( \frac{2}{2} \) is equivalent to 1, but \( \frac{4}{4} \) remains equivalent to 1 regardless of how it is expressed; thus, this statement does not accurately convey the relationship between fractions and whole numbers.

Conclusion

The correct answer, C, emphasizes the concept of expressing whole numbers as equivalent fractions, which is a fundamental understanding in mathematics. Options A and B misrepresent the number of fractions that can exist between whole numbers, while Option D incorrectly describes the relationship between division of equivalent fractions and whole numbers. Therefore, C stands out as the only accurate representation of the concept being tested.