Difficulty: Easy

Average Score: 78%

The number line shown will best help students understand which of the following?

Diagram for question

Rationale

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

A number line illustrates that whole numbers can be represented as fractions, specifically by expressing them with a denominator of 1. This understanding is crucial for students as it lays the foundation for comprehending fractions, equivalence, and operations involving rational numbers.

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

This statement is incorrect because there can be infinitely many fractions between any two whole numbers, not just two. The number line is designed to show a continuum of values, indicating that fractions can be created at various points between whole numbers.

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

This choice is also incorrect because, like the previous option, it implies a limitation that isn't true. Between any two whole numbers, there can be numerous proper fractions, not just two. The number line illustrates this continuous nature of fractions.

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

This statement is correct because it highlights that any whole number can indeed be expressed as a fraction by multiplying it by 1 (e.g., 3 = 3/1). This principle is fundamental for understanding how whole numbers relate to fractions and is visually represented on the number line.

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

This choice is misleading as it implies a transformation that does not accurately represent how equivalent fractions relate to whole numbers. Dividing equivalent fractions by a form of 1 does not lead to a whole number but maintains their equivalence as fractions.

Conclusion

The number line effectively demonstrates that whole numbers can be expressed as equivalent fractions through multiplication by a form of 1. While the incorrect options suggest limitations or misconceptions about the relationship between fractions and whole numbers, the correct answer emphasizes a key concept in understanding rational numbers, making it an essential tool for students learning about fractions.

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