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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.

The number line illustrates that any whole number can be represented as a fraction by expressing it as a ratio to 1, such as 2 = 2/1. This concept is fundamental in understanding fractions and their equivalences, as it shows how whole numbers fit within the broader framework of rational numbers.

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

This statement is misleading because the number line can contain multiple fractions between any two whole numbers, not just two. For instance, between 1 and 2, the fractions 1.5, 1.25, and 1.75 all exist. Therefore, the number of equivalent fractions is not limited to two.

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

Similar to option A, this is incorrect because the number of proper fractions between any two whole numbers can vary greatly. For example, between 1 and 2, there can be infinitely many proper fractions, such as 1.1, 1.2, 1.3, etc. Hence, the number line does not support the claim of exactly two proper fractions.

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

This statement accurately reflects the concept illustrated by the number line, showing that whole numbers can be expressed as fractions by multiplying by 1 (e.g., 3 = 3/1). This key idea helps students grasp the relationship between whole numbers and fractions.

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

This option is misleading because dividing by a form of 1 does not yield a whole number from two equivalent fractions. Instead, equivalent fractions maintain the same value and do not inherently convert to a whole number upon division by 1.

Conclusion

Understanding the relationship between whole numbers and fractions is crucial in mathematics. The number line effectively demonstrates that whole numbers can be expressed as equivalent fractions, reinforcing the concept of fractions in the broader context of rational numbers. This foundational understanding is essential for students as they advance in their mathematical studies.

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