Question

1. eddie attempted to order the following rational numbers from least to greatest, as shown.

$-\frac{1}{3}, \frac{7}{8}, 1.5, -3.5$
a. explain eddie’s error in ordering the numbers.
b. order the numbers from least to greatest.

Explanation:

Part a

Step1: Recall rational number order

Rational numbers include negatives, fractions, decimals, and integers. When ordering, negatives are less than positives, and we compare values (e.g., convert fractions/decimals for clarity).

Step2: Analyze Eddie's error (assumed, since his work isn't shown, but common error: miscomparing negative/positive or fraction/decimal. E.g., maybe he ordered \(-\frac{1}{3}\) as less than \(-3.5\) (wrong, since \(-\frac{1}{3}\approx -0.33\) is greater than \(-3.5\)) or messed up fraction/decimal comparison (e.g., \(\frac{7}{8}=0.875\) vs \(1.5\)). So likely error: misordering negative numbers (thinking \(-\frac{1}{3}\) is more negative than \(-3.5\)) or miscomparing \(\frac{7}{8}\) and \(1.5\).

Step1: Convert all to decimals

\(-\frac{1}{3}\approx -0.333\), \(\frac{7}{8}=0.875\), \(1.5 = 1.5\), \(-3.5=-3.5\), \(8 = 8\).

Step2: Order by value

Negatives: \(-3.5 < -\frac{1}{3}\) (since \(-3.5\) is more negative). Positives: \(\frac{7}{8}(0.875) < 1.5 < 8\). Combine: \(-3.5 < -\frac{1}{3} < \frac{7}{8} < 1.5 < 8\).

Answer:

Eddie likely misordered negative numbers (e.g., thought \(-\frac{1}{3} < -3.5\) but \(-\frac{1}{3}\approx -0.33 > -3.5\)) or miscompared \(\frac{7}{8}(0.875)\) and \(1.5\), due to not properly converting or understanding negative magnitude/positive fraction - decimal relationships.

Part b