Question

shawna needs to write \\(\frac{13}{5}\\) as a mixed number. her answer is shown below.\\(\frac{13}{5} = 1\frac{8}{5}\\)is shawna’s answer correct?\\(\boldsymbol{\text{yes, because } \frac{8}{5} \text{ is a fraction.}}\\)\\(\boldsymbol{\text{no, because } \frac{8}{5} \text{ is a fraction greater than 1.}}\\)

Explanation:

Step1: Recall Mixed Number Rules

A mixed number has a whole number and a proper fraction (numerator < denominator). For \(\frac{13}{5}\), divide 13 by 5: \(13\div5 = 2\) with remainder \(3\), so \(\frac{13}{5}=2\frac{3}{5}\). Shawna's answer is \(1\frac{8}{5}\), but \(\frac{8}{5}\) is improper (8 > 5), so her mixed number is invalid.

Step2: Evaluate Options

• First option: Claims "Yes" but \(\frac{8}{5}\) being a fraction doesn't make the mixed number correct (needs proper fraction).
• Second option: "No, because \(\frac{8}{5}\) is a fraction greater than 1" (improper, so mixed number part is wrong) is correct.

Answer:

No, because \(\boldsymbol{\frac{8}{5}}\) is a fraction greater than 1.