Convert: \(73 \div 18 = 4\) remainder \(1\)
Improper: \(\frac{73}{18}\)
Ans: \(\mathbf{4\frac{1}{18}}\)
Problem 10
\(\frac{13}{6} - \frac{11}{8}\)
LCD = 24
\(\frac{13 \times 4}{24} - \frac{11 \times 3}{24} = \frac{52}{24} - \frac{33}{24} = \frac{19}{24}\)
Note: Proper fraction (numerator < denominator).
Cannot convert to mixed
Ans: \(\mathbf{\frac{19}{24}}\)
Fraction Clash Teacher Guide • Computational Key Page 1 of 2
Part II Key Rubrics, Feedback & Challenge Answers
Page 2 Total: 5 Points
3
Problem 11 Solution LCD = 12
\(\text{Total Flour} = \frac{9}{4} + \frac{7}{6} = \frac{9 \times 3}{12} + \frac{7 \times 2}{12}\)
\(=\frac{27}{12} + \frac{14}{12} = \frac{41}{12}\text{ kg}\)
\(41 \div 12 = 3\) with remainder \(5 \rightarrow 3\frac{5}{12}\text{ kg}\)
Improper: \(\frac{41}{12}\text{ kg}\)
Mixed: \(\mathbf{3\frac{5}{12}\text{ kg}}\)
Problem 12 Solution LCD = 12
\(\text{Remaining} = \frac{19}{6} - \frac{5}{4} = \frac{19 \times 2}{12} - \frac{5 \times 3}{12}\)
\(=\frac{38}{12} - \frac{15}{12} = \frac{23}{12}\text{ m}\)
\(23 \div 12 = 1\) with remainder \(11 \rightarrow 1\frac{11}{12}\text{ m}\)
Improper: \(\frac{23}{12}\text{ m}\)
Mixed: \(\mathbf{1\frac{11}{12}\text{ m}}\)
4
Look for conceptual understanding of fraction size
Case A Diagnosis (Leo) 1 pt
Target Explanation: Leo added the denominators together (\(4+4=8\)). The denominator represents the size/type of equal parts, not a count. When fourths are added, the parts remain fourths: \(\frac{7+5}{4} = \frac{12}{4}\).
Correct Value: \(\mathbf{\frac{12}{4} = 3}\)
Case B Diagnosis (Sam) 1 pt
Target Explanation: Sam changed the denominator to 6 but failed to multiply each numerator by the equivalent scale factor. To convert to sixths, \(\frac{8}{3}\) must become \(\frac{16}{6}\) and \(\frac{3}{2}\) must become \(\frac{9}{6}\).
Correct Value: \(\mathbf{\frac{7}{6} = 1\frac{1}{6}}\)
5
1 Bonus pt
\(\frac{7}{2} - \frac{5}{3} + \frac{9}{4} \rightarrow \text{LCD}(2, 3, 4) = 12\)
\(=\frac{7 \times 6}{12} - \frac{5 \times 4}{12} + \frac{9 \times 3}{12} = \frac{42}{12} - \frac{20}{12} + \frac{27}{12}\)
\(=\frac{42 - 20 + 27}{12} = \frac{22 + 27}{12} = \frac{49}{12}\)
\(49 \div 12 = 4\) remainder \(1 \rightarrow 4\frac{1}{12}\)
Final Mixed #
\(\mathbf{4\frac{1}{12}}\)
(\(\frac{49}{12}\))
Fraction Clash Teacher Guide • Scoring & Exemplars Page 2 of 2
