CTET Paper II (Mathematics and Science) Feb 2014 Solved Paper

Concept:A ratio compares two quantities with the same unit. The ratio itself has no unit. When dividing units, the unit cancels out.Explanation:First expression: $\frac{10 \text{ cm}}{12 \text{ cm}}$. The cm cancel, giving the pure number $\frac{5}{6}$. Writing $\frac{5}{6} \text{ cm}$ is wrong because ratio has no unit.Second expression: $\frac{15 \text{ cm}}{15 \text{ m}}$. Units are different. Convert 15 m to 1500 cm, then ratio is $\frac{15}{1500} = \frac{1}{100}$, a pure number. The student wrote 1000 m, which is incorrect. This shows he attempted unit conversion but missed that the result is a ratio without unit.The student knows fractions and reduction to lowest terms (first expression: $\frac{10}{12} = \frac{5}{6}$). He also shows understanding of converting units (cm to m) but fails to recognize that the final quotient, being a ratio, should not have a unit.Answer:Option D: has concept of units, conversion of units, fractions but missed the concept that ratio does not have units.