Question

$\text{If}\frac{4}{7}\times \frac{21}{16}=K\text{then, which of the following}\text{shaded parts of the models represent a value}less\text{than}K?$

• A. Model A
• B. Model B
• C. Model C
• D. All models are possible

Answer 1

The correct option is B Model B

$\text{Calculating the product, we find:}$

$K=\frac{4}{7}\times \frac{21}{16}=\frac{4\times 21}{7\times 16}=\frac{1\times 21}{7\times 4}=\frac{1\times 3}{1\times 4}=\frac{3}{4}$

$\therefore \text{We look for the model with a shaded}\text{area}less\text{than}\frac{3}{4}$

$\text{Evaluating the models, we find:}$


$2<3<4⟹\frac{2}{4}<\frac{3}{4}<\frac{4}{4}$

$\therefore \text{The only model that represents a}\text{fraction}less\text{than}\frac{3}{4}\text{is}modelB.$