Question

$\text{A cake, weighing}"K"\text{kg, is cut into 8}\text{equal slices. If each slice is then equally}\text{shared among (2}\times K)\text{friends, how much}\text{cake does each friend get?}$

• A. $\frac{K}{4}kg$
• B. $\frac{1}{4}kg$
• C. $\frac{K}{16}kg$
• D. $\frac{1}{16}kg$

Answer 1

The correct option is D $\frac{1}{16}kg$

$\text{Weight of the cake (in kg)}=K$

$\text{Number of slices of the cake}=8$

$⟹\text{Weight of each slice}=\frac{K}{8}\text{kg}$

$\text{Number of friends between whom}\text{1 slice is shared}=(2\times K)$

$⟹\text{Weight of cake that each friend}\text{gets}=\frac{K}{8}\text{kg}÷(2\times K)$

$\text{Calculating}\frac{K}{8}÷(2\times K)\text{using the}keep-change-flip\text{method, we get:}$


$\text{Calculating}\frac{K}{8}\times \frac{1}{(2\times K)}\text{, we get:}$

$\frac{K}{8}\times \frac{1}{(2\times K)}=\frac{K\times 1}{8\times 2\times K}=\frac{K\times 1}{8\times 2\times K}=\frac{1}{8\times 2}=\frac{1}{16}$

$\therefore \text{The weight of cake that each friend}$$\text{gets is}\frac{1}{16}kg.$