Question

Which situations can be represented by the proportion 1/2 = 1/4? Check all that apply.

If 8 people can wash a car in •1/4 hour, then 4 people can wash the same car in 1/2 hour.
•If 8 people can eat 1/2 of a watermelon, then 4 people can eat 1/4 of the watermelon.
•If 1/2 pound of steak costs $8, then 1/4 pound of steak costs $4.
•If 1/2 a pot holds 4 fluid Ounces of water, then 1/4 of the pot holds 8 fluid ounces.

Answer 1

B AND C

Explanation:

Answer 2

No given situations can be represented by the proportion 1/2 = 1/4

Solution:

Given, we have to find which situations can be represented by the proportion
`(1)/(2) = (1)/(4)`

Let us check option by option.

Option 1:

If 8 people can wash a car in 1/4 hour, then 4 people can wash the same car in 1/2 hour.

Here the proportionality is obtained as:

`(8)/((1)/(4))=(4)/((1)/(2))`

`\begin{array}{l}{8 * 4=4 * 2} \\\\ {32=8} \\\\ {4=1 \rightarrow \text { wrong }}\end{array}`

Option 2:

If 8 people can eat 1/2 of a watermelon, then 4 people can eat 1/4 of the watermelon.

Proportionality is given as:

`\begin{array}{l}{(8)/(2)=(4)/((1)/(4))} \\\\ {\rightarrow 8 * 2=4 * 4} \\\\ {\rightarrow 8=8 \rightarrow 1=1 \rightarrow \text { wrong }}\end{array}`

Option 3:

If 1/2 pound of steak costs $8, then 1/4 pound of steak costs $4.

`\begin{array}{l}{((1)/(2))/(8)=((1)/(4))/(4)} \\\\ {\rightarrow (1)/(2) * 4=8 * (1)/(4)} \\\\ {\rightarrow (1)/(2)=2 * (1)/(4)} \\\\ {\rightarrow (1)/(2)=(1)/(2)} \\\\ {\rightarrow 1=1 \rightarrow \text { Wrong }}\end{array}`

Option 4:

If 1/2 a pot holds 4 fluid Ounces of water, then 1/4 of the pot holds 8 fluid ounces

`\begin{array}{l}{((1)/(2))/(4)=((1)/(4))/(8)} \\\\ {\rightarrow (1)/(2) * 8=4 * (1)/(4)} \\\\ {\rightarrow 4=1 \rightarrow \text { wrong }}\end{array}`

Hence, no given situation represents the proportion
`(1)/(2) = (1)/(4)`