In order to determine if the given statements are true or false, use the appropriate calculations, as follow:
a) In this case, calculate the proportion between cups of oil and cups of vinegar:
[tex]\frac{\frac{1}{3}}{\frac{1}{2}}=\frac{2}{3}[/tex]
The proportion is 3/2.
If now we have 1 1/2 cup of oil and 1 of vinegar, the proportion is:
[tex]\frac{1\frac{1}{2}}{1}=1\frac{1}{2}=\frac{3}{2}[/tex]
It is not the same proportion. Hence, the statement a is FALSE.
b) Determine the proportion between cups of sugar and cups of vinegar:
[tex]\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{2}{4}=\frac{1}{2}[/tex]
The proportion is 1/2.
Now for 2 cups of sugar and of vinegar the proportion is 2/1 = 2. This is not the required propoprtion. The statement is FALSE.
c) 2 cups of vinegar for each cup of sugar. The proportion is 1/2. This is the required proportion. Hence, the statement c is TRUE.
d) In this case, the proportion is:
[tex]\frac{\frac{2}{3}}{1}=\frac{2}{3}[/tex]
Which is the required proportion (calculated in part a). Hence, the statement d is TRUE.
