Question

do the following ratios for a proportion?
\\(\frac{1}{2}\\) cup sugar to 3 lemons
\\(2\frac{1}{2}\\) cups sugar to 15 lemons
\\(\bigcirc\\) proportional
\\(\bigcirc\\) not proportional

Explanation:

Step1: Write ratios as fractions

First ratio: $\frac{\frac{1}{2}}{3}$, Second ratio: $\frac{2\frac{1}{2}}{15}$

Step2: Simplify first ratio

$\frac{\frac{1}{2}}{3} = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$

Step3: Convert mixed number to improper fraction

$2\frac{1}{2} = \frac{5}{2}$

Step4: Simplify second ratio

$\frac{\frac{5}{2}}{15} = \frac{5}{2} \times \frac{1}{15} = \frac{1}{6}$

Step5: Compare the two simplified ratios

Both ratios equal $\frac{1}{6}$, so they form a proportion.

Answer:

Proportional