Question

1. you need \\(\frac{1}{4}\\) cups of butter for \\(3\frac{1}{2}\\) cups of oatmeal to make oatmeal cookies. how many cups of oatmeal do you need if you are using 1 cup of butter?

Explanation:

Step1: Define the ratio

Let \( x \) be the cups of oatmeal needed for 1 cup of butter. The ratio of butter to oatmeal should be constant. So we have the proportion: \(\frac{\frac{1}{4}}{3\frac{1}{2}}=\frac{1}{x}\)

Step2: Convert mixed number to improper fraction

\( 3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2} \)

Step3: Solve the proportion

Cross - multiply: \(\frac{1}{4}x = \frac{7}{2}\times1\)
Then, \( x=\frac{7}{2}\div\frac{1}{4}\)
Using the rule of dividing fractions (\(a\div\frac{b}{c}=a\times\frac{c}{b}\)), we get \( x = \frac{7}{2}\times4=\frac{28}{2}=14\)

Answer:

14